Constrained Stabilization of Multi-Input Linear Systems with Distinct Input Delays

Abstract

Abstract Quadratic Programming (QP) has been used to combine Control Lyapunov Functions (CLF) with Control Barrier Functions (CBF) for designing controllers that stabilize nonlinear systems with constraints. In this paper, we develop a predictor-based QP design for constrained stabilization of multi-input linear systems with distinct input delays. The difficulty of compensating input delays of different lengths lies in the fact that explicit expressions for the predictor states are not usually available, especially when the nominal controller for the delay-free system is nonlinear - as the case is with the standard QP controller. In this paper, we begin with a CLF and a CBF for the delay-free system and use their predicted values over different time horizons corresponding to the different input delays to form constraints for the QP problem. The controller combining the predicted CLF and CBF achieves the same closed-loop performance as the delay-free system after the longest delay has been compensated and renders the origin of the system locally asymptotically stable. We include numerical simulations to demonstrate the effectiveness of the proposed prediction-based controller.