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Game Theory for Autonomy: From Min-Max Optimization to Equilibrium and Bounded Rationality Learning

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Game Theory for Autonomy: From Min-Max Optimization to Equil...

American control Conference (ACC)

作者： Kyriakos G. Vamvoudakis Filippos Fotiadis João P. Hespanha Raphael Chinchilla Guosong Yang Mushuang Liu Jeff S. Shamma Lacra Pavel Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta GA USA Center for Control Dynamical Systems and Computation University of California Santa Barbara CA Department of Electrical and Computer Engineering Rutgers University Piscataway NJ USA Department of Mechanical and Aerospace Engineering University of Missouri Columbia MO USA Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign IL USA Department of Electrical and Computer Engineering University of Toronto Canada

Finding Nash equilibria in non-cooperative games can be, in general, an exceptionally challenging task. This is owed to various factors, including but not limited to the cost functions of the game being nonconvex/nonconcave, the players of the game having limited information about one another, or even due to issues of computational complexity. The present tutorial draws motivation from this harsh reality and provides methods to approximate Nash or min-max equilibria in non-ideal settings using both optimization- and learning-based techniques. The tutorial acknowledges, however, that such techniques may not always converge, but instead lead to oscillations or even chaos. In that respect, tools from passivity and dissipativity theory are provided, which can offer explanations about these divergent behaviors. Finally, the tutorial highlights that, more frequently than often thought, the search for equilibrium policies is simply vain; instead, bounded rationality and non-equilibrium policies can be more realistic to employ owing to some players’ learning imperfectly or being relatively naive – "bounded rational." The efficacy of such plays is demonstrated in the context of autonomous driving systems, where it is explicitly shown that they can guarantee vehicle safety.

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Design and experimental implementation of multi-loop LQR, PID, and LQG controllers for the trajectory tracking control of twin rotor MIMO system 3rd

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Design and experimental implementation of multi-loop LQR, PI...

3rd International Conference on Intelligent Communication, control and Devices, ICICCD 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Ayush Dharavath, Abhiraj Department of Electrical Engineering Incubation Center for Control Dynamical Systems and Computation Delhi Technological University New DelhiDelhi110042 India

ISBN: (纸本)9789811386176

One DOF (degree of freedom) Twin Rotor multi-input multi-output system (TRMS) is one of the benchmarked dynamical systems which has striking comparability with Helicopter. Design of controllers for such complex air vehicle is a daunting task as it has inherent nonlinearities and cross-coupling between its main and tail rotors. Therefore, it is an interesting laboratory benchmarked control problem, to test the performance of various controllers. The control techniques focused in this paper are the experimental implementation of multi-loop controllers such as Linear Quadratic Regulator (LQR), linear proportional integral derivative (L-PID), and Linear Quadratic Gaussian (LQG) controllers on TRMS system to verify the performance of these controllers. © Springer Nature Singapore Pte Ltd. 2020.

关键词： controllers

Experimental validation of fully informed particle swarm optimization tuned multi-loop L-PID controllers for stabilization of gantry crane system 3rd

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Experimental validation of fully informed particle swarm opt...

3rd International Conference on Intelligent Communication, control and Devices, ICICCD 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Dobhal, Daksh Kartikeya, Kumar Kaur, Manpreet Goel, Arnav Department of Electrical Engineering Incubation Center for Control Dynamical Systems and Computation Delhi Technological University New DelhiDelhi110042 India

ISBN: (纸本)9789811386176

Linear PID controllers are commonly used as an electrical component to decrease the error between anticipated set value and actual measured values for control of various benchmarked systems. The Multi-Loop Linear PID (ML-PID) controller, gives a robust and efficient performance in most of the situations. This paper presents the implementation of linear PID controller to stabilize and control the Gantry Crane System. Optimal performance is obtained for a few specific combinations of the proportional, integral, and derivative gains, which makes it essential to tune these values through Optimization techniques. The Fully Informed Particle Swarm Optimizer (FIPSO) is used to tune the gain values of the ML-PID controlled Gantry Crane System. These values are validated experimentally, and obtained results prove that the FIPSO tuned multi-loop linear PID controller quickly stabilizes the system subjected to external disturbances. © Springer Nature Singapore Pte Ltd. 2020.

关键词： controllers

Newton and interior-point methods for (constrained) nonconvex-nonconcave minmax optimization with stability and instability guarantees

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arXiv 2022年

作者： Chinchilla, Raphael Yang, Guosong Hespanha, João P. Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States Department of Electrical and Computer Engineering Rutgers University New BrunswickNJ08854 United States

We address the problem of finding a local solution to a nonconvex-nonconcave minmax optimization using Newton type methods, including primal-dual interior-point ones. The first step in our approach is to analyze the local convergence properties of Newton’s method in nonconvex minimization. It is well established that Newton’s method iterations are attracted to any point with a zero gradient, irrespective of it being a local minimum. From a dynamical system standpoint, this occurs because every point for which the gradient is zero is a locally asymptotically stable equilibrium point. We show that by adding a multiple of the identity such that the Hessian matrix is always positive definite, we can ensure that every non-local-minimum equilibrium point becomes unstable (meaning that the iterations are no longer attracted to such points), while local minima remain locally asymptotically stable. Building on this foundation, we develop Newton-type algorithms for minmax optimization, conceptualized as a sequence of local quadratic approximations for the minmax problem. Using a local quadratic approximation serves as a surrogate for guiding the modified Newton’s method towards a solution. For these local quadratic approximations to be well-defined, it is necessary to modify the Hessian matrix by adding a diagonal matrix. We demonstrate that, for an appropriate choice of this diagonal matrix, we can guarantee the instability of every non-local-minmax equilibrium point while maintaining stability for local minmax points. Using numerical examples, we illustrate the importance of guaranteeing the instability property. While our results are about local convergence, the numerical examples also indicate that our algorithm enjoys good global convergence properties. © 2022, CC BY.

