Constrained control and rate or increment for linear systems

Abstract

This chapter is divided into two parts. The first one concerns the problem of constraints on the control together with constraints on the control rate or increment. Linear systems in state space form, in both the continuous-time and discrete-time domains, are considered. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate (for the continuous-time case), such that the system evolves respecting incremental or rate constraints. A pole assignment technique is then used to solve the inverse problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on both control and its increment or rate. An illustrative example shows the application of the method on the double integrator problem. The second part completes the first one by adding a bounded disturbance to the system dynamics. This last is devoted to the control of linear systems with constrained control and rate or increment with additive bounded disturbances. A link is then performed as above to the pole assignment procedure to get robust stabilizing state feedback respecting all constraints. Hence, the obtained control law is within the admissible intervals for both the control magnitude and its rate or increment and is robust against additive bounded disturbances.