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研究了子系统切换次序固定的切换系统最优控制问题的数值解法。对于该类问题,主要是寻找最优切换时刻和最优控制策略使得性能指标最小。提出了切换时刻和控制向量同时参数化的方法,把该类问题转化成与之等价的非线性规划问题进行求解。为了优化切换时刻,引入一个新的标准化的时间变量,对时间段进行了标准化处理,然后用基于控制向量参数化的方法,把该切换系统最优控制问题转化成非线性规划问题,数值计算采用序列二次规划进行求解。最后对3个切换系统最优控制问题进行仿真,仿真结果证明该方法是有效的。
The numerical solution to the optimal control problem of switched systems with fixed subsystem switching order is studied. For such problems, it is mainly to find the optimal switching time and the optimal control strategy to minimize the performance index. A method of simultaneously parameterizing the switching time and the control vector is proposed, which transforms this kind of problem into an equivalent nonlinear programming problem. In order to optimize the switching time, a new standardized time variable is introduced to standardize the time period. Then, based on the control vector parameterization, the optimal control problem of the switched system is transformed into a nonlinear programming problem. The numerical calculation uses Sequence quadratic programming to solve. Finally, the optimal control of three switching systems is simulated. The simulation results show that the method is effective.