带滑动运动的混合系统最优控制算法
Algorithms for optimal control of hybrid systems with sliding motion
AI总结：
本文提出两种混合系统最优控制算法，分别适配有/无滑动模态的场景，推导了含跳变条件的伴随方程与弱最大值原理形式的最优性条件，证明了算法生成序列的聚点均满足该原理。
摘要：
本文研究两种求解混合系统最优控制问题的算法。第一种算法针对具有滑动模态的混合系统，该算法有多项区别于其他混合系统问题求解算法的特性：首先，它能够处理存在滑动模态的混合系统；其次，切换面上的系统运动由指数2微分-代数方程描述，可保证对滑动运动面的精确跟踪；第三，问题泛函的梯度借助伴随方程计算，本文提出的伴随方程考虑了滑动运动，且在转换时刻存在跳变条件。针对具有滑动模态、控制为分段可微的混合系统最优控制问题，我们以弱最大值原理的形式给出了最优性条件。第二种算法适用于无滑动运动的混合系统最优控制问题，针对该算法我们假设控制函数为可测函数。对于每种算法，本文都证明了算法生成序列的每个聚点都满足弱最大值原理。
英文摘要：
This paper concerns two algorithms for solving optimal control problems with hybrid systems. The first algorithm aims at hybrid systems exhibiting sliding modes. The first algorithm has several features which distinguishes it from the other algorithms for problems described by hybrid systems. First of all, it can cope with hybrid systems which exhibit sliding modes. Secondly, the systems motion on the switching surface is described by index 2 differential--algebraic equations and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problems functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. We state optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise differentiable controls. The second algorithm is for optimal control problems with hybrid systems which do not exhibit sliding motion. In the case of this algorithm we assume that control functions are measurable functions. For each algorithm, we show that every accumulation point of the sequence generated by the algorithm satisfies the weak maximum principle.
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