A Differentiable Contact Model to Extend Lagrangian and Hamiltonian Neural Networks for Modeling Hybrid Dynamics,
Y. D. Zhong, B. Dey, A. Chakraborty.
Under Review,
[Abstract],
[arXiv]
Hamiltonian Q-Learning: Leveraging Importance-sampling for Data Efficient RL,
U. Madhushani, B. Dey, N. E. Leonard, A. Chakraborty.
[Abstract],
[arXiv]
Value function based reinforcement learning (RL) algorithms, for example, Q-learning, learn optimal policies from datasets of
actions, rewards, and state transitions. However, when the underlying state transition dynamics are stochastic and evolve on a
high-dimensional space, generating independent and identically distributed (IID) data samples for creating these datasets poses
a significant challenge due to the intractability of the associated normalizing integral. In these scenarios, Hamiltonian Monte
Carlo (HMC) sampling offers a computationally tractable way to generate data for training RL algorithms. In this paper, we
introduce a framework, called Hamiltonian Q-Learning, that demonstrates, both theoretically and empirically, that Q values
can be learned from a dataset generated by HMC samples of actions, rewards, and state transitions. Furthermore, to exploit the
underlying low-rank structure of the Q function, Hamiltonian Q-Learning uses a matrix completion algorithm for reconstructing the
updated Q function from Q value updates over a much smaller subset of state-action pairs. Thus, by providing an efficient way to
apply Q-learning in stochastic, high-dimensional settings, the proposed approach broadens the scope of RL algorithms for real-world
applications.
Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data,
Y. D. Zhong, B. Dey, A. Chakraborty.
To appear at the 3rd Annual Learning for Dynamics & Control Conference (L4DC), Zurich, Switzerland, Jun 2021.
[Abstract],
[arXiv]
The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning
frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using
neural networks for learning dynamics from observed time-series data. In this work, we present a comparative analysis of the
energy-conserving neural networks - for example, deep Lagrangian network, Hamiltonian neural network, etc. - wherein the
underlying physics is encoded in their computation graph. We focus on ten neural network models and explain the similarities and
differences between the models. We compare their performance in 4 different physical systems. Our result highlights that using a
high-dimensional coordinate system and then imposing restrictions via explicit constraints can lead to higher accuracy in the
learned dynamics. We also point out the possibility of leveraging some of these energy-conserving models to design energy-based
controllers.
Topological limits to parallel processing capability of network architectures,
G. Petri, S. Musslick, B. Dey, K. Özcimder, D. Turner, N. K. Ahmed, T. L. Willke, J. D. Cohen,
Nature Physics, Feb 2021.
[Abstract]
[arXiv]
[doi]
The ability to learn new tasks and generalize to others is a remarkable characteristic of both human brains and recent artificial
intelligence systems. The ability to perform multiple tasks simultaneously is also a key characteristic of parallel architectures,
as is evident in the human brain and exploited in traditional parallel architectures. Here we show that these two characteristics
reflect a fundamental tradeoff between interactive parallelism, which supports learning and generalization, and independent
parallelism, which supports processing efficiency through concurrent multitasking. Although the maximum number of possible parallel
tasks grows linearly with network size, under realistic scenarios their expected number grows sublinearly. Hence, even modest
reliance on shared representations, which support learning and generalization, constrains the number of parallel tasks. This has
profound consequences for understanding the human brain’s mix of sequential and parallel capabilities, as well as for the development
of artificial intelligence systems that can optimally manage the tradeoff between learning and processing efficiency.
Frequency-compensated PINNs for Fluid-dynamics Design Problems,
T. Zhang, B. Dey, P. Kakkar, A. Dasgupta, A. Chakraborty,
Conference on Neural Information Processing Systems (NeurIPS), ML4Eng Workshop, Virtual, Dec 2020.
[Abstract]
[arXiv]
Incompressible fluid flow around a cylinder is one of the classical problems in fluid-dynamics with strong relevance with many
real-world engineering problems, for example, design of offshore structures or design of a pin-fin heat exchanger. Thus learning a
high-accuracy surrogate for this problem can demonstrate the efficacy of a novel machine learning approach. In this work, we propose
a physics-informed neural network (PINN) architecture for learning the relationship between simulation output and the underlying
geometry and boundary conditions. In addition to using a physics-based regularization term, the proposed approach also exploits the
underlying physics to learn a set of Fourier features, i.e. frequency and phase offset parameters, and then use them for predicting
flow velocity and pressure over the spatio-temporal domain. We demonstrate this approach by predicting simulation results over out
of range time interval and for novel design conditions. Our results show that incorporation of Fourier features improves the
generalization performance over both temporal domain and design space.
Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning,
Y. D. Zhong, B. Dey, A. Chakraborty,
International Conference on Learning Representations (ICLR), DeepDiffEq Workshop, Virtual, Apr 2020.
[Abstract]
[OpenReview]
[arXiv]
In this work, we introduce Dissipative SymODEN a deep learning architecture which can infer the dynamics of a physical system with
dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN
encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns
the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and
potential energy, paves the way for energy-based controllers.
Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control,
Y. D. Zhong, B. Dey, A. Chakraborty,
International Conference on Learning Representations (ICLR), Virtual, Apr 2020.
[Abstract]
[OpenReview]
[arXiv]
[Presentation]
[GitHub]
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical
system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with
fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a
physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a
transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and
potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized
coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This
framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for
synthesizing model-based control strategies.
A Formal Framework for Cognitive Models of Multitasking,
M. Lesnick, S. Musslick, B. Dey, J. D. Cohen.
PsyArXiv Preprints, Mar 2020.
[Abstract]
[PsyArXiv]
A Conditional Generative Model for Predicting Material Microstructures from Processing Methods,
A. Iyer, B. Dey, A. Dasgupta, W. Chen, A. Chakraborty,
Conference on Neural Information Processing Systems (NeurIPS), ML4PS Workshop, Vancouver, Canada, Dec 2019.
[Abstract]
[FullText]
Microstructures of a material form the bridge linking processing conditions - which can be controlled, to the material property -
which is the primary interest in engineering applications. Thus a critical task in material design is establishing the
processing-structure relationship, which requires domain expertise and techniques that can model the high-dimensional material
microstructure. This work proposes a deep learning based approach that models the processing-structure relationship as a conditional
image synthesis problem. In particular, we develop an auxiliary classifier Wasserstein GAN with gradient penalty (ACWGAN-GP) to
synthesize microstructures under a given processing condition. This approach is free of feature engineering, requires modest domain
knowledge and is applicable to a wide range of material systems. We demonstrate this approach using the ultra high carbon steel
(UHCS) database, where each microstructure is annotated with a label describing the cooling method it was subjected to. Our results
show that ACWGAN-GP can synthesize high-quality multiphase microstructures for a given cooling method.
A graph-theoretic approach to multitasking,
N. Alon, D. Reichmann, I. Shinkar, T. Wagner, S. Musslick, J. D. Cohen, T. Griffiths, B. Dey, K. Özcimder,
Conference on Neural Information Processing Systems (NeurIPS), Long Beach, CA, Dec 2017.
[Abstract]
[arXiv]
[doi]
(Oral Presentation, Acceptance Rate - 1.23%)
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of
units in the learning and processing of representations. However, how the richness of such interactions trades off against the
ability of a network to simultaneously carry out multiple independent processes - a salient limitation in many domains of human
cognition - remains largely unexplored. In this paper we use a graph-theoretic analysis of network architecture to address this
question, where tasks are represented as edges in a bipartite graph G = (A ∪ B, E). We define a new measure of
multitasking capacity of such networks, based on the assumptions that tasks that need to be multitasked rely on independent
resources, i.e., form a matching, and that tasks can be multitasked without interference if they form an induced matching. Our
main result is an inherent tradeoff between the multitasking capacity and the average degree of the network that holds regardless of the network architecture. These results are also extended to networks of depth greater than 2. On the positive side, we demonstrate that networks that are random-like (e.g., locally sparse) can have desirable multitasking properties. Our results shed light into the parallel-processing limitations of neural systems and provide insights that may be useful for the analysis and design of parallel architectures.
A Formal Approach to Modeling the Cost of Cognitive Control,
K. Özcimder, B. Dey, S. Musslick, G. Petri, N. K. Ahmed, T. L. Willke, J. D. Cohen,
39th Annual Meeting of the Cognitive Science Society (CogSci), pp. 895-900, London, UK, Jul 2017.
