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

• We find a sufficient condition for the complete type functional to be a Control Lyapunov-Krasovskii Functional.
• We propose a constructive method to find the optimal nonlinear controller for a class of time delay nonlinear systems.
• We apply this optimal nonlinear control law to a dehydration process in real time. Experimental results demonstrate the efficiency of this controller.
• A good performance of the system response is obtained under external disturbances.
• A comparison with an industrial PID, in terms of power savings is presented.

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.