基于Bang-Bang原理的时间最优控制问题求解

时间最优控制是工程实践中经常遇到的一类最优控制问题。对于较简单的时间最优控制问题可以应用古典变分法和庞特里雅金最大值原理进行分析求解。但在实际问题中，能求得解析解的仅是少数。因此，有必要寻求一种能够有效求解时间最优控制问题的数值方法。在分析时间最优控制问题已有求解方法优缺点的基础上，提出基于Bang—Bang原理和参数最优化方法（遗传算法-单纯形法）相结合求解一类仿射系统的时间最优控制问题的方法。对线性阻尼振子问题进行了数值仿真，结果表明该方法效果良好。

Time-optimal Control Based on Bang-Bang Theory

Time-optimal control is one of the optimal control problems that often appears in practice.The variational method and Maximum Principle can solve the optimal control problems.A lot of optimal control problems can not get the analysis results.So,it is necessary to build a numerical method that can solve optimal control problems very efficiently.In this paper,on the basis of an analysis of the advantages and disadvantages of the existing algorithms,we form a method that is composed of the theory of Bang-Bang control and parameters optimization method(Genetic algorithm-simplex method) and can solve time-optimal control problem for a kind of systems.Numerical simulation for the problem of linear damped oscillator shows the effectiveness of the method.