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

在过去的十年中，分布式模型预测控制(MPC)的设计已经成为一个活跃的研究领域，它通过显式地考虑输入、输出和状态约束来处理大的网络系统，并且满足一定的性能指标。联网系统可以是物理耦合的，例如分布参数系统，或者由通过约束或共同目标耦合的几个独立的子系统组成，例如多代理系统。由于高水平的连通性和计算负担，集中控制往往无法实现有效的控制。在一个小阶次的单一子系统上处理复杂和大规模系统的分布式框架在综合和实现方面很有吸引力。在已发表的关于分布式MPC设计的著作中，绝大多数依赖于系统动力学的状态空间表示，并以状态空间的形式发展了分析和综合条件。在本项目中，将研究输入/输出形式的空间分布式系统的分布式预测控制设计。输入/输出设计的重要性与实验识别的模型是输入/输出形式的事实有关。然后根据输入/输出动态求解控制器，并在实践中以数字方式实现所设计的控制器。此外，本文还探索了具有固定结构(预定义的时间和空间顺序)的分布式控制设计，以便作为局部控制律来实现。与状态空间全阶控制设计相比，低阶输入/输出形式的分布式固定结构控制器减少了MPC中两个采样时刻之间的大量在线计算。鉴于空间分布系统可以被视为一组子系统的互联，本文考虑了两种情况下的分布式预测控制设计：参数不变系统(其子系统具有相同的动态特性)和由时间/空间变化子系统组成的分布式系统(其特征为时间/空间线性参数变化(LPV)模型)。本课题研究了分布式MPC设计来解决调节器的问题，以后可以很容易地扩展以解决设定值跟踪问题。利用有限预测范围，渐近稳定性和性能指标将在分布式MPC设计条件的推导中得到解决，这些条件可以转化为线性矩阵不等式(LMI)约束，从而使问题易于实现和数值处理。所提出的参数不变和变空间分布系统的分布式预测控制设计方法将在偏微分方程控制的空间分布系统上进行测试和评估。

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.