关键词： Stability

Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks

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Non-Euclidean Monotone Operator Theory with Applications to ...

IEEE Conference on Decision and control

作者： Alexander Davydov Saber Jafarpour Anton V. Proskurnikov Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara USA School of Electrical and Computer Engineering Georgia Institute of Technology Department of Electronics and Telecommunications Politecnico di Torino Turin Italy

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces ℓ 1 and ℓ ∞ . We first establish properties of mappings which are monotone with respect to the non-Euclidean norms ℓ 1 or ℓ ∞ . In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates.

关键词： Casting Analytical models Recurrent neural networks Machine learning Aerospace electronics control systems Robustness

Extending dynamic mode decomposition to data from multiple outputs

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arXiv 2021年

作者： Boddupalli, Nibodh Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA United States

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system. Estimation of these spectral objects has become widely accessible with the numerous algorithms developed in recent years. We show how one such algorithm – extended dynamic mode decomposition – can be used on data from multiple outputs of a system. These outputs that are functions of state are called observables in the literature and could be known outputs like the state itself or unknown outputs like data from sensors used in systems of biological interest. To this end, we approximate the desired observables and their iterates in time using minimizers of regularized least-squares problems which have analytic solutions with heuristic provisions for expected estimates. © 2021, CC BY-SA.

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Non-Euclidean Monotone Operator Theory and Applications

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arXiv 2023年

作者： Davydov, Alexander Jafarpour, Saber Proskurnikov, Anton V. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa BarbaraCA93106-5070 United States Department of Electrical Computer and Energy Engineering University of Colorado BoulderCO80309-0020 United States Department of Electronics and Telecommunications Politecnico di Torino Turin10129 Italy

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as diagonally-weighted 1 or ∞ norms. This paper provides a natural generalization of monotone operator theory to finite-dimensional non-Euclidean spaces. The key tools are weak pairings and logarithmic norms. We show that the resolvent and reflected resolvent operators of non-Euclidean monotone mappings exhibit similar properties to their counterparts in Hilbert spaces. Furthermore, classical iterative methods and splitting methods for finding zeros of monotone operators are shown to converge in the non-Euclidean case. We apply our theory to equilibrium computation and Lipschitz constant estimation of recurrent neural networks, obtaining novel iterations and tighter upper bounds via forward-backward splitting. © 2023, CC BY.

关键词： Recurrent neural networks

Biologically plausible robust control with Neural Network weight reset for unmanned aircraft systems under impulsive disturbances

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Biologically plausible robust control with Neural Network we...

American control Conference (ACC)

作者： Ignacio Rubio Scola Luis Rodolfo Garcia Carrillo Andrew T. Sornborger João P. Hespanha Department of Industrial Products Engineering INTI CONICET and UNR Rosario Argentina Klipsch School of Electrical and Computer Engineering New Mexico State University Las Cruces NM USA Los Alamos National Laboratory Los Alamos NM USA Center for Control Dynamical Systems and Computation University of California Santa Barbara USA

Self-learning control techniques mimicking the functionality of the limbic system in the mammalian brain have shown advantages in terms of superior learning ability and low computational cost. However, accompanying stability analyses and mathematical proofs rely on unrealistic assumptions which limit not only the performance, but also the implementation of such controllers in real-world scenarios. In this work the limbic system inspired control (LISIC) framework is revisited, introducing three contributions that facilitate the implementation of this type of controller in real-time. First, an extension enabling the implementation of LISIC to the domain of SISO affine systems is proposed. Second, a strategy for resetting the controller’s Neural Network (NN) weights is developed, in such a way that now it is possible to deal with piece-wise smooth references and impulsive perturbations. And third, for the case when a nominal model of the system is available, a technique is proposed to compute a set of optimal NN reset weight values by solving a convex constrained optimization problem. Numerical simulations addressing the stabilization of an unmanned aircraft system via the robust LISIC demonstrate the advantages obtained when adopting the extension to SISO systems and the two NN weight reset strategies.

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Non-Euclidean Contraction Theory for Robust Nonlinear Stability

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arXiv 2021年

作者： Davydov, Alexander Jafarpour, Saber Bullo, Francesco The Department of Mechanical Engineering The Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to arbitrary norms, and characterize their properties. We introduce and study the sign and max pairings for the `1 and `∞ norms, respectively. Using weak pairings, we establish five equivalent characterizations for contraction, including the one-sided Lipschitz condition for the vector field as well as logarithmic norm and Demidovich conditions for the corresponding Jacobian. Third, we extend our contraction framework in two directions: we prove equivalences for contraction of continuous vector fields and we formalize the weaker notion of equilibrium contraction, which ensures exponential convergence to an equilibrium. Finally, as an application, we provide (i) incremental input-to-state stability and finite input-state gain properties for contracting systems, and (ii) a general theorem about the Lipschitz interconnection of contracting systems, whereby the Hurwitzness of a gain matrix implies the contractivity of the interconnected system. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems