A constructive approach for an optimal control applied to a class of nonlinear time delay systems

Abstract

In this contribution, we obtain a nonlinear controller for a class of nonlinear time delay systems, by using the inverse optimality approach. We avoid the solution of the Hamilton Jacobi Bellman type equation and the determination of the Bellman's functional by extending the inverse optimality approach for delay free nonlinear systems to time delay nonlinear systems. This is achieved by combining the Control Lyapunov Function framework and Lyapunov-Krasovskii functionals of complete type. Explicit formulas for an optimal control are obtained. The efficiency of the proposed method is illustrated via experimental results applied to a dehydration process whose model includes a delayed state linear part and a delayed nonlinear part. To give evidence of the good performance of the proposed control law, experimental comparison against an industrial Proportional Integral Derivative controller and optimal linear controller. Additionally experimental robustness tests are presented.