Optimal output tracking control with parameterized path for a class of nonlinear systems

Optimal backstepping controller was designed to solve the variable parameterized tracking problem of a class of SISO nonlinear system in strict feedback form. Parameterized path following problem consists of path following and speed assignment tasks. In the path following task, local performance index function was given for the linear part of system. Then nonlinear recursive backstepping procedure is used to get a global mapping, control law is designed based on Lyapunov function of new states from the mapping. Global performance index function is got by inverse optimal approach. In speed assignment task, gradient update law is adopted to achieve asymptotic convergence of speed error. Global asymptotic stability of the control system is proven. Validity of the proposed algorithm is shown by simulation results.