On the Optimality of Lyapunov-based Feedback Laws for Constrained Difference Inclusions
On the Optimality of Lyapunov-based Feedback Laws for Constrained Difference Inclusions
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基于Lyapunov的约束差分包含反馈律的最优性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
R. Sanfelice
中科院分区：
文献类型：
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作者：
Francesco Ferrante;R. Sanfelice
研究了约束差分包含的状态反馈最优控制和代价估计问题。充分条件，在Lyapunov不等式的形式，提供了一个上界的成本与解决方案的约束差分包含相对于一个给定的成本功能。在附加的充分条件下，我们不需要计算解就可以精确地确定成本。所提出的方法扩展到研究离散时间系统的约束最优控制问题。在这种情况下，闭环最优性的充分条件给出了一个受约束的稳态的Hamilton-Jacobi-Bellman方程。所提出的结果的应用和例子。
State-feedback optimal control and cost evaluation problems for constrained difference inclusions are considered. Sufficient conditions, in the form of Lyapunov-like inequalities, are provided to derive an upper bound on the cost associated with the solution to a constrained difference inclusion with respect to a given cost functional. Under additional sufficient conditions, we determine the cost exactly without computing solutions. The proposed approach is extended to study an optimal control problem for discrete-time systems with constraints. In this setting, sufficient conditions for closed-loop optimality are given in terms of a constrained steady-state-like Hamilton-Jacobi-Bellman equation. Applications and examples of the proposed results are presented.