Model predictive control via quadratic dissipativity constraint

A model predictive control (MPC) scheme is deployed via the quadratic dissipativity constraint (QDC) in this paper. Within the development, two new constraints, one a QDC-based stability constraint, the other an iterative-feasibility constraint, are derived for the model predictive control of linear systems. These two constraints are imposed on the first control vector of the MPC control sequence. The input-and-power-to-state stabilizability (IpSS) - an extension of ISS, and the iterative feasibility are simultaneously achieved as a result of the two mentioned constraints. Previous results on the quadratic dissipativity constraint for unconstrained systems are consolidated in this work, and extended to include the iterative-feasibility condition. The IpSS condition for constrained linear systems is proved herein. Since terminal constraints are not employed in this open-loop strategy, it has the potential for further extension to distributed or decentralized control of interconnected systems, as well as for other types of MPC such as economic MPC. Numerical simulations with an open-loop unstable interconnected system are provided to demonstrate the effectiveness of the quadratic dissipativity constraint for model predictive control.