Iterative Learning Instantaneous Optimal Control of Discrete Systems and Optimization
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摘要: 以线性离散系统为研究对象,以瞬时最优化控制和智能算法中的迭代学习控制为基础,以系统响应期望值与实际值之差为反馈信号,以离散系统的二次型性能泛函为目标函数,提出了迭代学习型瞬时最优控制算法.该方法以瞬时最优化控制算法初始化控制信号,并采用迭代学习控制在线实时修正控制信号以提高主动控制的效果.针对迭代学习型瞬时最优化控制算法迭代的特性,采用范数方法给出了该算法收敛的充分条件.数值算例表明,迭代学习型瞬时最优控制算法较离散瞬时最优控制算法有较明显的优势.同时,基于改进遗传算法,对主动控制器位置优化进行了讨论.数值分析结果表明:部分楼层设置主动控制器且安装位置经过优化后,其控制效果可接近甚至优于全楼层设置主动控制器时的控制效果.Abstract: Through combination of the instantaneous optimal control (IOC) and the iterative learning control (ILC), one new hybrid control strategy called the iterative learning instantaneous optimal control was proposed. The discrete linear system was chosen as the target model for the new control strategy, and the quadratic performance functional of the discrete system was taken as the objective function to be minimized. During the controlling process of the system, the core idea of the ILC was introduced in order to modify the control signals which were initialized by the IOC. With the method of matrix norms, the sufficient condition for convergence of the new control strategy was established. Compared with the IOC, the iterative learning instantaneous optimal control gives simulation results of improved effectiveness. Furthermore, based on the improved genetic algorithm (GA), the optimization of the actuator positions in a multistory building to be controlled was investigated. Results of the numerical simulation indicate that, while the actuators are partially positioned at some optimally seleted floors, the control effects may reach or even be better than those in the case of full installation of actuators at all floors.
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