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Automation & Control Systems
Shaojie Zhang, Kun Ji, Han Zhang
Summary: In this paper, a model-free incremental adaptive optimal control scheme is proposed for nonlinear systems in the presence of disturbance and input time-delay. The approximate model of the nonlinear system is obtained using an incremental method, and the relevant matrix parameters are identified through recursive least squares estimation. A time-delay matrix function is constructed using a neural network to eliminate the input time-delay, and the external disturbance of the nonlinear system is handled using H-infinity optimal control. The control law is obtained using incremental adaptive dynamic programming algorithm by solving Hamilton-Jacobi-Isaacs equation. Convergence analysis of the proposed control scheme is provided, and simulations are conducted to verify its effectiveness.
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
(2023)
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Operations Research & Management Science
Sudeep Kundu, Karl Kunisch
Summary: The study examines the application of policy iteration in solving the HJB equation with control constraints, utilizing an implicit upwind scheme to solve the linear equations. Numerical examples are conducted to compare the results with the unconstrained cases.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2021)
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Automation & Control Systems
Yaping Tang, Weiwei Sun, Dongqing Liu
Summary: This paper focuses on the simultaneous exponential stabilization of a set of stochastic port-controlled Hamiltonian (PCH) systems. The paper considers the limited bandwidth of channels, fading channels, transmission delays, and actuator saturation constraint. Sufficient criterions are given for controller design based on dissipative Hamiltonian structural and saturating actuator properties.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Proceedings Paper
Automation & Control Systems
Yuqing Zheng, Guoshan Zhang
Summary: This paper proposes an optimal algorithm based on policy iteration to learn the H-infinity state feedback control solution for nonlinear systems with input saturation. The algorithm constructs the Hamilton-Jacobi-Isaacs equation to handle constraints on input, and utilizes an actor-critic-disturbance neural network to implement the policy iteration. Experimental results demonstrate the effectiveness of the algorithm in ensuring system stability.
PROCEEDINGS OF THE 33RD CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2021)
(2021)
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Computer Science, Information Systems
Bor-Sen Chen, Min-Yen Lee
Summary: In this study, we investigate the strategies for multi-player noncooperative and cooperative target tracking games in a stochastic jump diffusion system. We propose a method to transform the nonlinear system into a linear matrix inequalities-constrained multi-objective optimization problem, which can be efficiently solved using a multi-objective evolution algorithm. The Pareto optimal solution of the optimization problem is proven to be the Nash equilibrium solution of the target tracking strategy. We also simplify the cooperative strategy into a single-objective optimization problem. Two simulation examples are provided to demonstrate the effectiveness of the proposed strategies.
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Computer Science, Information Systems
Bor-Sen Chen, Po-Hsun Wu, Min-Yen Lee
Summary: Deep neural network schemes based on big data-driven methods have been successfully used in image classification, communication, translation of language, and speech recognition. However, applying them to complex robust nonlinear filter design in signal processing requires more effort. The proposed robust H-infinity HJIE-embedded DNN-based filter design aims to solve the challenge of robust state estimation in nonlinear stochastic signal systems under uncertain external disturbance and output measurement noise.
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Computer Science, Information Systems
Bor-Sen Chen, Po-Hsun Wu
Summary: This study proposes a novel HJIE-embedded deep learning approach to solve the robust H-infinity observer-based reference tracking control design problem of nonlinear stochastic systems. The proposed method utilizes a deep neural network to output the solution of the HJIE by inputting state estimation error and tracking error. This approach achieves the theoretical H-infinity observer-based reference tracking control strategy as the deep learning algorithm converges.
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Automation & Control Systems
Bin Zhang, Yingmin Jia, Yuqi Zhang
Summary: In this article, a DDP-based iterative algorithm is proposed for solving finite-horizon two-person zero-sum differential games. The DDP technique expands the HJI partial differential equation into higher-order differential equations. By using value function and saddle point approximations, the DDP expansion is transformed into an algebraic matrix equation in integral form. The DDP iterative algorithm is developed based on the algebraic matrix equation to learn the solution to the differential games. Strict proof is provided to guarantee the iterative convergences of the value function and saddle point. The effectiveness of the proposed method is demonstrated through simulation examples.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
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Automation & Control Systems
Peng Li, Yijing Wang, Zhiqiang Zuo
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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
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Computer Science, Theory & Methods
Ellya L. Kawecki, Iain Smears
Summary: The research demonstrates the convergence of adaptive discontinuous Galerkin and C-0-interior penalty methods for fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman and Isaacs equations with Cordes coefficients. By considering a broad family of methods on adaptively refined conforming simplicial meshes, a novel intrinsic characterization approach was utilized to identify the weak limits of bounded sequences of nonconforming finite element functions. The study also provides detailed theory for the limit space and original auxiliary function spaces that are of interest for adaptive nonconforming methods in more general problems.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2022)
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Automation & Control Systems
Yu-Chen Lin, Ha Ly Thi Nguyen, Ji-Fan Yang, Hung-Jui Chiou
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IET CONTROL THEORY AND APPLICATIONS
(2022)
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Operations Research & Management Science
Hidekazu Yoshioka, Motoh Tsujimura
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Mathematics, Interdisciplinary Applications
Xiaochi Wu
Summary: This paper investigates the existence of value for a two-person zero-sum differential game with symmetric incomplete information and signal revealing, proving that the game has a value and its value function is the unique bounded continuous viscosity solution of a suitable Hamilton-Jacobi-Isaacs equation.
DYNAMIC GAMES AND APPLICATIONS
(2021)
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Computer Science, Theory & Methods
Kazufumi Ito, Christoph Reisinger, Yufei Zhang
Summary: This work introduces numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems arising from exit time problems of diffusion processes. By employing policy iteration, the problem is reduced to a sequence of linear Dirichlet problems approximated by a neural network. The numerical solutions converge globally in the H-2-norm with superlinear speed, optimal feedback controls are constructed from numerical value functions.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2021)
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Mathematics, Applied
Karl Kunisch, Donato Vasquez-Varas
Summary: This article analyzes a learning technique for finite horizon optimal control problems and its approximation based on polynomials, and illustrates the practicality and efficiency of the method.
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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
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INFORMATION SCIENCES
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Xiong Yang, Haibo He, Qinglai Wei, Biao Luo
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Shan Xue, Biao Luo, Derong Liu, Yueheng Li
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2019 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN)
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