Prioritization-based switched feedback control for linear SISO systems with time-varying state and input constraints

Abstract

The problem of stabilization by means of state feedback is discussed for linear single input single output systems while satisfying time-varying polytopic constraints on both the states and the control input. The core of the switched control concept derived in this work is a standard state feedback controller, stabilizing the system in the unconstrained case, whereas its control signal is optimally limited in order to achieve feasibility of the states and the input in the constrained case. For the derivation of the limiting function, feasible dynamic limits are designed which correspond to one additional control law per constraint. A switching logic for these limits is then constructed with the solution of an optimization problem. Thereby, an explicit order of constraints prioritization is taken into account in order to obtain a unique switching logic. Throughout the derivation, the property of differential flatness is exploited, which allows the reduction of the respective system to the control of a (constrained) integrator chain. The performance of the control approach as pure feedback as well as in a constrained two-degree-offreedom setup is finally discussed by means of simulation studies. Furthermore, a comparison of the achieved results with a model predictive control approach is carried out.