Adaptive Tracking Control of Nonlinear Systems Subject to Matched Uncertainties

Abstract

In thisMatched uncertainties chapter, anTracking control adaptive tracking controlTracking control scheme is designed for a class of continuous-time uncertain nonlinear systemsUncertain nonlinear systems based on the approximate solution of the HJB equation. Considering matched uncertaintiesMatched uncertainties, the tracking controlTracking control of the continuous-time uncertain nonlinear system can be transformed to the optimal tracking controlTracking control of the associated nominal systemNominal system. By building the nominal error systemError system and modifying its cost functionCost function, the solution of the relevant HJB equation can be contributed to the adaptive tracking controlTracking control of the continuous-time uncertain nonlinear system. In view of the complexity on solving the HJB equation, its approximate solution is pursued by the policy iterationPolicy iteration algorithm under the ADP framework, where a critic neural network is constructed to approximate the optimal cost functionCost function. Therein, an action networkAction network is used to directly calculate the approximate optimal controlApproximate optimal control law, which constitutes the tracking controlTracking control law for the original uncertain system together with the steady control law. The weight convergence of the critic networkCritic network and the stability of the closed-loop systemClosed-loop system are provided as the theoretical guarantee based on the Lyapunov theory. Two simulation examples are studied to verify the theoretical results and the effectiveness of the proposed tracking controlTracking control scheme.