Feedback Control Based on Positively Invariant Sets for Linear Constrained Systems

The control problem of linear discrete-time systems with constraints of control, state and initial state is studied. State feedback control law of linear constrained systems is designed based on positively invariant sets of linear systems so that all given initial states of system asymptotically transfer to the origin while all constraints are satisfied. Firstly, the problem of the existence of the state feedback control law is presented and the constrained control problem is converted to the nonlinear optimization problem with positively invariant sets approach and optimization theory. Then, nonlinear optimization problem is solved through random testing method and state feedback control law of linear constrained system is obtained. Finally, simulation results show that control law obtained is effective

I. Introduction

Engineering systems usually run with fixed bounds, and the control actions must satisfy strict limitations. Therefore, constrained control problem emerges and has been studied in the optimal control theory. Although some methods have been obtained, because of the nonlinearity and complexity of these methods, the implement of constrained control problem is difficult.