Controllability and necessary second-order optimality conditions in optimal control problems
E.R. Avakov, G.G. Magaril-Il'yaev
TL;DR
This paper establishes sufficient conditions for local controllability in control systems, especially when linear controllability fails, and derives necessary second-order optimality conditions for general optimal control problems.
Contribution
It introduces new controllability criteria applicable when linear approximation is not controllable and derives necessary second-order optimality conditions.
Findings
Provides sufficient controllability conditions for non-linearly controllable systems.
Derives necessary second-order optimality conditions for optimal control problems.
Enhances understanding of controllability beyond linear approximations.
Abstract
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a corollary, we obtain necessary second-order optimality conditions for a general optimal control problem.
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Taxonomy
TopicsAerospace Engineering and Control Systems · Differential Equations and Numerical Methods · Optimization and Variational Analysis