基于值函数的非线性系统多模型操作空间划分与最优控制一体化研究

Multi-model approach is an ideal candidate for dealing with nonlinear dynamical processes with wide operating ranges and large set-point changes, and has attracted much attention in the past years. It is indicated that doing investigation of multi-model approach has not only a practical application prospect for the nonlinear systems control and similar problems, but also has theoretical significance..This project aims to provide a systematic methodology of partitioning operating range and integrated optimal control in multi-model approach for nonlinear systems based on evaluating of value function, which will improve the overall control performance of nonlinear systems and the theory about multi-model approach. According to the hybrid character of multi-model based systems, a hybrid model framework will be adopted to synthesize the multi linear subsystems which produced by nonlinear systems, and associated optimal control problem will be established. This will allow for the optimal control problem to apply the optimal principle of hybrid systems, and the operating range can be partitioned by evaluating the associated value function corresponding to the optimality conditions. As a result, given the optimal partition of operation range, the numerical solution to optimal control for the optimal control problem over finite horizon will be computed by simultaneous dynamical optimal strategies which will speed up the corresponding algorithm. Consequently, a hybrid model-based MPC(Model Predictive Control) for nonlinear systems will be designed and implemented, and the adverse effects of model mismatch resulted from simultaneous method can be weakened by the MPC strategy. In the end, the overall control performance, such as response, stability and robustness etc, of the obtained closed-loop systems will be analyzed, and all the obtained results will be implemented to an injection molding process to demonstrate that the proposed systematic methodology is a useful and effective tool for nonlinear systems control problem. If we could achieve these mentioned goals, the multi-model approach would be greatly accelerated.

多模型方法是解决非线性控制问题的有效途径之一, 对多模型方法的研究具有重要的理论意义和应用价值. 本课题针对非线性动态系统, 把多模型方法下操作空间的划分和最优控制耦合在一起, 进行一体化的研究, 旨在提高非线性系统的整体控制性能, 完善多模型控制方法.首先根据多模型结构固有的混杂特性, 采用混杂模型框架对多模型进行合成, 建立统一的优化控制命题; 然后根据混杂系统最优控制理论, 在最优切换条件下依值函数来划分操作空间, 并采用联立法对相应的有限时域优化控制命题进行数值求解; 进而, 采用预测控制来降低联立求解下模型失配所带来的不利影响, 以进一步提高系统整体控制性能. 最后, 在操作空间划分和最优控制一体化结构下, 对所得闭环控制系统的控制品质及稳定性等进行分析, 并基于实验室已有的注塑机装置进行测试和验证, 从而建立起系统性的非线性系统多模型方法操作空间划分和最优控制一体化的理论体系.

非线性是实际系统固有的特性, 所以非线性控制问题一直是控制理论与应用研究领域的热点和难点. 多模型方法是解决非线性控制问题的有效途径之一, 对多模型方法的研究具有重要的理论意义和应用价值, 其中“分解和合成”问题是多模型方法的核心问题...本课题针对非线性多模型方法的核心问题, 采用一体化的研究思路, 首次把操作空间的划分和最优控制集成起来, 使得多模型的分解是在最优控制性能指标下的分解, 而后续的合成是在最优分解下的合成, 多模型的划分和后续的合成构成了闭环, 从而提高了非线性系统的整体控制性能. 本课题“多模型操作空间划分与最优控制一体化方法”不同于传统的“分解和合成”方法, 传统的分解合成属于开环, 二者是分割开来进行的, 而本课题是在统一框架下集成进行的...本研究首先根据多模型结构固有的混杂特性, 采用混杂模型框架对多模型进行合成, 建立了统一的优化控制命题; 然后依据混杂系统最优控制理论, 在最优切换条件下依值函数来划分操作空间, 给出了不同特性系统下的操作空间划分算法; 并采用联立法对所得最优空间划分下的有限时域优化控制命题进行数值求解, 在所构造数值求解算法的基础上, 采用预测控制来降低联立求解下模型失配所带来的不利影响, 进一步提高了系统整体的控制性能. 在操作空间划分和最优控制一体化结构下, 对状态可测系统、状态不可测系统、输入输出模型系统等不同情况下所得闭环控制系统的控制品质及稳定性仿真分析, 表明了多模型操作空间划分与最优控制一体化方法的有效性, 是一种系统性的“分解和合成”一体化方法, 完善了现有非线性多模型方法的理论体系.