The Experts below are selected from a list of 9312 Experts worldwide ranked by ideXlab platform
John T. Wen - One of the best experts on this subject based on the ideXlab platform.
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Feedback stabilization of nonlinear affine systems
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Dan O. Popa, John T. WenAbstract:A class of iterative methods have been proposed for the path planning of nonholonomic systems. These methods warp an initial path iteratively to an acceptable final path by using Newton-Raphson algorithms. In this paper we modify the iterative off-line method to render it a feedback controller. The main idea is to couple the Iteration Variable to the actual time, thus the control is executed during the path Iteration, before convergence. We show that this scheme guarantees the closed loop asymptotic stability for systems with drift.
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ICRA - Feedback stabilization of nonholonomic systems in presence of obstacles
Proceedings of IEEE International Conference on Robotics and Automation, 1Co-Authors: Fernando Lizarralde, John T. WenAbstract:A class of iterative methods have recently been proposed for the path planning of nonholonomic systems. These methods warp an initial path iteratively to an acceptable final path by using Newton-Raphson or gradient type of algorithms. Once a path is found off-line, a feedback controller is then used to follow the path. In this paper, we propose a modification of these off-line methods to transform them directly into a feedback controller. The main idea is to couple the Iteration Variable to the actual time, thus the control is executed during the path Iteration, before the convergence. We show that this scheme guarantees the closed loop asymptotic stability when the system model is known, and possesses certain robustness when the model information is imperfect. By using interior penalty functions, inequality constraints can also be handled by the algorithm. Simulation results are included, showing promise of the approach.
Xin Chen - One of the best experts on this subject based on the ideXlab platform.
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An iterative method for optimal feedback control and generalized HJB equation
IEEE CAA Journal of Automatica Sinica, 2018Co-Authors: Xuesong Chen, Xin ChenAbstract:In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman ( GHJB ) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the Iteration Variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems.
I. Norman Katz - One of the best experts on this subject based on the ideXlab platform.
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Convergence of an iterative algorithm for solving Hamilton-Jacobi type equations
Mathematics of Computation, 2001Co-Authors: Jerry Markman, I. Norman KatzAbstract:Solutions of the optimal control and H∞-control problems for non-linear affine systems can be found by solving Hamilton-Jacobi equations. However, these first order nonlinear partial differential equations can, in general, not be solved analytically. This paper studies the rate of convergence of an iterative algorithm which solves these equations numerically for points near the origin. It is shown that the procedure converges to the stabilizing solution exponentially with respect to the Iteration Variable. Illustrative examples are presented which confirm the theoretical rate of convergence.
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An Iterative Algorithm for Solving Hamilton--Jacobi Type Equations
SIAM Journal on Scientific Computing, 2000Co-Authors: Jerry Markman, I. Norman KatzAbstract:Solutions of the optimal control and $H_\infty$-control problems for nonlinear affine systems can be found by solving Hamilton--Jacobi equations. However, these first-order nonlinear partial differential equations can, in general, not be solved analytically. This paper introduces an iterative algorithm which solves these equations numerically for points near the origin. The procedure converges to the stabilizing solution exponentially with respect to the Iteration Variable. The algorithm is implemented on both illustrative and comparative examples.
Xuesong Chen - One of the best experts on this subject based on the ideXlab platform.
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An iterative method for optimal feedback control and generalized HJB equation
IEEE CAA Journal of Automatica Sinica, 2018Co-Authors: Xuesong Chen, Xin ChenAbstract:In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman ( GHJB ) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the Iteration Variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems.
Yangquan Chen - One of the best experts on this subject based on the ideXlab platform.
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Variable Gain Feedback $PD^{\alpha}$ -Type Iterative Learning Control for Fractional Nonlinear Systems With Time-Delay
IEEE Access, 2019Co-Authors: Jing Wang, Yi Liu, Dong Shen, Yangquan ChenAbstract:A Variable gain feedback PD α -type iterative learning control (ILC) update rate is proposed for the fractional-order nonlinear systems with time delay. The learning update rate combines the open-loop and closed-loop strategy, in which the system's current tracking error and the previous iterative control of the tracking error are simultaneously used to correct the control effect. So, the proposed method could both speed up the convergence rate along the Iteration direction and reduce the tracking error along the time direction. Furthermore, the algorithm ensures that the system has good learning efficiency and control performance at the different running time and iterative batches due to the time-Iteration-Variable learning gain. The sufficient condition for the convergence of the proposed algorithm is analyzed. Finally, the validity of the proposed method is verified on a numerical example and a wind power generation system.
