Design of model predictive control with guaranteed delay-dependent and disturbance-dependent recursive feasibility for switched delayed systems

This paper introduces a novel model of predictive control for linear switched systems with state delay structure. The proposed method ensures delay-dependent and disturbance-dependent recursive feasibility. It achieves this by defining a quadratic cost function and computing its upper bound based on the maximum state delay and disturbance energy. The recursive feasibility constraints of the subsystems are then obtained using the maximum limit of the cost function (CF) and vertices of a polytopic disturbance. To relax the limitation of strict reduction in energy during switching moments, reduce the constraints imposed at each moment, and reduce the dwell-time limitation, a coordinated strategy of the MPC and the PDT switching law is formed using multiple Lyapunov functions. In this strategy, an optimization problem with a new set of linear matrix inequality constraints is formulated, which can be efficiently solved using common software. To account for the online nature of the strategy, the timing of each constraint is carefully chosen to adjust the rate of energy changes in the subsystems and switching moments. A numerical simulation is conducted to show the effectiveness of the suggested strategy, and the results confirm its success in achieving the desired control objectives.