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Time Domain Decomposition in Final Value Optimal Control of the Maxwell System

John E. Lagnese, G. Leugering (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time...

Time minimal control of batch reactors

B. Bonnard, G. Launay (2010)

ESAIM: Control, Optimisation and Calculus of Variations


In this article we consider a control system modelling a batch reactor in which three species X1, X2, X3 are reacting according to the scheme X1 → X2 → X3, each reaction being irreversible. The control is the temperature T of the reactions or the derivative of this temperature with respect to time. The terminal constraint is to obtain a given concentration of the product X2 at the end of the batch. The objective of our study is to introduce and to apply all the mathematical tools to compute the...

Time minimal synthesis with target of codimension one under generic conditions

B. Bonnard, M. Pelletier (1995)

Banach Center Publications

We consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraint belonging to a manifold of codimension one, for systems of the form v ̇ = X + u Y , | u | ≤ 1 and v ∈ R 2 or R 3 , under generic assumptions. The analysis is localized near the terminal manifold and is developed to control a class of chemical systems.

Time optimal control of the heat equation with pointwise control constraints

Karl Kunisch, Lijuan Wang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained....

Time-optimal boundary control of a parabolic system with time lags given in integral form

Adam Kowalewski, Anna Krakowiak (2006)

International Journal of Applied Mathematics and Computer Science

In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.

Time-optimal boundary control of an infinite order parabolic system with time lags

Adam Kowalewski, Anna Krakowiak (2008)

International Journal of Applied Mathematics and Computer Science

In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.

Time-optimal control of infinite order hyperbolic systems with time delays

Adam Kowalewski (2009)

International Journal of Applied Mathematics and Computer Science

In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.

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