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The minimum energy problem for positive discrete-time linear systems with fixed final state. (English) Zbl 1182.49017

Bru, Rafael (ed.) et al., Positive systems. Proceedings of the third multidisciplinary international symposium on positive systems: theory and applications (POSTA 09), Valencia, Spain, September 2–4, 2009. Berlin: Springer (ISBN 978-3-642-02893-9/pbk; 978-3-642-02894-6/ebook). Lecture Notes in Control and Information Sciences 389, 141-149 (2009).
Summary: The non-negativity of controls in positive linear discrete-time systems usually gives rise to complementarity conditions in the first-order Karush-Kuhn-Tucker optimality conditions - this complicates the analytic solution and usually leads to numerical solutions. The intrinsic relationship between reachable sets and the minimum-energy problem is exploited in this paper to obtain an analytic solution of the minimum-energy control problem for positive linear discrete-time systems with any pair of fixed terminal (initial and final) states.
For the entire collection see [Zbl 1173.93001].

MSC:

49K10 Optimality conditions for free problems in two or more independent variables
93C55 Discrete-time control/observation systems
15B48 Positive matrices and their generalizations; cones of matrices
93C05 Linear systems in control theory
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