基于连续时间PWA模型的混杂系统预测控制研究

As the complexity of controlled industrial processes enlarges, the hybrid dynamical systems, which constitutes an important class of mathematical models that explicitly account for the intricate coupling between continuous dynamics and discrete events, is an ideal candidate model for capturing the whole dynamics of these systems, and has attracted much attention in the past years. ..The generic discrete hybrid system model is mainly due to the fact that mode switches can only occur at sampling instants, which may lead to non-negligible modelling errors. To elimate the defect of the generic discrete model of hybrid systems, this project aims to provide a continuous-time piecewise affine (PWA) model-based predictive control method for hybrid systems. In this project, the hybrid system is formulated by continuous-time PWA model that can avoid the modelling errors, and an associated predictive control proposition for this model is constructed. By analysing the predictive control proposition and given the initial state and the final state of the considered hybrid system, an algorithm that the dwell time of mode may be merged/deleted is designed to determine the accurate optimal mode transition sequence and the mode transition instants. Then the optimal control problem under the constructed predictive control proposition can be transformed into a normal optimal control problem of a fixe-sequence multi-stage process, and the optimal control can be computed quickly. Finally, a new strategy of feedback compensation will be proposed based on the continuous-time PWA system to meet the demand of zero steady-state error. If we could achieve these mentioned goals, the predictive control of hybrid system would be greatly accelerated. It is indicated that doing investigation of continuous-time PWA model-based predictive control has not only a practical application prospect for the complex systems control and similar problems, but also has theoretical significance.

工业被控对象日益复杂, 混杂系统是这类复杂系统的有效建模工具, 基于混杂系统的预测控制成为研究热点. 由于混杂系统模态演化的阶跃性, 通用的离散化混杂系统模型会带来严重的建模误差, 不仅不能满足控制的性能要求甚至会导致系统不稳定. 为避免离散化模型造成的建模误差问题, 本课题以连续时间PWA模型来刻画混杂系统, 通过分析给定初态和终态的系统行为, 精确求解最优切换序列及切换时刻, 在此基础上设计高效的预测控制求解算法, 并构建基于连续时间PWA模型的校正策略, 从而实现基于连续时间PWA模型的可在线求解的混杂系统预测控制算法.

工业被控对象日益复杂, 混杂系统是这类复杂系统的有效建模工具, 基于混杂系统的预测控制成为研究热点. 由于混杂系统模态演化的阶跃性, 通用的离散化混杂系统模型会带来严重的建模误差, 不仅不能满足控制的性能要求甚至会导致系统不稳定. 为避免离散化模型造成的建模误差问题, 本课题以连续时间PWA模型来刻画混杂系统, 通过分析给定初态和终态的系统行为, 精确求解切换时刻, 在此基础上设计了高效的预测控制求解算法, 并针对模型失配, 构建了混杂系统模型预测控制的输出校正策略, 通过引入离散变量, 把系统的模态切换过渡过程一并考虑, 从而实现基于混杂模型的可在线校正的预测控制算法, 提高了控制性能.