[Abstract]
[arXiv]
[doi]
[Talk Slides]
This paper introduces a formal method to model the level of demand on control when executing cognitive processes. The cost of
cognitive control is parsed into an intensity cost which encapsulates how much additional input information is required
so as to get the specified response, and an interaction cost which encapsulates the level of interference between individual
processes in a network. We develop a formal relationship between the probability of successful execution of desired processes and
the control signals (additive control biases). This relationship is also used to specify optimal control policies to achieve a
desired probability of activation for processes. We observe that there are boundary cases when finding such control policies which
leads us to introduce the interaction cost. We show that the interaction cost is influenced by the relative strengths of individual
processes, as well as the directionality of the underlying competition between processes.
Multitasking Capability Versus Learning Efficiency in Neural Network Architectures,
S. Musslick, A. M. Saxe, K. Özcimder, B. Dey, G. Henselman, J. D. Cohen,
39th Annual Meeting of the Cognitive Science Society (CogSci), pp. 829-834, London, UK, Jul 2017.
[Abstract]
[doi]
One of the most salient and well-recognized features of human goal-directed behavior is our limited ability to conduct multiple
demanding tasks at once. Previous work has identified overlap between task processing pathways as a limiting factor for
multitasking performance in neural architectures. This raises an important question: insofar as shared representation between tasks
introduces the risk of cross-talk and thereby limitations in multitasking, why would the brain prefer shared task representations
over separate representations across tasks? We seek to answer this question by introducing formal considerations and neural network
simulations in which we contrast the multitasking limitations that shared task representations incur with their benefits for task
learning. Our results suggest that neural network architectures face a fundamental tradeoff between learning efficiency and
multitasking performance in environments with shared structure between tasks.
Controlled vs. Automatic Processing: A Graph-Theoretic Approach to the Analysis of Serial vs. Parallel Processing in Neural Network Architectures,
S. Musslick, B. Dey, K. Özcimder, M. M. A. Patwary, T. L. Willke, J. D. Cohen,
38th Annual Meeting of the Cognitive Science Society (CogSci), pp. 1547-1552, Philadelphia, PA, Aug 2016.
[Abstract]
[doi]
The limited ability to simultaneously perform multiple tasks is one of the most salient features of human performance and a
defining characteristic of controlled processing. Based on the assumption that multitasking constraints arise from shared
representations between individual tasks, we describe a graph-theoretic approach to analyze these constraints. Our results are
consistent with previous numerical work, showing that even modest amounts of shared representation induce dramatic constraints on
the parallel processing capability of a network architecture. We further illustrate how this analysis method can be applied to
specific neural networks to efficiently characterize the full profile of their parallel processing capabilities. We present
simulation results that validate theoretical predictions, and discuss how these methods can be applied to empirical studies of
controlled vs. and automatic processing and multitasking performance in humans.
Beacon-referenced pursuit for collective motions in three dimensions,
K. S. Galloway, B. Dey,
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, No. 2234, Feb 2020.
[Abstract]
[doi]
Motivated by real-world applications of unmanned aerial vehicles, this paper introduces a decentralized control mechanism to
guide steering control of autonomous agents manoeuvring in the vicinity of multiple moving entities (e.g. other autonomous agents)
and stationary entities (e.g. fixed beacons or points of reference) in a three-dimensional environment. The proposed control law,
which can be perceived as a modification of the three-dimensional constant bearing (CB) pursuit law, provides a means to allocate
simultaneous attention to multiple entities. We investigate the behaviour of the closed-loop dynamics for a system with one agent
referencing two beacons, as well as a two-agent mutual pursuit system wherein each agent employs the beacon-referenced CB pursuit
law with regards to the other agent and a stationary beacon. Under certain assumptions on the associated control parameters, we
demonstrate that this problem admits circling equilibria with agents moving on circular orbits with a common radius, in planes
perpendicular to a common axis passing through the beacons. As the common radius and distances from the beacon are determined by
the choice of parameters in the pursuit law, this approach provides a means to engineer desired formations in a three-dimensional
setting.
Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons,
E. N. Davison, Z. Aminzare, B. Dey, N. E. Leonard,
Chaos, Vol. 29, pp. 033105, Mar 2019.
[Abstract]
[arXiv]
[doi]
We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex
network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling
as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of
the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple
timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network
of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we
generalize our results to directed trees of model neurons with heterogeneous inputs.
