Predictive control for delay systems: theory and applications

In industrial processes, time delay often occurs in many dynamical systems, such as chemical processes, communication systems, and vehicle systems. Presence of time delay in a process increases the difficulty of controlling such systems. These delays can affect the state, input, and output; they can be constant or time varying, known or unknown, deterministic or stochastic depending on the systems under consideration. In this chapter, we propose a robust model predictive control (MPC) algorithm for a class of uncertain discrete-time systems with both states and input delays. We consider the constant and time-varying delay cases as well as the state feedback case. The uncertainty is assumed polytopic with a known upper bound. By the augmented system description we reduce a robust model predictive control law to a convex optimization involving linear matrix inequalities (LMIs). After defining an optimization problem that minimizes a cost function at each time instant, we compute a state feedback by minimizing the upper bound of the cost function subject to constraints on inputs. We give closed-loop stability conditions on the systematic construction of a Lyapunov–Krasovskii functional and compare its robustness properties with the standard MPC in the presence of parameter uncertainties and delay systems. Finally, we study the constrained control problem for a quarter-vehicle model and nonlinear system using the proposed robust MPC.