A switched extremum seeking control without steady-state oscillation using gradient-based adaptive-amplitude perturbation

To enhance the steady-state and dynamic performance of the extremum seeking control (ESC), a switched ESC scheme is proposed in this paper. Firstly, to solve nonconvex optimization problems, a novel adaptive law for perturbation is established utilizing the hybrid gradient information to accomplish a trade-off between the dynamic and steady-state performance. It is shown that the adaptive-amplitude ESC achieves global optimization despite the existence of local extrema. Then, to overcome the adverse effect of inaccurate gradient estimation on steady-state accuracy, a Lyapunov-based switched strategy is employed to start the bisection-based ESC. The plant output converges to the equilibrium rapidly and accurately without steady-state oscillation. Furthermore, the stability of the proposed scheme is theoretically proved. Numerical simulation examples are carried out to demonstrate the effectiveness of the proposed scheme.