Feedback Controlled Bifurcation of Evolutionary Dynamics with Generalized Fitness,
B. Dey, A. Franci, K. Özcimder, N. E. Leonard,
2016 American Control Conference (ACC), pp. 6049-6054, Milwaukee, WI, Jun 2018.
[Abstract]
[FullText]
[doi]
Coexistence and interaction of multiple strategies in a large population of individuals can be observed in a variety of natural
and engineered settings. In this context, replicator-mutator dynamics provide an efficient tool to model and analyze the evolution
of the fractions of the total population committed to different strategies. Although the literature addresses existence and
stability of equilibrium points and limit cycles of these dynamics, linearity in fitness functions has typically been assumed. We
generalize these dynamics by introducing a nonlinear fitness function, and we show that the replicator-mutator dynamics for two
competing strategies exhibit a quintic pitchfork bifurcation. Then, by designing slow-time-scale feedback dynamics to control the
bifurcation parameter (mutation rate), we show that the closed-loop dynamics can exhibit oscillations in the evolution of
population fractions. Finally, we introduce an ultraslow-time-scale dynamics to control the associated unfolding parameter
(asymmetry in the payoff structure), and demonstrate an even richer class of behaviors.
Beacon-referenced Mutual Pursuit in Three Dimensions,
K. S. Galloway, B. Dey,
2016 American Control Conference (ACC), pp. 62-67, Milwaukee, WI, Jun 2018.
[Abstract]
[arXiv]
[doi]
Cyclic pursuit frameworks provide an efficient way to create useful global behaviors out of pairwise interactions in a collective
of autonomous robots. Earlier work studied cyclic pursuit with a constant bearing (CB) pursuit law, and has demonstrated the
existence of a variety of interesting behaviors for the corresponding dynamics. In this work, by attaching multiple branches to a
single cycle, we introduce a modified version of this framework which allows us to consider any weakly connected pursuit graph
where each node has an outdegree of 1. This provides a further generalization of the cyclic pursuit setting. Then, after showing
existence of relative equilibria (rectilinear or circling motion), pure shape equilibria (spiraling motion) and periodic orbits,
we also derive necessary conditions for stability of a 3-agent collective. By paving a way for individual agents to join or leave
a collective without perturbing the motion of others, our approach leads to improved reliability of the overall system.
Collective motion under beacon-referenced cyclic pursuit,
K. S. Galloway, B. Dey,
Automatica, Vol. 91, pp. 17-26, May 2018.
[Abstract]
[doi]
[arXiv]
Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an
efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered cyclic pursuit
with a constant bearing (CB) pursuit law, and demonstrated the existence of circling equilibria for the corresponding dynamics. In
this work, we propose a beacon-referenced version of the CB pursuit law, wherein a stationary beacon provides an additional
reference for the individual agents in a collective. When implemented in a cyclic framework, we show that the resulting dynamics
admit relative equilibria corresponding to a circling orbit around the beacon, with the circling radius and the distribution of
agents along the orbit determined by parameters of the proposed pursuit law. We also derive necessary conditions for stability of
the circling equilibria, which provides a guide for parameter selection. Finally, by introducing a change of variables, we
demonstrate the existence of a family of invariant manifolds related to spiraling motions around the beacon which preserve the
"pure shape" of the collective, and study the reduced dynamics on a representative manifold.
Bistability and resurgent epidemics in reinfection models,
R. Pagliara, B. Dey, N. E. Leonard,
IEEE Control Systems Letters, Vol. 2, No. 2, pp. 290-295, Apr 2018.
[Abstract]
[doi]
Spreading processes that propagate through local interactions have been studied in multiple fields (e.g., epidemiology, complex
networks, social sciences) using the SIR (Susceptible-Infected-Recovered) and SIS (Susceptible-Infected-Susceptible) frameworks.
SIR assumes individuals acquire full immunity to the infection after recovery, while SIS assumes individuals acquire no immunity
after recovery. However, in many spreading processes individuals may acquire only partial immunity to the infection or may become
more susceptible to reinfection after recovery. We study a model for reinfection called SIRI
(Susceptible-Infected-Recovered-Infected). The SIRI model generalizes the SIS and SIR models and allows for study of systems in
which the susceptibility of agents changes irreversibly after first exposure to the infection. We show that when the rate of
reinfection is higher than the rate of primary infection, the SIRI model exhibits bistability with a small difference in the
initial fraction of infected individuals determining whether the infection dies out or spreads through the population. We find this
critical value and show that when the infection does not die out there is a resurgent epidemic in which the number of infected
individuals decays initially and remains at a low level for an arbitrarily long period of time before rapidly increasing towards an
endemic equilibrium in which the fraction of infected individuals is non-zero.
