带有约束的自适应预测控制系统性能极限分析

Compared with feedback control and optimal control, predictive control has been applied widely owing to its advanced implementation strategy of receding horizon optimization and its convenience to handle constraints. Currently, most of the studies on predictive control mainly focus on stability and robustness, lacking the quantitative outcomes of its adaptive properties and ability of dealing with constraints to system performance. This grant aims to analyze the fundamental performance limitations on predictive control systems. By exploiting the unique property for the implementation strategy of receding horizon optimization, analyzing the similarities and differences between predictive control and optimal control, studying the effects of constraints and uncertainties to system performance, we devote to developing systematic theory for the performance limitation analysis of predictive control systems. Thus demonstrate the adaptive properties of predictive control to the constraints and uncertain circumstances, including the external disturbances and model mismatch. By quantizing the effects of utilizing given information under uncertain environment in the receding horizon optimization process of predictive control, we analyze the consequent performance enhancement for the whole performance of the system to provide the theoretical basis for the quantitative analysis of predictive control. This grant is in the theoretical frontier and aims to provide the theoretical results on explaining the advantages of predictive control in dealing with constraints, disturbances and uncertainties compared with other control methods, and lays the foundation to design the best controllers which can reach the performance limitations.

与反馈和最优控制相比，预测控制因其滚动优化机制及对约束的处理能力，在实际中得到广泛应用。目前对预测控制的分析以稳定性和鲁棒性研究为主，缺乏对其处理约束和自适应机理的本质探究及对系统性能的定量分析。本项申请针对预测控制系统性能极限展开研究，探索其特有的滚动优化机制，挖掘其与最优控制之间本源性异同，分析约束和不确定性对系统性能的影响，形成预测控制系统性能极限分析的系统性理论方法，从而论证系统存在约束、干扰和模型失配等不确定性情况下，预测控制对该不确定性特有的自适应性质，分析预测控制在滚动优化中对不确定环境下的信息利用方式及产生的定量关系。基于此，研究预测控制对于系统整体性能产生的提升作用，为定量分析预测控制系统性能提供理论依据。本研究在理论上具有前沿性，将为阐释预测控制相对于其他控制方法在处理约束、干扰和不确定性方面的优势提供理论依据，并为设计达到系统性能极限即性能最优的控制器奠定理论基础。

与传统的控制方法相比，预测控制的滚动优化机制及其对约束的处理能力使其在工业实际中得到了广泛的应用，然而目前关于预测控制系统的理论分析主要集中在保证和提高算法的稳定性、最优性和鲁棒性上。充分考虑预测控制擅长处理约束、不确定性等因素的特点，并由此对预测控制性能进行定量分析的研究较少。本课题针对预测控制系统性能极限展开研究，从解析和定量研究的角度对预测控制系统的性能极限问题进行分析。充分挖掘预测控制独特的"滚动优化"作用方式所蕴含的特有性质以及与最优控制之间的本源性异同，并探究其对动态系统性能所产生的影响，针对存在约束、干扰和模型失配等不确定性情况的系统，分析滚动优化机制所特有的自适应性质和信息利用方式对系统性能的影响及提升作用，探讨基于性能极限分析的预测控制器设计方法。本研究在理论上具有前沿性，并为预测控制在工程实践中的广泛应用提供了理论支撑。