Output Feedback-Based Adaptive Optimal Output Regulation for Continuous-Time Strict-Feedback Nonlinear Systems

This article investigates the optimal output regulation problem for continuous-time strict-feedback nonlinear systems, in which the full states are not measurable in real-time, and a priori knowledge of system dynamics and an admissible control policy are both unavailable. Fundamental challenges here differing from existing works are twofold: 1) only output data rather than full state data are available; 2) policy iteration cannot be performed since admissible control policy is not available. To solve the problem, an adaptive observer and an adaptive solver are designed and simultaneously applied to observe the states, estimate the uncertain parameters, and solve the nonlinear regulator equations. Then, a data-driven value iteration algorithm is designed based on the observed data to solve a positive semidefinite Hamilton–Jacobi–Bellman equation resulting from the formulated problem with rigorous convergence analysis. It is guaranteed that the resulting closed-loop system is uniformly ultimately bounded under the designed data-driven value iteration algorithm. Finally, a simulation study on the designed algorithm is presented using a van der Pol oscillator to demonstrate its effectiveness.