Cluster synchronization of diffusively coupled nonlinear systems: A Contraction-Based Approach,
Z. Aminzare, B. Dey, E. N. Davison, N. E. Leonard,
Journal of Nonlinear Science, pp. 1-23, Apr 2018.
[Abstract]
[doi]
[arXiv]
Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of
biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with
linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the
system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the
network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network
connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics.
For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than
those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when
cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and
control of complex networked systems.
Constant bearing pursuit on branching graphs,
K. S. Galloway, B. Dey,
56th IEEE Conference on Decision and Control (CDC), pp. 4410-4415, Melbourne, Australia, Dec 2017.
[Abstract]
[arXiv]
[doi]
[Talk Slides]
Cyclic pursuit frameworks provide an efficient way to create useful global behaviors out of pairwise interactions in a collective
of autonomous robots. Earlier work studied cyclic pursuit with a constant bearing (CB) pursuit law, and has demonstrated the
existence of a variety of interesting behaviors for the corresponding dynamics. In this work, by attaching multiple branches to a
single cycle, we introduce a modified version of this framework which allows us to consider any weakly connected pursuit graph
where each node has an outdegree of 1. This provides a further generalization of the cyclic pursuit setting. Then, after showing
existence of relative equilibria (rectilinear or circling motion), pure shape equilibria (spiraling motion) and periodic orbits,
we also derive necessary conditions for stability of a 3-agent collective. By paving a way for individual agents to join or leave
a collective without perturbing the motion of others, our approach leads to improved reliability of the overall system.
Synchronization bound for networks of nonlinear oscillators,
E. N. Davison, B. Dey, N. E. Leonard,
54th Annual Allerton Conference on Communication, Control, and Computing, pp. 1110-1115, Allerton, IL, Sep 2016.
[Abstract]
[doi]
Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the
behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for
synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which
synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes.
We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the
oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with
inputs provides a promising step toward control of key aspects of networked oscillatory systems.
Stability and pure shape equilibria for beacon-referenced cyclic pursuit,
K. S. Galloway, B. Dey,
2016 American Control Conference (ACC), pp. 161-166, Boston, MA, Jul 2016.
[Abstract]
[doi]
[Talk Slides]
Cyclic pursuit systems provide a means to generate useful global behaviors in a collective of autonomous agents based on dyadic
pursuit interactions between neighboring agents in a cycle graph. Here we consider a modified version of the cyclic pursuit
framework in which a stationary beacon provides an additional reference for the agents in the system. Building on the framework
proposed in our previous work, we derive necessary conditions for stability of circling equilibria in the n-agent system.
Furthermore, we employ a change of variables to reveal the existence of a family of invariant manifolds related to spiral motions
which maintain the formation shape up to geometric similarity.
Station keeping through beacon-referenced cyclic pursuit,
K. S. Galloway, B. Dey,
2015 American Control Conference (ACC), pp. 4765-4770, Chicago, IL, Jul 2015.
[Abstract]
[arXiv]
[doi]
[Talk Slides]
This paper investigates a modification of cyclic CB pursuit in a multi-agent system in which each agent pays attention to a
neighbor and a beacon. The problem admits shape equilibria with collective circling about the beacon, with the circling radius and
angular separation of agents determined by choice of parameters in the feedback law. Stability of circling shape equilibria is
shown for a 2-agent system, and the results are demonstrated on a collective of mobile robots tracked by a motion capture system.
Biomimetic algorithms for coordinated motion: Theory and implementation,
U. Halder, B. Dey,
2015 IEEE Conference on Robotics and Automation (ICRA), pp. 5426-5432, Seattle, WA, May 2015.
[Abstract]
[arXiv]
[doi]
[Talk Slides]
Drawing inspiration from flight behavior in biological settings (e.g. territorial battles in dragonflies, and flocking in
starlings), this paper demonstrates two strategies for coverage and flocking. Using earlier theoretical studies on mutual motion
camouflage, an appropriate steering control law for area coverage has been implemented in a laboratory testbed equipped with
wheeled mobile robots and a Vicon high speed motion capture system. The same test-bed is also used to demonstrate another strategy
(based on local information), termed topological velocity alignment, which serves to make agents move in the same direction. The
present work illustrates the applicability of biological inspiration in the design of multiagent robotic collectives.
