Minimum Time Control of the Rocket Attitude Reorientation Associated with Orbit Dynamics

Zhu, Jihong; Trélat, Emmanuel; Cerf, Max

doi:10.1137/15m1028716

Cited by 18 publications

(24 citation statements)

References 27 publications

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“…We will see later that the solutions of the problem of order zero (defined in the following Section) lie on this singular surface S. Finally, the possibility of chattering in problem (P S ) is demonstrated in [92]. A chattering arc appears when trying to connect a regular arc with an optimal singular arc.…”

Section: Singular Arcs and Necessary Conditions For Optimalitymentioning

confidence: 91%

“…u = (u 1 , u 2 ) ∈ R 2 is the control input of the system satisfying |u| = u 2 1 + u 2 2 ≤ 1. See more details of the model and the problem formulation in [92].…”

Section: Formulation Of (P S ) and Difficultiesmentioning

confidence: 99%

“…We refer the interested readers to section 6.2 of [92] for a more detailed comparison. In fact, in aerospace applications, indirect methods are preferred because they provide, in general, more precise optimal trajectories.…”

Section: Comparison Of the Indirect And Direct Approachesmentioning

confidence: 99%

“…In particular, we make a brief survey on the chattering phenomenon (also called Fuller phenomenon), and explain how to dealt with the chattering phenomenon with numerical continuations. The chattering phenomenon, which appears systematically in aerospace applications (in trajectory optimization [91] and in attitude-trajectory optimization problems [92,93]), is the situation where the optimal control switches an infinite number of times over a compact time interval.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Geometric optimal control and applications to aerospace

2017

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This article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal control with various concepts of differential geometry. The ultimate objective is to derive optimal synthesis results for general classes of control systems. Continuation or homotopy methods consist in solving a series of parameterized problems, starting from a simple one to end up by continuous deformation with the initial problem. They help overcoming the difficult initialization issues of the shooting method. The combination of geometric control and homotopy methods improves the traditional techniques of optimal control theory. A nonacademic example of optimal attitude-trajectory control of (classical and airborne) launch vehicles, treated in details, illustrates how geometric optimal control can be used to analyze finely the structure of the extremals. This theoretical analysis helps building an efficient numerical solution procedure combining shooting methods and numerical continuation. Chattering is also analyzed and it is shown how to deal with this issue in practice.

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Section: Singular Arcs and Necessary Conditions For Optimalitymentioning

confidence: 91%

“…u = (u 1 , u 2 ) ∈ R 2 is the control input of the system satisfying |u| = u 2 1 + u 2 2 ≤ 1. See more details of the model and the problem formulation in [92].…”

Section: Formulation Of (P S ) and Difficultiesmentioning

confidence: 99%

Section: Comparison Of the Indirect And Direct Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geometric optimal control and applications to aerospace

2017

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“…In this paper, we consider the control system

\overset{x}{true} false(t false) = f false(t, x false(t false), u false(t false) false),

where f is a smooth function

double-struckR \times R^{n} \times R^{m} \to R^{n}

, the state

x false(t false) \in R^{n}

, the control u (·) ∈ L ∞ ([0, t f ];Ω), and Ω is the subset of

R^{m}

: [ a 1 , b 1 ] × ⋯ × [ a m , b m ]. We make two additional hypothesis: the controls we consider are “bang‐bang”, with a finite number of switching times:

\begin{matrix} alignleft \\ align-1 (H_{1}) & align-2 \forall i \in ⟦ 1, m ⟧, u_{i} (t) \in \{a_{i}, b_{i}\}, a . e . \\ align-1 (H_{2}) & align-2 \forall i \in ⟦ 1, m ⟧, u_{i} does not chatter . \end{matrix}

A control is chattering when it switches infinitely many times over a compact time interval (see). Therefore, our method does not apply to those controls.…”

Section: Tracking Algorithmmentioning

confidence: 99%

Redundancy implies robustness for bang‐bang strategies

Olivier

Haberkorn

Trélat

et al. 2018

Optim Control Appl Methods

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Summary We develop in this paper a method ensuring robustness properties of bang‐bang strategies, for general nonlinear control systems. Our main idea is to add bang arcs in the form of needle‐like variations of the control. With such bang‐bang controls having additional degrees of freedom, steering the control system to some given target amounts to solving an overdetermined nonlinear shooting problem, what we do by developing a least‐square approach. In turn, we design a criterion to measure the quality of robustness of the bang‐bang strategy, based on the singular values of the end‐point mapping, and which we optimize. Our approach thus shows that redundancy implies robustness, and we show how to achieve some compromises in practice, by applying it to the attitude control of a 3d rigid body.

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Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature

Yegorov

Mairet

Gouzé

2018

Optim Control Appl Methods

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For both fundamental biology and engineering applications, it is relevant to investigate how microorganisms adapt to changing environmental conditions. In this work, we consider a continuous-time dynamic problem of resource allocation between metabolic and gene expression machineries for a self-replicating prokaryotic cell population. In compliance with evolutionary principles, the criterion is to maximize the accumulated structural biomass. In the model, we include both degradation of proteins into amino acids and recycling of the latter (i. e., using as precursors again). Based on the analytical investigation of our problem by Pontryagin's maximum principle, we develop a numerical algorithm for approximating the switching curve of the optimal feedback control strategy. The obtained field of extremal state trajectories consists of chattering arcs and one steadystate singular arc. The constructed feedback control law can serve as a benchmark for comparing actual bacterial strategies of resource allocation. We also study the influence of temperature, whose increase intensifies protein degradation. While the growth rate suddenly decreases with the increase of temperature in a certain range, the optimal control synthesis appears to be essentially less sensitive.1 BIOCORE team, INRIA Sophia-Antipolis Méditerranée (as a part

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Minimum Time Control of the Rocket Attitude Reorientation Associated with Orbit Dynamics

Cited by 18 publications

References 27 publications

Geometric optimal control and applications to aerospace

Geometric optimal control and applications to aerospace

Redundancy implies robustness for bang‐bang strategies

Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature

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