Journal ArticleDOI
The Riccati Equation for Optimal Control Problems with Mixed State-Control Constraints: Necessity and Sufficiency
TLDR
In this paper, a complete study of second-order conditions for the optimal control problem with mixed state-control constraints is conducted and a necessary condition in terms of the corresponding Riccati equation is obtained.Abstract:
The goal of this paper is to conduct a complete study of second-order conditions for the optimal control problem with mixed state-control constraints. The conjugate point theory is presented and a necessary condition in terms of the corresponding Riccati equation is obtained. Sufficiency criteria are developed in terms of strengthened necessary conditions, including the Riccati equation. The results generalize the known ones for pure control constraints as well as for the mixed state-control constraints.read more
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Journal ArticleDOI
Optimization Problems with Perturbations: A Guided Tour
TL;DR: The emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of Lagrange multipliers is not a singleton, may be unbounded, or is even empty.
Journal ArticleDOI
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.
Journal ArticleDOI
Optimization methods for the verification of second order sufficient conditions for bang-bang controls
TL;DR: In this article, the authors present an optimization method for finding optimal bang-bang controls and verifying second-order sufficient conditions (SSC) which have been derived by Agrachev, Stefani, and Zezza, and by Maurer and Osmolovskii.
Journal ArticleDOI
Second Order Sufficient Conditions for Time-Optimal Bang-Bang Control
TL;DR: This paper studies explicit representations of the critical subspace and shows that the quadratic form can be simplified by a transformation that uses a solution to a linear matrix differential equation, which leads to an easily implementable test for SSC in the case of a bang-bang control with one or two switching points.
Journal ArticleDOI
Second-order sufficient conditions for control problems with mixed control-state constraints
Helmut Maurer,Sabine Pickenhain +1 more
TL;DR: In this article, the second-order sufficient conditions for local minima of optimal control problems with state and control constraints were extended to include general boundary conditions and a direct sufficiency criterion based on a quadratic function that satisfies a Hamilton-Jacobi inequality.