Adaptive output feedback extremum seeking receding horizon control of linear systems

In this paper, we present a control algorithm that incorporates real-time optimization (RTO) and receding horizon control (RHC) technique to solve an output feedback extremum seeking control problem for a linear unknown system. The development of the controller consist of two steps. First, the optimum setpoint that minimizes a given performance function is obtained via an update law and secondly, the control input that drives the system to the optimum is computed. State estimation filters and a parameter update law are used at each iteration step, to update the unknown states and parameters in the optimization scheme. The resulting controller is able to drive the system states to the desired unknown optimum by requiring a Lyapunov restriction and a satisfaction of a persistency of excitation condition. Two simulation examples are provided to demonstrate the effectiveness of the proposed method.