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An instantaneous semi-Lagrangian approach for boundary control of a melting problem

Youness Mezzan, Moulay Hicham Tber (2021)

Applications of Mathematics

In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions...

An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

Andreas Rauh, Luise Senkel, Harald Aschemann, Vasily V. Saurin, Georgy V. Kostin (2016)

International Journal of Applied Mathematics and Computer Science

In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance,...

An intersection theorem for set-valued mappings

Ravi P. Agarwal, Mircea Balaj, Donal O'Regan (2013)

Applications of Mathematics

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T : X ⇉ X , S : Y ⇉ X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.

An observability estimate for parabolic equations from a measurable set in time and its applications

Kim Dang Phung, Gengsheng Wang (2013)

Journal of the European Mathematical Society

This paper presents a new observability estimate for parabolic equations in Ω × ( 0 , T ) , where Ω is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω and a subset of positive measure in ( 0 , T ) . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.

An optimal control approach to cancer treatment under immunological activity

Urszula Ledzewicz, Mohammad Naghnaeian, Heinz Schättler (2011)

Applicationes Mathematicae

Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.

An optimal control problem for a fourth-order variational inequality

A. Khludnev (1992)

Banach Center Publications

An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem...

Currently displaying 521 – 540 of 4405