Accumulative Quadratic Constraint
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This chapter addresses a decentralised model predictive control (DeMPC) scheme for networks of linear systems that suffer from a coupling delay element. The accumulative quadratic supply rates are considered in this chapter for dealing with the delay in the interactive inputs of neighbouring subsystems. The stabilisability conditions are developed in conjunction with the delay robustly dissipative criteria, and in association with the newly introduced ‘asymptotically accumulative quadratic constraint’ (AAQC) and the ‘positively accumulative quadratic constraint’ (PAQC). In this chapter, the storage function of a Lyapunov–Krasovskii functional form is used in the dissipation inequality. This storage function may initially increase even when there are not any disturbances, then starts converging to a neighbourhood of the origin as a result of the employment of the AAQC-based or PAQC-based attractivity constraints in decentralised MPC. With the accumulative supply rates, the monotonically decreasing property of a single-time-step supply rate can be relaxed. The AAQC and PAQC are, thus, less conservative than the APRC and QDC in previous chapters and well suited to the interconnected systems having a coupling delay element in this chapter.