Infinite Horizon Overtaking Optimal Control Problems for Fractional System

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-08-23 DOI:10.1007/s00245-025-10293-z

Jianping Huang, Huacheng Zhou

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引用次数: 0

Abstract

In this paper, we study infinite horizon overtaking optimal control problems for fractional system involving linear quadratic performance index which is allowed to be unbounded. When the controllability or stabilizability condition is not assumed and the nonhomogeneous term and the weight function are global integrability, it is shown that the solution of the overtaking optimal control can be derived by solving the linear quadratic optimal control problem with the state equation and running cost rate function in the controllable subspace based on the orthogonal projection. When the nonhomogeneous term and the weight function are not global integrability, both the existence and nonexistence of solutions for overtaking optimal control in various cases are established by characterizing the weight function. Several examples are also included to verify the above-mentioned theory. There results reveal that the overtaking optimality approach can be adopted to solve some optimal control problems with unbounded performance index and at the same time, the limitation of this approach is also exposed.

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分数阶系统的无限视界超车最优控制问题

本文研究了允许无界的含线性二次性能指标的分数阶系统的无限视界超车最优控制问题。在不假设可控性或稳定性条件，且非齐次项和权函数全局可积的情况下，利用正交投影在可控子空间中求解具有状态方程和运行代价率函数的线性二次最优控制问题，得到了超车最优控制的解。当非齐次项和权函数不是全局可积时，通过对权函数的刻画，建立了各种情况下超越最优控制解的存在性和不存在性。文中还列举了几个实例来验证上述理论。结果表明，超车最优性方法可用于解决一些性能指标无界的最优控制问题，同时也暴露出该方法的局限性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.