约束预测控制系统的性能极限分析与优化设计

Performance limits analysis of control systems plays important role in exploring the capability scope of controllers, judging control performance and guiding optimized controller design. This grant aims to address the fundamental performance limits of predictive control systems and optimized design. Firstly, for the given system, we exploit the convergent properties of value iteration based on the Principle of Optimality. Then we analyze performance limits of predictive control under ideal case and address the influences of controller parameters to the performance limitations. For the predictive control systems with constraints, quantitative impacts of constraints on performance limits are analyzed by means of geometric method of optimization theory. For the uncertain systems with model errors, by selecting ideal performance limitations as a benchmark, we compare the actual performance with ideal performance limits. The analytic expressions between upper and lower bounds of the ratio and the supreme of model uncertainty are obtained, based on which the influences to the performance limits are provided. Finally, based on the analysis, the optimized strategy is provided to make sure that the performances of the system keep forward to the ideal performance limitations as close as possible even under constraints or uncertain conditions. This research is in the theoretical frontier and aims to provide the advantage of predictive control on performance under dynamic environment and lays the foundation to innovate the predictive controller design methods.

控制系统的性能极限分析对于探索控制器的能力范围，评判控制性能及引导控制器的优化设计具有重要意义。本项目针对预测控制系统的性能极限分析及优化设计展开研究，首先针对给定的系统，基于最优性原理，挖掘值迭代收敛特性，用于分析理想情况下预测控制的性能极限，进而论证控制器各参数对性能极限的影响。然后针对带有约束的预测控制系统，利用优化理论的几何方法，分析该约束形式对于性能极限的定量影响；针对模型不确定系统，以理想性能极限作为基准，将系统实际性能与性能极限对比，建立比值上下界与模型不确定性上界间的解析形式，进而分析其对系统性能极限的影响。最后基于性能极限分析结果，给出预测控制优化设计方法，使系统即使在约束和不确定条件下依然能够尽可能趋近于理想的性能极限。本项目在理论上具有前沿性，将为定量阐释预测控制在动态环境下的性能优势及创新预测控制的设计方法提供依据。

与传统的控制方法相比，预测控制所特有的滚动优化机制能够在约束动态不确定环境下表现出更好的性能。本项目从探索“预测控制方法为什么好，好在哪里，好多少”的研究动机出发，针对预测控制系统的性能极限分析与优化设计进行了研究，通过挖掘预测控制与最优控制的理论同源性，分析两种方法的异同，从定量和解析的角度对预测控制系统的性能极限问题进行了详细分析，进而得到预测控制特有的滚动优化机制在典型动态环境下的性能表征。针对约束预测控制系统，分析了滚动优化机制所特有的自适应特性和信息利用方式对于系统性能的影响及提升作用。在此基础上，开发了一种新型的基于在线性能极限分析的自适应预测控制方法。该算法能够依据对系统性能的要求，基于在线性能极限分析结果，自适应调整控制器参数，使得闭环预测控制系统的性能始终保持在一定的优化范围内。本项目的研究成果具有理论前沿性，并可为工程实践中的应用提供理论支撑。