Inverse Optimal Adaptive Fuzzy Output Feedback Control for Nonlinear Systems With Output Quantization

The existing results on inverse optimal control are limited to nonlinear systems without quantized signals. To remove this limitation, for strict-feedback nonlinear systems under output quantization, a new adaptive fuzzy inverse method is presented in this article, which achieves the optimal performance without relying on the Hamilton–Jacobi–Bellman equation. Considering that only quantized output is applied to feedback, first of all, a novel quantized state observer is devised. Second, the unknown nonlinearities are approximated by fuzzy logic systems. Third, to overcome the issue that the partial derivatives of virtual controllers do not exist after quantization, the command filtering technology is applied. Then, by combining the tuning functions and the projection operator, an auxiliary intermediate controller and a parameter adaptive law are constructed. Furthermore, an adaptive inverse optimal controller under output quantization is established. It is shown that all signals in the closed-loop system are semiglobally uniformly ultimately bounded, and the inverse optimal practical stabilization is realized. Eventually, the effectiveness of this approach is demonstrated through two examples.