Locally optimal and globally inverse optimal controller for multi-input nonlinear systems

The H_infin-optimal control for nonlinear systems is hard to obtain because one must solve the Hamilton-Jacobi-Isaacs (HJI) equation. To overcome this problem, a nonlinear controller is proposed by Ezal, Pan, and Kokotovic. The controller guarantees local optimality and global inverse optimality, that is, it behaves as a linear optimal controller in the region where the linearized dynamics dominates, and is inverse optimal in the global sense. However, the system class under their consideration is single-input strict-feedback nonlinear systems which is somewhat restrictive. In this paper, we propose a nonlinear optimal controller for a class of multi-input nonlinear systems. Moreover, under the proposed controller, the closed-loop system is globally exponentially stable, whereas the controller proposed by Ezal et al. just guarantees global asymptotic stability.