Quadratic Constraint for Decentralised Model Predictive Control
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The asymptotically positive realness constraint (APRC) and quadratic dissipativity constraint (QDC) are introduced in this chapter as an effective tool for designing decentralised control systems, especially the decentralised model predictive control, in the discrete-time domain. We derive the convergence conditions for interconnected systems on the grounds of global system dissipation, subsystem dissipation, coupling structure, and dissipation-based constraints (APRC or QDC in the case of quadratic constraints) of all controlled subsystems. These conditions are suitable for the decentralised and distributed control of interconnected systems that prohibit artificial constraints on the unmeasurable coupling vectors. A convex quadratic constraint on the current-time control vector is subsequently developed from the dissipation-based constraint and applied to the model predictive control (MPC) as an enforced attractivity constraint. The attractivity constraints for controlled subsystems can be fully decoupled in this approach. Only linear-time-invariant (LTI) interconnected systems are under the scope of this chapter.