- Title
- A convexity result for the optimal control of a class of positive nonlinear systems
- Creator
- Blanchini, Franco; Colaneri, Patrizio; Middleton, Richard H.
- Relation
- 19th IFAC World Congress . Proceedings of the 19th IFAC World Congress (Cape Town, South Africa 24-29 August, 2014) p. 1507-1512
- Publisher Link
- http://dx.doi.org/10.3182/20140824-6-ZA-1003.00241
- Publisher
- International Federation of Automatic Control (IFAC)
- Resource Type
- conference paper
- Date
- 2014
- Description
- In this paper a class of input-parametrized bilinear positive systems is considered. This class is characterized by the fact that the input variables affect only the diagonal entries of the dynamical matrix. The considered class of systems is amenable to interpret a variety of dynamical models arising in system biology and compartmental systems. Given a final time tf, it is proven that the any component of the state vector at tf is a convex functional of the input variables. If a linear cost of the final state is considered this result has the important consequence that any Pontryagin solution of the associated optimal control problem is optimal and can be numerically computed by using standard gradient-type algorithms. A few extension are given next and an example is provided to illustrate the theory.
- Subject
- optimal control of hybrid systems; switching control; stability and stabilization of hybrid systems
- Identifier
- http://hdl.handle.net/1959.13/1064729
- Identifier
- uon:17634
- Identifier
- ISBN:9783902823625
- Language
- eng
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