考虑控制和状态约束的行星着陆最优控制结构

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-04-14 DOI:10.1051/cocv/2022065

Clara Leparoux, Bruno H'eriss'e, F. Jean

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引用次数: 10

摘要

研究了行星着陆条件下的垂直动力下降问题，该问题考虑了滑坡体和推力指向约束，并考虑了最终成本的最小化。首次利用庞特里亚金极大值原理证明了最优控制的最大-最小-最大或最大-奇异-最大形式，并将此结果推广到考虑大气影响的问题表述中。它还表明，在一般情况下不会出现单数结构。第二次，从理论上分析了更具体问题公式的最优轨迹，表明在每个最大或最小弧线上，状态约束最多只能有一个接触点或边界区间。

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Structure of optimal control for planetary landing with control and state constraints

This paper studies a vertical powered descent problem in the context of planetary landing, considering glide-slope and thrust pointing constraints and minimizing any final cost. In a first time, it proves the Max-Min-Max or Max-Singular-Max form of the optimal control using the Pontryagin Maximum Principle, and it extends this result to a problem formulation considering the effect of an atmosphere. It also shows that the singular structure does not appear in generic cases. In a second time, it theoretically analyzes the optimal trajectory for a more specific problem formulation to show that there can be at most one contact or boundary interval with the state constraint on each Max or Min arc.

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来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

自引率

7.10%

发文量

期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.