Distributed Model Predictive Control Design for Parameter-Invariant and Parameter-Varying Spatially-Distributed Systems in Input/Output Form

点击翻译按钮获取中文摘要

Distributed model predictive control (MPC) design has become an active research area in the last decade to deal with large, networked systems by explicitly taking input, output and state constraints into account with certain performance criterion satisfied. The networked systems can either be physically coupled, e.g. distributed parameter systems, or comprised of several independent subsystems coupled via constraints or a common objective, e.g. multi-agent systems. Centralized control often fails to realize an effective control due to high level of connectivity and computational burden. The distributed framework that handles a complex and large-scale system on a single subsystem of small order is appealing in terms of synthesis and implementation. Among the published works on distributed MPC design, the vast majority of them relies on state-space representation of system dynamics, and develops analysis and synthesis conditions in state-space form. In this project, distributed MPC design for spatially-distributed systems in input/output form will be studied. The importance of input/output design is related to the fact that experimentally identified models are in input/output form. It is then natural to solve for controllers based on input/output dynamics and implement designed controllers digitally in practice. Furthermore, distributed control design with fixed structure (of predefined temporal and spatial orders) is explored here to be implemented as a local control law. Compared to the state-space full-order control design, the distributed fixed-structure controller in input/output form of smaller order alleviates extensive on-line calculation between two sampling instants in MPC.Knowing that spatially-distributed systems can be treated as the interconnection of an array of subsystems, considered here are distributed MPC design for both parameter-invariant systems, whose subsystems exhibit identical dynamics, and distributed systems which consist of time/space varying subsystems and can be characterized as temporal/spatial linear parameter-varying (LPV) models. The distributed MPC design is studied in this project to address the regulator problem, which can be easily extended later to solve the set point tracking problem. With the use of a finite prediction horizon, asymptotic stability and performance specifications will be addressed in the derivation of distributed MPC design conditions, which can be cast into linear matrix inequality (LMI) constraints to render the problems implementable and numerically tractable. The proposed methods on distributed MPC design for both parameter-invariant and -varying spatially-distributed systems will be tested and evaluated on PDE governed spatially-distributed systems.