Optimal Impulsive Control for Cancer Therapy

2021 ◽  
Author(s):  
João P. Belfo ◽  
João M. Lemos
Keyword(s):  
Cancer Therapy ◽  
Impulsive Control ◽  
Optimal Impulsive Control

scholarly journals No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints

2021 ◽  
Author(s):  
Giovanni Fusco ◽  
Monica Motta
Keyword(s):  
Original Problem ◽  
State Constraints ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Continuous Data ◽  
Lipschitz Continuous ◽  
Extended Sense ◽  
Unbounded Controls ◽  
Locally Lipschitz ◽  
Optimal Impulsive Control

AbstractIn this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data.

scholarly journals Optimal Impulsive Control

2019 ◽  
Author(s):  
Aram Arutyunov ◽  
Dmitry Karamzin ◽  
Fernando Lobo Pereira
Keyword(s):  
Impulsive Control ◽  
Optimal Impulsive Control

scholarly journals Numerical Algorithms For State-Linear Optimal Impulsive Control Problems Based On Feedback Necessary Optimality Conditions

2020 ◽  
pp. 152-158
Author(s):  
Stepan Sorokin ◽  
Maxim Staritsyn
Keyword(s):  
Optimality Conditions ◽  
Impulsive Control ◽  
Numerical Algorithms ◽  
Necessary Optimality Conditions ◽  
Maximum Principles ◽  
Control Problems ◽  
Impulsive Systems ◽  
Feedback Controls ◽  
Non Local ◽  
Optimal Impulsive Control

We propose and compare three numeric algorithms for optimal control of state-linear impulsive systems. The algorithms rely on the standard transformation of impulsive control problems through the discontinuous time rescaling, and the so-called “feedback”, direct and dual, maximum principles. The feedback maximum principles are variational necessary optimality conditions operating with feedback controls, which are designed through the usual constructions of the Pontryagin’s Maximum Principle (PMP); though these optimality conditions are formulated completely in the formalism of PMP, they essentially strengthen it. All the algorithms are non-local in the sense that they are aimed at improving non-optimal extrema of PMP (local minima), and, therefore, show the potential of global optimization.

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