A Computationally Efficient Stabilizing Model Predictive Control of Switched Systems Hariprasad K, Sharad Bhartiya ⋆ Department of Chemical Engineering, Indian Institute of Technology-Bombay, Mumbai - 400 076, India Abstract: Many applications in engineering exhibit switching character due to discrete and continuous aspects in their dynamic behavior. Switching characteristics of hybrid systems bring discontinuity and nonlinearity in their course of operation and pose major challenges in developing stabilizing Model Predictive Control (MPC) for them. For Piecewise Affine (PWA) Systems, the MPC problem requires on-line solution of Mixed Integer Programs (MIPs) for obtaining the input profile. Since, complexity of the optimization problem that needs to be solved in MPC increases combinatorially with respect to the integer variables, on-line computing of MPC control law for large scale problems and/or problems with large horizons is expensive. In this paper we, propose a MPC formulation, under the popular framework of terminal cost - terminal set MPC, which enables tuning the complexity of the control algorithm. The proposed approach introduces an idea of a pre-terminal set, within which the inputs have enough power to trap states inside it. Since the pre-terminal set lies in the terminal mode which contains origin, this eliminates the need for binary decision variables to model mode transitions after the trajectory enters in pre-terminal set, thereby reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC. Keywords: Switched systems, Hybrid systems, Stabilizing model predictive control (MPC), Stability, Piecewise Affine Systems (PWA). 1. INTRODUCTION Switched systems represent a class of hybrid dynamical systems, wherein occurrence of a discrete event is accom- panied by a switch in the flow field or operating mode of the system. Models of switched systems consist of multiple sets of differential equations, with each set corresponding to a mode of operation. Continuous states of the switched system evolve in a given mode until certain conditions are satisfied after which the system transitions to a new mode of operation (Hariprasad et al., 2012). Switched system dynamics appear in diverse areas such as power electronic devices, manufacturing systems, communication networks, models in economics and finance and chemical process systems and many others (Chatterjee, 2007). Synthesizing regulators for such switched systems is particularly chal- lenging since it requires a co-ordinated switching strategy, in addition to steering the states to the origin. Model Predictive Control (MPC) has emerged as an in- dustrially relevant control strategy in recent times. MPC can handle hard constraints on the manipulated and con- trol variables to achieve economically optimal process operation. MPC control algorithms compute a profile of manipulated inputs by optimizing a desired open loop performance objective over a future horizon for a given ⋆ Corresponding Author: bhartiya@che.iitb.ac.in (Sharad Bhar- tiya),Tel: +91 22 25767225. initial state, and implement the first move of the profile. This procedure is repeated at each sampling time, with the updated process measurement as initial state, bringing a receding horizon nature to the control strategy (Camacho and Bourdons, 2004). The fact that different modes of operation can be expressed as constraints, makes MPC a natural choice for constrained control of switching systems. Switching characteristics of hybrid systems bring disconti- nuity and nonlinearity in their course of operation, which pose major challenges while devising stabilizing MPC for hybrid systems (Mayne et al., 2000). For MPC to be an acceptable solution, for control of hybrid systems, it should have the following features: (i) nominal and robust stability, (ii) computational tractability for on line imple- mentation. The current generation of MPC algorithms for switched systems have primarily focused on the former feature and neglected the issue of computational tractabil- ity, leaving it entirely to the solver. Consequently most practical implementations of MPC have been limited to the control of small systems. In this work, we present a model predictive control scheme of switching systems which provide computational benefits over existing formu- lations. Finite horizon stabilizing MPC for hybrid systems is pre- sented by Bemporad and Morari (Bemporad and Morari, 1999), wherein the system states were constrained to reach the origin after finite moves. Bemporad et al.(Bemporad Third International Conference on Advances in Control and Optimization of Dynamical Systems March 13-15, 2014. Kanpur, India 978-3-902823-60-1 © 2014 IFAC 607 10.3182/20140313-3-IN-3024.00121