Backstepping control of pure-feedback multi-input extremum seeking system

To solve control problems of pure-feedback multi-input extremum seeking systems based on state feasible domain constraint, extremum seeking method, backstepping control and adaptive control were combined. Firstly, system states’ extremum reference trajectory was designed by extremum seeking method. Secondly, the controller was designed by appropriate Lyapunov function selected by backstepping control method. At last, unknown parameters estimation law was designed by adaptive control method. Objective function extremum was searched under the condition of feasible region constraint was satisfied. Simulation result shows that the proposed design method is effective.