Nonlinear Adaptive Inverse Optimal Controller Design Considered Optimality for Nominal Systems
Shun KAIZU, Kojiro HAGINO
An inverse optimal adaptive control design method for nonlinear strict-feedback systems with unknown parameters is presented. Generally, it is known that the optimal control problems can be reduced to the Hamilton-Jacobi-Bellman (HJB) equations, but to solve their equations is extremely difficult. For this reason, an adaptive controller minimizing some meaningful cost functionals without solving the HJB equation is designed. Such design methods are called inverse optimal design and have been researched recently. In these designs, a cost functional is decided by controller design, but its functional may not be desirable. Our goal is to design an adaptive controller so as to make a desirable cost functional smaller. In order to acheive the goal, we construct a controller by following steps, that is, 1) An adaptive inverse optimal controller is constructed by pointwise min-norm design, 2) Parameters of the designed controller is tuned. Illustrative examples show that although the constructed controllers may not be optimal, they make desirable cost functional smaller and have favorable stability property.