Second order optimality conditions in the smooth case and applications in optimal control
TLDR
In this article, the authors present an algorithm called COTCOT (Conditions of Order Two and COnjugate Times) for computing the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal.Abstract:
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate Times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. This algorithm involves both normal and abnormal cases.read more
Citations
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Optimal Control and Applications to Aerospace: Some Results and Challenges
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The turnpike property in finite-dimensional nonlinear optimal control
TL;DR: Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry as mentioned in this paper, and they refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal controller problem.
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Smooth Regularization of Bang-Bang Optimal Control Problems
TL;DR: A strong convergence result of the solution of the regularized problem to the Solution of the initial problem is proved.
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Time-Minimal Control of Dissipative Two-Level Quantum Systems: The Generic Case
TL;DR: In this paper, the authors complete preliminary results from the work of Bonnard and Sugny (2009) concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation.
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Optimal location of controllers for the one-dimensional wave equation
TL;DR: In this paper, the authors considered the problem of minimizing the norm of the control operator over all possible measurable subsets of the homogeneous one-dimensional wave equation of Lebesgue measure.
References
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Book
Mathematical Theory of Optimal Processes
TL;DR: The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems as discussed by the authors, which can be applied in a variety of situations, including linear equations with variable coefficients.
Journal ArticleDOI
The Mathematical Theory of Optimal Processes
Richard Bellman,L. S. Pontryagin,V. G. Boltyanskii,Revaz Valerianovich Gamkrelidze,E. F. Mishchenko,K. N. Trirogoff,Lucien W. Neustadt +6 more
Journal ArticleDOI
The Mathematical Theory of Optimal Processes
TL;DR: The Mathematical Theory of Optimal Processes (MTOP) as mentioned in this paper is a mathematical theory of optimal processes that is closely related to our approach to optimal process analysis, but with a different focus.
Book
Foundations of Optimal Control Theory
Ernest Bruce Lee,Lawrence Markus +1 more
TL;DR: This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research.