Backstepping Control of Multi-input Extremum Seeking Systems Based on State Feasible Region Constraint

In order to solve the control problem of multi-input extremum seeking systems based on state feasible region constraint, extremum seeking method, backstepping control and adaptive control were combined. Firstly, system states' extremum reference trajectory was designed by extremum seeking method. Secondly, backstepping controller was designed by appropriate Lyapunov function selected by inversion control method. At last, unknown parameters estimation law were designed by adaptive control method. Objective function extreme value is seeked under the condition of feasible region constraint is satisfied. Simulation result shows that the proposed design method is effectiveness.