论文信息 - Neural Network -based Nearly Optimal Hamilton-Jacobi-Bellman Solution for Affine Nonlinear Discrete-Time Systems

Neural Network -based Nearly Optimal Hamilton-Jacobi-Bellman Solution for Affine Nonlinear Discrete-Time Systems

In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time systems. The method is based on least-squares successive approximation solution of the Generalized Hamilton-Jacobi-Bellman (HJB) equation. Since successive approximation using the GHJB has not been applied for nonlinear discrete-time systems, the proposed recursive method solves the GHJB equation in discrete-time on a well-defined region of attraction. The definition of GHJB, Pre-Hamiltonian function, HJB equation and method of updating the control function for the affine nonlinear discrete time systems are proposed. A neural network is used to approximate the GHJB solution. It is shown that the result is a closed-loop control based on a neural network that has been tuned a priori in off-line mode. Numerical example show that for nonlinear discrete-time systems, the updated control laws will converge to the suboptimal control.

Zheng Chen | S. Jagannathan

[1] D. Kleinman. On an iterative technique for Riccati equation computations , 1968 .

[2] B. Finlayson. The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[3] George N. Saridis,et al. An Approximation Theory of Optimal Control for Trainable Manipulators , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[4] P. K. Jain,et al. Lebesgue measure and integration , 1986 .

[5] Frank L. Lewis,et al. Neural Network Control of Robot Manipulators , 1996, IEEE Expert.

[6] John N. Tsitsiklis,et al. Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[7] Randal W. Beard,et al. Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation , 1997, Autom..

[8] F. Burk,et al. Lebesgue Measure and Integration: Burk/Lebesgue , 1997 .

[9] Sergey Edward Lyshevski. Control Systems Theory with Engineering Applications , 2001 .

[10] Ming Xin,et al. A new method for suboptimal control of a class of nonlinear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[11] Geng Li,et al. Gain tuning in discrete-time adaptive control for robots , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[12] F. Lewis,et al. A Hamilton-Jacobi setup for constrained neural network control , 2003, Proceedings of the 2003 IEEE International Symposium on Intelligent Control.