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Linear Control Systems with Nonconvex Integrands

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Turnpike Theory of Continuous-Time Linear Optimal Control Problems

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 104))

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Abstract

In this chapter we study the existence and structure of optimal trajectories of linear control systems with autonomous nonconvex integrands. For these control systems we establish the existence of optimal trajectories over an infinite horizon and show that the turnpike phenomenon holds. We also study the structure of approximate optimal trajectories in regions close to the endpoints of the time intervals. It is shown that in these regions optimal trajectories converge to solutions of the corresponding infinite horizon optimal control problem which depend only on the integrand.

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Authors and Affiliations

  1. Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel

    Alexander J. Zaslavski

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  1. Alexander J. Zaslavski
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Zaslavski, A.J. (2015). Linear Control Systems with Nonconvex Integrands. In: Turnpike Theory of Continuous-Time Linear Optimal Control Problems. Springer Optimization and Its Applications, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-19141-6_3

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