Optimization and Control of Nonlinear Systems Using the Second Variation

Breakwell, J. V.; Speyer, Jason L.; Bryson, Arthur E.

doi:10.1137/0301011

Cited by 131 publications

(56 citation statements)

References 3 publications

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“…For unconstrained optimal control problems, a neighbouring extremal solution was derived using second variation for situation where only the initial and/or terminal conditions are perturbed [9]. This method is extended to dynamic optimization problems with perturbations in additional parameter vector [10].…”

Section: Introductionmentioning

confidence: 99%

On combining neighbouring extremals with control parameterization

Liu

Lin

Loxton

et al. 2015

2015 34th Chinese Control Conference (CCC)

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Abstract:In this paper, we consider the neighbouring extremals for a class of optimal control problems with control constraints. We first solve the optimal control problem using control parameterization method to obtain the optimal open-loop control and the optimal reference state. Then, a neighbouring feedback control law is derived for small state perturbations caused by changes on reference state at switching times.

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Section: Introductionmentioning

confidence: 99%

On combining neighbouring extremals with control parameterization

Liu

Lin

Loxton

et al. 2015

2015 34th Chinese Control Conference (CCC)

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“…Since the initial presentations by Bryson and others, [1][2][3][4] NOC laws have been used for the guidance of low-thrust trajectories 5 and advanced launch systems. 6 More recently, 7 NOC has been used to handle parameter changes in the dynamic model.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Computation of Neighboring Optimal Control Laws

Ross

Fahroo

Yan

2002

AIAA Guidance, Navigation, and Control Conference and Exhibit

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Feedback solutions to the neighboring optimal control problem are typically obtained by solving the matrix Riccati differential equation. In this paper, we propose a new approach based on solving linear algebraic equations in real-time. Our method is based on a pseudospectral discretization of the linear time-varying boundary value problem that arises from an application of the Minimum Principle. We show how feedback control laws can be computed without any explicit integration, construction of transition matrices or solving the matrix Riccati differential equation. This facilitates a real-time implementation of the scheme and the design of predictive guidance and control laws. A numerical example of a low thrust orbit transfer problem shows the effectiveness of the method for neighboring optimal guidance.

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“…Linearization around a nominal trajectory and optimal control of the resulting time-varying system was introduced in the early optimal control litterature, e.g. [5,Chapter 6.4], and [4]. The derivation of the time-varying linear system is in general quite involved, since it is required to find the nominal solution.…”

mentioning

confidence: 99%

“…Define the change of variables z x x 0 . This will transform the system intoż g´z ρµ ẋ 0 (4) where g´z ρµ f´z · ϕ´ρµ ρµ. Notice thaṫ…”

mentioning

confidence: 99%