Title :
Fixed final time optimal control approach for bounded robust controller design using Hamilton-Jacobi-Bellman solution
Author :
Kar, I.N. ; Adhyaru, D.M. ; Gopal, M.
Author_Institution :
Dept. of Electr. Eng., Indian Inst. of Technol., New Delhi, India
fDate :
9/1/2009 12:00:00 AM
Abstract :
In this study, an optimal control algorithm based on Hamilton-Jacobi-Bellman (HJB) equation, for the bounded robust controller design for finite-time-horizon nonlinear systems, is proposed. The HJB equation formulated using a suitable nonquadratic term in the performance functional to take care of magnitude constraints on the control input. Utilising the direct method of Lyapunov stability, we have proved the optimality of the controller with respect to a cost functional, that includes penalty on the control effort and the maximum bound on system uncertainty. The bounded controller requires the knowledge of the upper bound of system uncertainty. In the proposed algorithm, neural network is used to approximate the time-varying solution of HJB equation using least squares method. Proposed algorithm has been applied on the nonlinear system with matched and unmatched system uncertainties. Necessary theoretical and simulation results are presented to validate proposed algorithm.
Keywords :
Lyapunov methods; control system synthesis; neurocontrollers; nonlinear control systems; robust control; time optimal control; time-varying systems; Hamilton-Jacobi-Bellman equation; Lyapunov stability; finite-time-horizon nonlinear systems; neural network; robust controller; time optimal control; time-varying solution;
Journal_Title :
Control Theory & Applications, IET
DOI :
10.1049/iet-cta.2008.0288