Indirect Adaptive Optimal Tracking Switching Control of Nonlinear Systems

In this article, for continuous-time nonlinear systems with unknown dynamics and multiple equilibrium points, an indirect adaptive optimal tracking switching controller consisting of multiple linear indirect adaptive optimal tracking controllers, a robust compensator, and an optimal switching mechanism is proposed by combining optimal tracking scheme with embedding-transformation technique and adaptive algorithm. First, multiple linearized models are used to establish a controller design model of nonlinear system near the multiple equilibrium points. Second, a parameter identification algorithm based on Lyapunov stability is utilized to estimate unknown system parameters online. After that, by using embedding-transformation technology, minimum principle, and quadratic programming technique, the linear indirect adaptive optimal tracking switching controller and optimal switching function for the controller design model are obtained. Then, the compensator is designed according to the error between the optimal linearized model and the nonlinear system. Finally, convergence of the indirect adaptive algorithm and stability of the closed-loop system are verified by theoretical analysis, and the effectiveness and superiority are demonstrated by simulation experiments.