Control-theoretic data smoothing,
B. Dey, P. S. Krishnaprasad,
53rd IEEE Conference on Decision and Control (CDC), pp. 5064-5070, Los Angeles, CA, Dec 2014.
[Abstract]
[doi]
[Talk Slides]
The problem of recovering continuous time signals from a set of discrete measurements is ill-posed in a classical sense
(non-uniqueness of solution). Our approach introduces generative models with inputs, states and outputs, and regularizes this
problem by trading total fit-error against suitable penalty functionals of input and state. This enables us to apply techniques
from optimal control and obtain solutions in a semi-analytical way. Using a modified version of Pontryagin's maximum principle,
this paper treats data smoothing as an optimal control problem. In addition to addressing data smoothing problems in Euclidean
settings, our results are also applicable to problems arising in finite dimensional matrix Lie group settings. In particular, this
paper discusses an example problem on SE(2), and exploits symmetry and reduction to an integrable Hamiltonian system as
means to data smoothing.
Trajectory smoothing as a linear optimal control problem,
B. Dey, P. S. Krishnaprasad,
50th Annual Allerton Conference on Communication, Control, and Computing, pp. 1490-1497, Allerton, IL, Oct 2012.
[Abstract]
[doi]
[Talk Slides]
In many areas of science and engineering there is a need for techniques to robustly extract velocity and its derivatives from a
finite sample of observed positions. The extracted information can be used to infer related quantities such as curvature and speed,
which are important for analysis of strategies and feedback laws associated with the motion. In this work a novel approach is
proposed to reconstruct trajectories from a set of discrete observations. A simple linear model is used as the generative model for
trajectories, and high values of the jerk (derivative of the acceleration) path integral are penalized during reconstruction. The
positions, reconstructed in this way, can be represented as a linear combination of the sample data. The regularization (penalty)
parameter plays a very important role in the reconstruction process, and it may be determined from data using ordinary cross
validation.
Stabilizing a flexible beam on a cart: A distributed port Hamiltonian approach,
R. N. Banavar, B. Dey,
10th Biannual European Control Conference (ECC), pp. 300-305, Budapest, Hungary, Aug 2009.
[Abstract]
[doi]
[Talk Slides]
Motion planning and stabilization of the inverted pendulum on a cart is a much studied problem in the control community. We focus
our attention on asymptotically stabilizing a vertically upright flexible beam fixed on a moving cart. The flexibility of the beam
is restricted only to the direction along the traverse of the cart. The control objective is to attenuate the effect of
disturbances on the vertically upright profile of the beam. The control action available is the motion of the cart. By regulating
this motion, we seek to regulate the shape of the beam. The problem presents a combination of a system described by a partial
differential equation (PDE) and a cart modeled as an ordinary differential equation (ODE) as well as controller which we restrict
to an ODE. We set our problem in the port controlled Hamiltonian framework. The interconnection of the flexible beam to the cart
is viewed as a power conserving interconnection of an infinite dimensional system to a finite dimensional system. The energy
Casimir method is employed to obtain the controller. In this method, we look for some constants of motion which are invariant of
the choice of controller Hamiltonian. These Casimirs relate the controller states to the states of the system. We finally prove
stability of the equilibrium configuration of the closed loop system.
Stabilizing a Flexible Beam on a Cart: A Distributed Port-Hamiltonian Approach,
R. Banavar, B. Dey,
Journal of Nonlinear Science, Vol. 20, No. 2, pp. 131-151, Apr 2010.
[Abstract]
[doi]
Motion planning and stabilization of the inverted pendulum on a cart is a much-studied problem in the control community. We focus
our attention on asymptotically stabilizing a vertically upright flexible beam fixed on a moving cart. The flexibility of the beam
is restricted only to the direction along the traverse of the cart. The control objective is to attenuate the effect of
disturbances on the vertically upright profile of the beam. The control action available is the motion of the cart. By regulating
this motion, we seek to regulate the shape of the beam. The problem presents a combination of a system described by a partial
differential equation (PDE) and a cart modeled as an ordinary differential equation (ODE) as well as a controller which we restrict
to an ODE. We set our problem in the port-controlled Hamiltonian framework. The interconnection of the flexible beam to the cart
is viewed as a power-conserving interconnection of an infinite-dimensional system to a finite-dimensional system. The
energy-Casimir method is employed to obtain the controller. In this method, we look for some constants of motion that are invariant
of the choice of controller Hamiltonian. These Casimirs relate the controller states to the states of the system. We finally prove
the stability of the equilibrium configuration of the closed-loop system.
