Computation of the Largest Constraint Admissible Set for Linear Continuous-Time Systems with State and Input Constraints

Abstract

We present a new method for the approximation of the largest constraint admissible set (CAS) for linear continuous-time systems with state and input constraints. The CAS is the set of initial states for which the controlled system does not violate the input or state constraints. The presented approach is based on a suitable discretization of the continuous-time system. In fact, we will show that CAS in the continuous-time case can be computed analogously to the discrete-time case, given an appropriate sampling time was chosen. We stress that the computation of CAS for continuous-time systems is considerably more difficult than for discrete-time systems, since one has to guarantee that the system does not violate the constraints in between the sampling instances.