Optimal control of constrained piecewise affine systems with state- and input-dependent disturbances∗
Optimal control of constrained piecewise affine systems with state- and input-dependent disturbances∗
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具有状态和输入相关扰动的约束分段仿射系统的最优控制*
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
D. Mayne
中科院分区：
文献类型：
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作者：
S. Raković;E. Kerrigan;D. Mayne
研究具有分段仿射（1范数或∞范数）阶段代价和末端代价的分段仿射系统的有限视界最优控制问题。给出约束集作为多面体的并集，证明了部分值函数和部分最优控制律在状态集的多面体上是分段仿射的，该状态集可以通过允许控制策略在有限步数内转向到终端状态集。现有的结果只考虑了没有干扰的系统，或者具有独立于状态和输入的干扰的系统的情况。本文将这些结果推广到干扰依赖于状态和输入的情况。
Finite horizon optimal control of piecewise affine systems with a piecewise affine (1-norm or ∞-norm) stage cost and terminal cost is considered. Provided the respective constraint sets are given as the unions of polyhedra, it is shown that the partial value functions and partial optimal control laws are piecewise affine on a polyhedral cover of the set of states that can be steered, by an admissible control policy, to a terminal set of states in a finite number of steps. Existing results only consider the case of systems without disturbances, or systems with disturbances that are independent of the state and input. This paper extends these results to the case where the disturbance is dependent on the state and input.