Using an agent-based model to explore the effects of colony size in modulating pesticide exposure in bumblebees,
J. Crall, B. De Bivort, B. Dey, A. Ford-Versypt,
Frontiers in Ecology and Evolution, Vol. 7, pp. 51, Mar 2019.
[Abstract]
[doi]
Neonicotinoids are a globally prevalent class of pesticides that can negatively affect bees and the pollination services they provide. While there is evidence suggesting that colony size may play an important role in mitigating neonicotinoid exposure in bees, mechanisms underlying these effects are not well understood. Here, a recently developed agent-based computational model is used to investigate how the effects of sub-lethal neonicotinoid exposure on intranest behavior of bumblebees (Bombus impatiens) are modulated by colony size. Simulations from the model, parameterized using empirical data on bumblebee workers exposed to imidacloprid (a common neonicotinoid pesticide), suggest that colony size has significant effects on neonicotinoid-sensitivity within bumblebee nests. Specifically, differences are reduced between treated and untreated workers in larger colonies for several key aspects of behavior within nests. Our results suggest that changes in both number of workers and nest architecture may contribute to making larger colonies less sensitive to pesticide exposure.
Social decision-making driven by artistic explore-exploit tension,
K. Özcimder, B. Dey, A. Franci, R. Lazier, D. Trueman, N. E. Leonard,
Interdisciplinary Science Reviews, Nov 2018.
[Abstract]
[FullText]
[doi]
We studied social decision-making in the rule-based improvisational dance There Might Be Others, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore–exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modelled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a ‘dial’ in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance.
Chronic neonicotinoid exposure disrupts bumblebee nest behavior, social networks, and thermoregulation,
J. D. Crall, C. M. Switzer, R. L. Oppenheimer, A. N. Ford-Versypt, B. Dey, A. Brown, M. Eyster, C. Guérin, N. E. Pierce, S. A. Combes, B. L. de Bivort,
Science, Vol. 362, No. 6415, pp. 683-686, Nov 2018.
[Abstract]
[doi]
Neonicotinoid pesticides can negatively affect bee colonies, but the behavioral mechanisms by which these compounds impair colony growth remain unclear. Here, we investigate imidacloprid’s effects on bumblebee worker behavior within the nest, using an automated, robotic platform for continuous, multicolony monitoring of uniquely identified workers. We find that exposure to field-realistic levels of imidacloprid impairs nursing and alters social and spatial dynamics within nests, but that these effects vary substantially with time of day. In the field, imidacloprid impairs colony thermoregulation, including the construction of an insulating wax canopy. Our results show that neonicotinoids induce widespread disruption of within-nest worker behavior that may contribute to impaired growth, highlighting the potential of automated techniques for characterizing the multifaceted, dynamic impacts of stressors on behavior in bee colonies.
BeeNestABM: An open-source agent-based model of spatiotemporal distribution of bumblebees in nests,
A. Ford-Versypt, J. Crall, B. Dey,
Journal of Open Source Software, Vol. 3, No. 27-718, Jul 2018.
[Abstract]
[doi]
This software features the MATLAB source code for an interactive computational model that can be used to study the localized responses of bumblebees to sublethal exposures to a prevalent class of pesticides called neonicotinoids. The code involves an agent-based stochastic model for the interactions between and movements of individual bees within a nest and the nest-related disruptions that occur due to pesticide exposure.
Investigating group behavior in dance: an evolutionary dynamics approach,
K. Özcimder, B. Dey, R. J. Lazier, D. Trueman, N. E. Leonard,
2016 American Control Conference (ACC), pp. 6465-6470, Boston, MA, Jul 2016.
[Abstract]
[doi]
[Talk Slides]
We investigate group behavior in dance using an evolutionary dynamic model. Our approach is motivated by observations of
nineteen dancers during a performance in which they choose a sequence of dance movements from a finite set of allowable
movement modules as they perform. Results show evidence that subgroups of dancers performing the same movement module
with greater representation are aware of their dominance, which in turn influences their switching rates between
modules. We introduce the notion of awareness of dominance into the well-studied framework of replicator-mutator
dynamics, where modules are represented as strategies. By letting awareness of dominance tune mutation strength, we demonstrate
its influence in the evolution of strategies. The tuning yields a feedback controlled bifurcation in the model dynamics, which
predicts persistence of dominant strategies as observed in the behavior of the dance group.