随机系统输出反馈预测控制理论及算法研究

With consideration of the fact that actual systems are often influenced by stochastic factors and of partial unmeasured system states, this project studies the design method of output feedback model predictive control (MPC) for stochastic systems. The goal is to develop the theory and general framework of the output feedback MPC for stochastic systems. The project selects two typical stochastic systems as the target systems, i.e. stochastic multiplicative uncertainty + perturbed system and Markov uncertainty + perturbed system. By using the results and methods of MPC qualitative theory, stochastic processes theory, optimization theory and constrained control theory, the project will explore the methods to guarantee system constraints under a probability, estimate and predict the system states, as well as handle disturbances. Based on these methods, the system probability characteristic will be fully utilized to design the output feedback MPC, which will reduce the conservativeness and ensure the closed-loop system stochastic stable. Furthermore, in order to make it practical, the efficient algorithms of output feedback MPC for stochastic systems will be also developed and the experimental results will be used to test the effectiveness of the proposed algorithms. Since the main study work is about how to make full use of the random characteristics when developing the synthesis approach of output feedback model predictive control, compared with the robust MPC, the resulted approach will be able to reduce the design conservativeness and improve the effectiveness. It not only has the important academic value, but also can provide the more effective constrained optimal control or planning methods to related fields, which will promote the popularization and application of model predictive control.

本项目针对实际系统往往受到随机因素影响，且状态不完全可测的情况，研究随机系统输出反馈预测控制器的设计方法，旨在针对随机系统提出完整的输出反馈预测控制设计理论和框架。项目选取两类典型系统，即乘型+扰动系统和Markov+扰动系统，借鉴预测控制定性综合理论成果、随机过程理论、优化理论以及约束控制理论，探索随机系统概率条件下系统约束处理和满足机制、系统状态估计方法以及外界扰动处理方法；以此为基础，探索如何在保证随机系统闭环概率稳定的前提下，有效利用概率特征设计输出反馈预测控制器，降低设计的保守性；进而，从实际实施出发，研究输出反馈预测控制器的高效算法，并通过实验研究检验项目成果的有效性。本项目由于充分着眼于系统随机特征的利用，故可以克服已有鲁棒预测控制设计的保守性，提高设计的可行性，这一研究不仅具有重要学术价值，而且可以为相关领域提供更为有效的约束优化控制和规划方法，促进预测控制的推广应用。

不确定系统的预测控制，通常是采用鲁棒方法。但实际应用中，不确定系统往往符合一定的统计规律。这类系统如果采用鲁棒方法，则存在较大的保守性。因此，本项目是针对原有鲁棒预测控制设计对于不确定性具有概率特征系统的不足，并结合系统输出反馈的结构特点，面向乘型参数不确定系统和Markov跳变系统以及加型噪声系统，提出研究其输出反馈预测控制的综合方法。为此，我们主要针对乘型和Markov系统以及加型噪声系统，提出了多步概率控制集和扰动概率集的定义、设计条件和设计方法及其改进设计方法；在此基础上，结合tube技术，项目发展了完整的随机系统输出反馈预测控制器的综合设计方法；在理论研究的基础上，我们将理论研究的成果，结合智能交通网络系统和污水处理系统等实际对象，研究了理论方法的应用技术以及软测量技术。通过本项目的研究，我们建立了比较完整的概率预测控制的设计思路和框架，并为理论成果的实际应用提供了算法基础。