Dissipativity-constrained learning of MPC with guaranteeing closed-loop stability

This paper addresses the data-driven approximation of model predictive control (MPC) designed for nonlinear plant systems. MPC has high ability of handling complex system-specifications and of improving the control performance, while it requires high computational complexity. Aiming at reducing the complexity, this paper addresses the data-driven approximation of MPC. To this end, the control law in MPC is described by the Koopman operator, which is a linear operator defined on the infinite-dimensional lifted state space. Then, the problem of data-driven finite-dimensional approximation of the operator is addressed. The problem is formulated as an optimization problem subject to a specified dissipativity constraint, which guarantees closed-loop stability and is modeled by a set of matrix inequalities. This paper also presents a computationally efficient algorithm of solving the optimization problem. Finally, a numerical simulation of controller construction is performed. The approximated MPC control law shows the stability of the overall control system while demonstrating high control performance.