Optimal adaptive control of nonlinear continuous-time systems in strict feedback form with unknown internal dynamics

A novel approach is proposed for multi-input multi-output (MIMO) optimal adaptive control of nonlinear continuous-time systems in strict feedback form with uncertain internal dynamics. First, it is shown that the optimal adaptive tracking problem of strict feedback systems can be reduced to an optimal regulation problem of affine nonlinear continuous-time systems expressed as a function of tracking error by designing a properly chosen adaptive feedforward control input. Then, an optimal adaptive feedback scheme is introduced for the affine system to estimate the solution of the Hamilton-Jacobi-Bellman (HJB) equation online which becomes the optimal feedback control input for the closed-loop system. A Lyapunov based approach is employed to show that the tracking error converges to zero as well as the cost function estimation and the internal dynamics estimation errors provided the system input is persistently exciting. Finally, numerical results are provided to verify the theoretical results.