非线性和不确定系统经济模型预测控制综合方法研究

There widely exists a class of control problems of simultaneously achieving economy and stability in control engineering of saving energy and raising profit such as driving vehicles. For this problem, the project studies synthesis methods of economic model predictive control (EMPC) of nonlinear and uncertain systems by combining the ideas of multi-objectives decision, nonlinear (switched) control theory and dynamic programming principle. The goal of the project is to establish stabilizing EMPC schemes with guaranteed such theoretical results as robust stability, disturbance rejection and average economic performance. The work mainly includes: 1) Considering the problem of operating economic optimization and stabilizing control at the same time, we construct EMPC schemes of constrained nonlinear systems for both given economic criteria and varying economic criteria, where receding optimization feasibility and stability of the corresponding closed-loop systems are estabilished; 2) For the obtained stabilizing schemes, we intensively investigate the robust problems (e.g. robust stability, disturbance rejection) of nonlinear EMPC by considering the effects of internal and external uncertainties on the systems; 3) Based on (robust) stability results estabilished , we separately conquer the difficulties in analyzing finite horizon and infinite horizon average economic performances of systems in closed-loop with nonlinear EMPC under the constraint conditions; 4) The effectiveness of the theoretical results of the project is demonstrated by the optimal eco-driving control problem of vehicles. The development of the project will provide some promiseful results on theories and techniques to advanced control and saving energy and raising profit of complex processes.

针对车辆行驶等节能增效控制工程中广泛存在的经济性与稳定性同步控制问题，本项目拟综合多目标决策思想、非线性（切换）控制理论和动态规划原理，研究非线性和不确定系统经济模型预测控制(EMPC)综合方法，获得稳定EMPC策略及其鲁棒稳定性、扰动抑制性能和平均经济性能等理论结果。主要内容包括：1）考虑复杂系统经济优化和稳定控制同步操作问题，构造约束非线性系统经济指标给定和可变情形下EMPC策略，建立策略滚动优化可行性和闭环系统稳定性；2）在稳定策略基础上，深入研究系统内部和外部不确定扰动作用下的非线性EMPC闭环系统鲁棒稳定性和扰动抑制等鲁棒性问题；3）基于（鲁棒）稳定性结果，突破约束条件下非线性EMPC闭环系统有限时域和无穷时域平均经济性能分析难点；4）结合车辆经济性行驶优化控制问题验证项目理论成果的有效性。本项目的研究将为复杂对象先进控制和实现节能增效目标提供有指导意义的理论结果和技术基础。

本项目针对节能增效控制工程中广泛存在的经济性与稳定性同步控制问题，开展非线性和不确定系统经济模型预测控制的稳定性与鲁棒性理论及应用研究。项目基于控制Lyapunov（障碍）函数和双模控制策略，结合滚动时域优化原理和Lyapunov稳定性分析方法，提出了约束非线性系统经济指标给定和可变情形下的EMPC策略及其稳定性综合与性能分析方法，再引入字典序多目标优化方法，提出了非线性系统多目标EMPC策略和可变优先级多目标EMPC策略；在此基础上，采用微分对策原理和输入-状态稳定性理论以及创新设计鲁棒收缩约束条件，提出了不确定非线性系统EMPC策略及其鲁棒性综合方法；最后，考虑大规模网联车队系统节能与安全稳定控制问题，应用本项目组的理论成果，实现了智能网联车队系统的节能与安全稳定控制目标。标注本项目资助发表的学术期刊论文32篇、会议论文13篇，其中，Automatica、IEEE/IET汇刊等SCI收录源期刊论文13篇，自动化学报、控制与决策等国内EI收录源期刊论文13篇；授权国家发明专利5件和登记软件著作权2个。研究成果在国际会议上交流4人次，在7次国内会议上交流9人次。培养博士研究生3名和硕士研究生18名（毕业13名）。