The Experts below are selected from a list of 156162 Experts worldwide ranked by ideXlab platform
Li Chen - One of the best experts on this subject based on the ideXlab platform.
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dynamic programming principle for stochastic recursive Optimal Control Problem with delayed systems
ESAIM: Control Optimisation and Calculus of Variations, 2012Co-Authors: Li ChenAbstract:In this paper, we study one kind of stochastic recursive Optimal Control Problem for the systems described by stochastic differential equations with delay (SDDE). In our framework, not only the dynamics of the systems but also the recursive utility depend on the past path segment of the state process in a general form. We give the dynamic programming principle for this kind of Optimal Control Problems and show that the value function is the viscosity solution of the corresponding infinite dimensional Hamilton-Jacobi-Bellman partial differential equation.
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brief paper maximum principle for the stochastic Optimal Control Problem with delay and application
Automatica, 2010Co-Authors: Li ChenAbstract:In this paper, we consider an Optimal Control Problem for the stochastic system described by stochastic differential equations with delay. We obtain the maximum principle for the Optimal Control of this Problem by virtue of the duality method and the anticipated backward stochastic differential equations. Our results can be applied to a production and consumption choice Problem. The explicit Optimal consumption rate is obtained.
Jiongmin Yong - One of the best experts on this subject based on the ideXlab platform.
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a linear quadratic Optimal Control Problem for mean field stochastic differential equations in infinite horizon
Mathematical Control and Related Fields, 2015Co-Authors: Jianhui Huang, Jiongmin YongAbstract:A linear-quadratic (LQ, for short) Optimal Control Problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the Control system is studied followed by the discussion of the well-posedness of the LQ Problem. The Optimal Control can be expressed as a linear state feedback involving the state and its mean, through the solutions of two algebraic Riccati equations. The solvability of such kind of Riccati equations is investigated by means of semi-definite programming method.
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a deterministic linear quadratic time inconsistent Optimal Control Problem
arXiv: Optimization and Control, 2012Co-Authors: Jiongmin YongAbstract:A time-inconsistent Optimal Control Problem is formulated and studied for a Controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium Control is introduced, which can be regarded as a time-consistent solution to the original time-inconsistent Problem. Under certain conditions, we constructively prove the existence of such an equilibrium Control which is represented via a forward ordinary differential equation coupled with a backward Riccati--Volterra integral equation. Our constructive approach is based on the introduction of a family of $N$-person non-cooperative differential games.
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a deterministic linear quadratic time inconsistent Optimal Control Problem
Mathematical Control and Related Fields, 2011Co-Authors: Jiongmin YongAbstract:A time-inconsistent Optimal Control Problem is formulated and studied for a Controlled linear ordinary differential equation with a quadratic cost functional. A notion of time-consistent equilibrium strategy is introduced for the original time-inconsistent Problem. Under certain conditions, we construct an equilibrium strategy which can be represented via a Riccati--Volterra integral equation system. Our approach is based on a study of multi-person hierarchical differential games.
Jun Zou - One of the best experts on this subject based on the ideXlab platform.
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a convergent adaptive edge element method for an Optimal Control Problem in magnetostatics
Mathematical Modelling and Numerical Analysis, 2017Co-Authors: Jun ZouAbstract:This work is concerned with an adaptive edge element solution of an Optimal Control Problem associated with a magnetostatic saddle-point Maxwell’s system. An a posteriori error estimator of the residue type is derived for the lowest-order edge element approximation of the Problem and proved to be both reliable and efficient. With the estimator and a general marking strategy, we propose an adaptive edge element method, which is demonstrated to generate a sequence of discrete solutions converging strongly to the exact solution satisfying the resulting Optimality conditions and guarantee a vanishing limit of the error estimator.
Mohammad Saleh Tavazoei - One of the best experts on this subject based on the ideXlab platform.
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formulation and numerical solution for fractional order time Optimal Control Problem using pontryagin s minimum principle
IFAC-PapersOnLine, 2017Co-Authors: S. Sepehr Tabatabaei, Mohammad Javad Yazdanpanah, Mohammad Saleh TavazoeiAbstract:Abstract The main purpose of this paper is to use variational calculus and Pontryagin’s minimum principle to propose a solution scheme for time Optimal Control Problem stated on the fractional systems defined in the sense of Caputo. After deriving the necessary Optimality conditions, a novel numerical solution is used to solve the Problem. Afterwards, a simple case study shows the effectiveness of the proposed method.
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Formulation and Numerical Solution for Fractional Order Time Optimal Control Problem Using Pontryagin’s Minimum Principle
IFAC-PapersOnLine, 2017Co-Authors: S. Sepehr Tabatabaei, Mohammad Javad Yazdanpanah, Mohammad Saleh TavazoeiAbstract:Abstract The main purpose of this paper is to use variational calculus and Pontryagin’s minimum principle to propose a solution scheme for time Optimal Control Problem stated on the fractional systems defined in the sense of Caputo. After deriving the necessary Optimality conditions, a novel numerical solution is used to solve the Problem. Afterwards, a simple case study shows the effectiveness of the proposed method.
Peter Benner - One of the best experts on this subject based on the ideXlab platform.
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on the existence and uniqueness of the solution of a parabolic Optimal Control Problem with uncertain inputs
arXiv: Optimization and Control, 2018Co-Authors: Peter Benner, Akwum Onwunta, Martin StollAbstract:In this note, we consider the existence and uniqueness of the solution of a time-dependent Optimal Control Problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic Problems, we furthermore characterize the Optimal Control of the stochastic Problem.
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an isoperimetric Optimal Control Problem for a non isothermal chemical reactor with periodic inputs
Chemical Engineering Science, 2017Co-Authors: Alexander Zuyev, Andreas Seidelmorgenstern, Peter BennerAbstract:Abstract In this paper, we study the Optimal Control Problem for a continuous stirred tank reactor (CSTR) that represents a reaction of the type “ A → product”. The reactor dynamics is described by a nonlinear system of ordinary differential equations Controlled by two inputs: the inlet concentration and the inlet temperature. We formulate the Problem of maximizing the average product of this reactor for a fixed consumption of the input component over a period of time. This kind of isoperimetric Optimal Control Problem is analyzed by using the Pontryagin maximum principle with Lagrange multipliers. We show that the Optimal Controls are bang-bang and propose an upper bound for the number of switchings for the linearized Problem with periodic boundary conditions. Numerical simulations confirm that our Control strategy can be used to improve the reactor performance over a specified period of time in comparison to the steady-state operation.
