Output feedback tracking control for polynomial nonlinear systems with measurement noises and mismatched disturbances

Abstract

In this paper, the output feedback tracking control problem is investigated for polynomial nonlinear systems (PNSs) with measurement noises and mismatched disturbances. First, in order to suppress measurement noises, a polynomial observer is introduced to simultaneously estimate states and mismatched disturbances. Next, based on the idea of backstepping control, a novel output feedback controller is designed for PNSs to compensate mismatched disturbances. Command filters are employed to avoid the repeated derivatives of virtual control and measurement noises in the recursive controller design. Then, a sufficient condition in terms of the parameter-dependent linear matrix inequality (PDLMI) is derived to guarantee the boundedness of tracking errors and estimation errors. By utilizing the sum of squares (SOS) decomposition technique, the PDLMI is solved to obtain desired controller parameters. Finally, an example of dynamic point-the-bit rotary steerable drilling tool system is performed to demonstrate the effectiveness and feasibility of the proposed strategy.