Singular controls and chattering arcs in optimal control problems arising in biomedicine
Urszula Ledzewicz, Heinz Schättler (2009)
Control and Cybernetics
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Urszula Ledzewicz, Heinz Schättler (2009)
Control and Cybernetics
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Andrei Dmitruk, Ivan Samylovskiy (2013)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs appear in a nontrivial way.
Jorge Antonio Torres-Muñoz, Irandi Gutierrez-Carmona, Alma Rosa Dominguez-Bocanegra (2016)
Kybernetika
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The present work is centred on the problem of biomass productivity optimization of a culture of microalgae Spirulina maxima. The mathematical tools consisted of necessary and sufficient conditions for optimal control coming from the celebrated Pontryagin's Maximum Principle (PMP) as well as the Bellman's Principle of Optimality, respectively. It is shown that the optimal dilution rate turns to be a bang-singular-bang control. It turns out that, the experimental results are in accordance...
Heinz Schättler, Miroslava Jankovic (1993)
Forum mathematicum
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Hans Oberle, Ricki Rosendahl (2008)
Control and Cybernetics
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Zhou, W.S., Cai, S.F. (2006)
Lobachevskii Journal of Mathematics
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Rabtsevich, V.A. (2000)
Memoirs on Differential Equations and Mathematical Physics
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Masatomo Takahashi (2007)
Colloquium Mathematicae
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A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular...
Rabtsevich, V.A. (2000)
Memoirs on Differential Equations and Mathematical Physics
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Marcin Boryc, Łukasz Kruk (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.
Marcin Boryc, Łukasz Kruk (2015)
Annales UMCS, Mathematica
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A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique