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In this chapter we discuss controllability of discrete-time deterministic control systems which are useful in the turnpike theory. We introduce a notion of an \({\mathcal M}\) -positive matrix and show that under certain condition for a generic cost function the corresponding MDP has the unique minimizing Markov actions which form a \({\mathcal M}\) -positive matrix. In this case our controllability results are true and the strong turnpike property holds and is stable. This will be shown in Chap. 8 .

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Controllability Properties

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  • 发表日期：

    2025年

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  • Alexander J. Zaslavski

摘要

In this chapter we discuss controllability of discrete-time deterministic control systems which are useful in the turnpike theory. We introduce a notion of an \({\mathcal M}\) -positive matrix and show that under certain condition for a generic cost function the corresponding MDP has the unique minimizing Markov actions which form a \({\mathcal M}\) -positive matrix. In this case our controllability results are true and the strong turnpike property holds and is stable. This will be shown in Chap. 8 .