Tracking control design for periodic piecewise polynomial systems with multiple disturbances

The present study examines the state tracking problem of periodic piecewise polynomial systems subject to multiple disturbances and actuator faults. Specifically, the fundamental period is partitioned into several subintervals and the piecewise matrix polynomial functions can be put together to approximate the dynamics over each period, which are characterized by Bernstein polynomials. Moreover, the system dynamics contains both matched and mismatched disturbances, wherein the matched disturbance is unknown and resulted from some exogenous system, and mismatched case is norm-bounded. The control law is configured by integrating the output of the disturbance observer with state-feedback reliable control law. Particularly, a disturbance observer is designed to estimate the disturbance caused by an exogenous system. Besides, by considering time-varying polynomial Lyapunov function and making use of Bernstein polynomial approach, a set of sufficient conditions is derived which are expressed in terms of linear matrix inequalities. Further, by virtue of MATLAB software the desired controller and observer gain matrices can be computed. In conclusion, the potential and significance of the theoretical findings are confirmed by presenting a numerical example with simulation results.

Automated summary

This study focuses on the state tracking problem of periodic piecewise polynomial systems subject to multiple disturbances and actuator faults. It proposes a method of approximating the system dynamics over each period using Bernstein polynomials and designs a disturbance observer to estimate the disturbance caused by an exogenous system. By considering time-varying polynomial Lyapunov function and linear matrix inequalities, a set of sufficient conditions for control is derived. MATLAB software is used to compute the desired controller and observer gain matrices. A numerical example with simulation results is provided to confirm the potential and significance of the theoretical findings.