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An Approximate Optimal Control for Discrete Models: Its Design

机译：离散模型的近似最优控制：其设计

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摘要

Constructive schemes for designing approximate optimal controls based on the Kro-tov sufficient conditions of optimality, extension principle, and global estimation are described. Different approximations for Bellman-type relations and effective indirect schemes based on degeneracy and turnpike nature of solutions of applied problems are studied. Irrespective of the initial formulation of a problem, discrete-time models (exact or approximate models obtained from discretization of the initial model) are used in the final design stage. Examples are given. Design of control laws for attaining the desired aim is a cardinal problem in control theory and involves numerous formulations and their theoretical investigation corresponding to diverse practical situations. When properties and aims are expressed as extremal problems, then the study consists in designing an optimal control. The existing fruitful theoretical results and techniques pertain to relations of the dynamic programming method and Hamilton-Jacobi-Bellman equation and its generalizations and analogs for different formulations.
机译：描述了基于Kro-tov的最优性，扩展原理和全局估计的充分条件设计近似最优控制的建设性方案。研究了贝尔曼型关系的不同近似和基于简并性和应用问题解的收费性质的有效间接方案。不管问题的最初表述如何，在最终设计阶段都将使用离散时间模型（从初始模型的离散化获得的精确模型或近似模型）。举例说明。为达到期望目的而设计的控制律是控制理论中的一个主要问题，涉及众多的表述及其对应于各种实际情况的理论研究。当特性和目标表示为极端问题时，则该研究在于设计最佳控制。现有的卓有成效的理论结果和技术涉及动态规划方法与Hamilton-Jacobi-Bellman方程及其不同公式的推广和类似物之间的关系。

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