Abstract
The finite horizon Linear-Quadratic (LQ) optimal control problem with nonnegative state constraints (denoted by LQ + ) is studied for positive linear systems in discrete time. Necessary and sufficient optimality conditions are obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ + problem by means of a corresponding Hamiltonian system. In addition, necessary and sufficient conditions are reported for the LQ + -optimal control to be given by the standard LQ-optimal state feedback law. Sufficient conditions are also reported for the positivity of the LQ-optimal closed-loop system. In particular, such conditions are obtained for the problem of minimal energy control with penalization of the final state. Moreover a positivity criterion for the LQ-optimal closed-loop system is derived for positive systems with a positively invertible (dynamics) generator.
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Beauthier, C., Winkin, J.J. (2009). On the Positive LQ-Problem for Linear Discrete Time Systems. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_4
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DOI: https://doi.org/10.1007/978-3-642-02894-6_4
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