Decentralised predictive controllers with parameterised quadratic constraints for nonlinear interconnected systems

A decentralised model predictive control scheme for nonlinear interconnected systems is developed with parameterised stabilising constraints in this paper. Both control and state constraints are inclusive in the problem formulation. An extension to the input-to-state stabilisation framework is given with a newly derived input-to-power-and-state stabilisability (IpSS) condition for interconnected systems. In this work, we consider C¹ continuous nonlinear input-affine state-space models with unknown but bounded input disturbance, and develop an LMI-based robust stabilisability condition for the global system. The interactive signals are also unknown and bounded in this development. With an open-loop perspective, the stabilising constraint for model predictive control in this approach is a dynamic quadratic constraint on the initial control vector, which is converted from a dissipation-based constraint using compound output signals. Numerical simulation for three dynamically-coupled subsystems is provided to illustrate the theoretical development.