广义线性二次型问题拐点性质的必要条件

IF 1.8 4区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS Mathematics of Control Signals and Systems Pub Date : 2024-04-17 DOI:10.1007/s00498-024-00385-6
Roberto Guglielmi, Zhuqing Li
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引用次数: 0

摘要

在本文中,我们为无限维环境下的广义线性二次(LQ)最优控制问题提出了几个必要的转弯属性条件。这里的 "广义 "是指运行成本中既考虑二次项,也考虑线性项。岔道特性反映了这样一个事实,即在足够大的时间跨度内,最优轨迹和最优控制在大部分时间内都接近系统的稳定状态。我们证明,岔道特性与控制系统的某些系统理论特性密切相关。我们提供了适当的条件,从系统的可探测性和可稳定性的角度来描述转弯特性。随后,我们证明了广义 LQ 和 LQ 优化控制问题的指数转弯特性之间的等价性。
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Necessary conditions for turnpike property for generalized linear–quadratic problems

In this paper, we develop several necessary conditions of turnpike property for generalized linear–quadratic (LQ) optimal control problem in infinite-dimensional setting. The term ‘generalized’ here means that both quadratic and linear terms are considered in the running cost. The turnpike property reflects the fact that over a sufficiently large time horizon, the optimal trajectories and optimal controls stay for most of the time close to a steady state of the system. We show that the turnpike property is strongly connected to certain system theoretical properties of the control system. We provide suitable conditions to characterize the turnpike property in terms of the detectability and stabilizability of the system. Subsequently, we show the equivalence between the exponential turnpike property for generalized LQ and LQ optimal control problems.

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来源期刊
Mathematics of Control Signals and Systems
Mathematics of Control Signals and Systems 工程技术-工程:电子与电气
CiteScore
2.90
自引率
0.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Mathematics of Control, Signals, and Systems (MCSS) is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing. Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential equations, differential algebraic equations or difference equations. Potential topics include, but are not limited to controllability, observability, and realization theory, stability theory of nonlinear systems, system identification, mathematical aspects of switched, hybrid, networked, and stochastic systems, and system theoretic aspects of optimal control and other controller design techniques. Application oriented papers are welcome if they contain a significant theoretical contribution.
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