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Optimal Control of Volterra Equations with Impulses
S. A. Belbas,W. H. Schmidt +1 more
TLDR
In this paper, the authors considered an optimal control problem for a system governed by a Volterra integral equation with impulsive terms and proved necessary optimality conditions of a form analogous to a discrete maximum principle.Abstract:
We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional includes both, an integrated cost rate (continuous part) and switching costs at the discrete impulse times (discrete part). We prove necessary optimality conditions of a form analogous to a discrete maximum principle. For the particular case of a system governed by impulsive ordinary differential equations, we obtain an impulsive maximum principle as a special case of the necessary optimality conditions for impulsive Volterra equations.read more
Citations
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Book
Volterra Integral Equations: An Introduction to Theory and Applications
TL;DR: A comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs) can be found in this paper, where the reader is presented with a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems.
Journal ArticleDOI
Well-posedness and regularity of backward stochastic Volterra integral equations
TL;DR: In this article, a Pontryagin type maximum principle is presented for optimal control of stochastic Volterra integral equations with adapted M-solutions via Malliavin calculus.
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Linear quadratic control problems of stochastic Volterra integral equations
TL;DR: In this article, a class of stochastic Fredholm−Volterra integral equations (SVIEs) with deterministic coefficients is introduced to replace conventional forward-backward SVIEs.
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Hyers–Ulam stability of impulsive integral equations
TL;DR: In this paper, the Hyers-Ulam stability of linear impulsive Volterra integral equations with the help of open mapping theorem approach was studied and an existence and uniqueness theorem for the solutions of a class of nonlinear impulsive integral equation with a bounded variable delay was given.
Posted Content
Optimal control of impulsive Volterra equations with variable impulse times
S. A. Belbas,W. H. Schmidt +1 more
TL;DR: The present work continues and complements the previous work on impulsive Volterra control with fixed impulse times, and obtains necessary conditions of optimality for impulsiveVolterra integral equations with switching and impulsive controls with variable impulse time-instants.
References
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Integral equations and applications
TL;DR: The theory of integral and integrodifferential Volterra equations has been studied extensively in the literature, see as mentioned in this paper for an overview. But the main application of integral equations in abstract spaces has not yet been discussed.
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Impulsive control in continuous and discrete-continuous systems
TL;DR: The text introduces the reader to the interesting area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation.
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Optimal Control with Integral State Equations
Morton I. Kamien,Eitan Muller +1 more
TL;DR: In this paper, the authors considered a control problem with investment I(s) the control variable and capital stock k(t), the state variable, and showed that M(t = m(t) and m(u s)0 if u < s.