scholarly journals Maximum Principle for Optimal Control Problems of Forward-Backward Regime-Switching Systems Involving Impulse Controls

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Shujun Wang ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Markov Chains ◽  
Regime Switching ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Optimal Controls ◽  
Switching Systems ◽  
Impulse Controls

This paper is concerned with optimal control problems of forward-backward Markovian regime-switching systems involving impulse controls. Here the Markov chains are continuous-time and finite-state. We derive the stochastic maximum principle for this kind of systems. Besides the Markov chains, the most distinguishing features of our problem are that the control variables consist of regular and impulsive controls, and that the domain of regular control is not necessarily convex. We obtain the necessary and sufficient conditions for optimal controls. Thereafter, we apply the theoretical results to a financial problem and get the optimal consumption strategies.

scholarly journals Existence of Solutions for Optimal Control Problems on Time Scales whose States are Absolutely Continuous

2016 ◽  
Vol 17 (1) ◽  
pp. 81
Author(s):  
Iguer L D Santos
Keyword(s):  
Optimal Control ◽  
Time Scales ◽  
Optimal Control Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Control Problems ◽  
Optimal Controls ◽  
Absolutely Continuous

This paper considers a class of optimal control problems on time scales described by dynamic equations on time scales. We have established sufficient conditions for theexistence of optimal controls.

scholarly journals Sufficiency for Purely Essentially Bounded Optimal Controls

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 238
Author(s):  
Gerardo Sánchez Licea
Keyword(s):  
Nonlinear Dynamics ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Optimal Controls ◽  
Embedding Theorems ◽  
State Control ◽  
Discontinuous Solutions ◽  
Piecewise Continuous

For optimal control problems of Bolza with variable and free end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality restrictions, and nonlinear pointwise mixed time-state-control inequality and equality constraints, sufficient conditions for strong minima are derived. The algorithm used to prove the main theorem of the paper includes a crucial symmetric inequality, making this technique an independent self-contained method of classical concepts such as embedding theorems from ordinary differential equations, Mayer fields, Riccati equations, or Hamilton–Jacobi theory. Moreover, the sufficiency theory given in this article is able to detect discontinuous solutions, that is, solutions which need to be neither continuous nor piecewise continuous but only essentially bounded.

scholarly journals Controlled singular evolution equations and Pontryagin type maximum principle with applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiao-Li Ding ◽  
Iván Area ◽  
Juan J. Nieto
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Type Theorem ◽  
Control Problems ◽  
Optimal Controls ◽  
Special Cases ◽  
The Impact

<p style='text-indent:20px;'>Due to the propagation of new coronavirus (COVID-19) on the community, global researchers are concerned with how to minimize the impact of COVID-19 on the world. Mathematical models are effective tools that help to prevent and control this disease. This paper mainly focuses on the optimal control problems of an epidemic system governed by a class of singular evolution equations. The mild solutions of such equations of Riemann-Liouville or Caputo types are special cases of the proposed equations. We firstly discuss well-posedness in an appropriate functional space for such equations. In order to reduce the cost caused by control process and vaccines, and minimize the total number of susceptible people and infected people as much as possible, an optimal control problem of an epidemic system is presented. And then for associated control problem, we use a generalized Liapunov type theorem and the spike perturbation technique to obtain a Pontryagin type maximum principle for its optimal controls. In order to derive the maximum principle for an optimal control problems, some techniques from analytical semigroups are employed to overcome the difficulties. Finally, we discuss the potential applications.</p>

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