Existence of regular synthesis for general control problems
TLDR
In this article, it has been shown that the Pontrjagin maximum principle can be used as an assumption on a closed-loop control to generate open-loop optimal controls.About:
This article is published in Journal of Differential Equations.The article was published on 1980-12-01 and is currently open access. It has received 49 citations till now. The article focuses on the topics: Optimal control & Linear system.read more
Citations
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Optimal Control and Applications to Aerospace: Some Results and Challenges
TL;DR: This article surveys the usual techniques of nonlinear optimal control such as the Pontryagin Maximum Principle and the conjugate point theory, and how they can be implemented numerically, with a special focus on applications to aerospace problems.
Book ChapterDOI
Shortest paths of bounded curvature in the plane
TL;DR: Given two oriented points in the plane, the authors determine and compute the shortest paths of bounded curvature joining them and propose a solution based on the minimum principle of Pontryagin.
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Some Properties of the Value Function and Its Level Sets for Affine Control Systems with Quadratic Cost
TL;DR: In this paper, the authors consider the optimal control problem for analytic affine systems, and prove that the value function S is subanalytic if there are no minimizing abnormal extremals.
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Sufficient conditions for relative minima of broken extremals in optimal control theory
John Noble,Heinz Schättler +1 more
TL;DR: In this article, the authors formulate a version of the method of characteristics based on parametrizations of extremals by their terminal values and give sufficient conditions for imbedding a reference trajectory into a local field of broken extremals.
References
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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.
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Mathematical Methods of Optimal Control
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Subanalytic sets and feedback control
TL;DR: The theory of subanalytic sets is used in this article to prove that analytic control systems are controllable, and that for every point p in the state space there exists a piecewise analytic feedback control that steers every state into p.
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Application of Optimization Theory for Bounded State Variable Problems to the Operation of Train
TL;DR: The method is applied and the optimal control law has really been obtained straightforward and definitely and the author's is again confirmed to be very convenient to solve a bounded state variable problem.
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Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method
TL;DR: In this paper, the optimal control of a plant described by ordinary differential equations is considered, and sufficient optimality conditions are derived, one of which essentially gives a correct foundation to the dynamic programming method for the class of problems being studied.