The Experts below are selected from a list of 10776 Experts worldwide ranked by ideXlab platform

Jinghao Zhu - One of the best experts on this subject based on the ideXlab platform.

Sasa V Rakovic - One of the best experts on this subject based on the ideXlab platform.

  • minkowski Bellman inequality and Equation
    Automatica, 2021
    Co-Authors: Sasa V Rakovic
    Abstract:

    Abstract This note introduces, and studies, the Minkowski–Bellman inequality and Equation. The necessary and sufficient conditions for the characterization and existence of Minkowski functions that satisfy the Minkowski–Bellman inequality, and for the characterization and existence of the unique Minkowski function that satisfies the Minkowski–Bellman Equation, are derived. The complete topological characterization of the associated optimal set-valued control map is also derived.

Qi Zhang - One of the best experts on this subject based on the ideXlab platform.

  • The Relationship between Maximum Principle and Dynamic Programming Principle for Stochastic Recursive Control Problem with Random Coefficients
    2020
    Co-Authors: Dong Yuchao, Meng Qingxin, Qi Zhang
    Abstract:

    This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the relationship between the Hamilton system with random coefficients and stochastic Hamilton-Jacobi-Bellman Equation is obtained. It is very different from the deterministic coefficients case since stochastic Hamilton-Jacobi-Bellman Equation is a backward stochastic partial differential Equation with solution being a pair of random fields rather than a deterministic function. A linear quadratic recursive utility optimization problem is given as an explicitly illustrated example based on this kind of relationship

  • dynamic programming principle and associated hamilton jacobi Bellman Equation for stochastic recursive control problem with non lipschitz aggregator
    ESAIM: Control Optimisation and Calculus of Variations, 2018
    Co-Authors: Qi Zhang
    Abstract:

    In this work we study the stochastic recursive control problem, in which the aggregator (or generator) of the backward stochastic differential Equation describing the running cost is continuous but not necessarily Lipschitz with respect to the first unknown variable and the control, and monotonic with respect to the first unknown variable. The dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman Equation are established in this setting by the generalized comparison theorem for backward stochastic differential Equations and the stability of viscosity solutions. Finally we take the control problem of continuous-time Epstein−Zin utility with non-Lipschitz aggregator as an example to demonstrate the application of our study.

  • dynamic programming principle and associated hamilton jacobi Bellman Equation for stochastic recursive control problem with non lipschitz aggregator
    arXiv: Optimization and Control, 2015
    Co-Authors: Qi Zhang
    Abstract:

    In this work we study the stochastic recursive control problem, in which the aggregator (or called generator) of the backward stochastic differential Equation describing the running cost is continuous but not necessarily Lipschitz with respect to the first unknown variable and the control, and monotonic with respect to the first unknown variable. The dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman Equation are established in this setting by the generalized comparison theorem of backward stochastic differential Equations and the stability of viscosity solutions. Finally we take the control problem of continuous-time Epstein-Zin utility with non-Lipschitz aggregator as an example to demonstrate the application of our study.

Bao-zhu Guo - One of the best experts on this subject based on the ideXlab platform.

  • convergence of an upwind finite difference scheme for hamilton jacobi Bellman Equation in optimal control
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Bing Sun, Bao-zhu Guo
    Abstract:

    This technical note considers convergence of an upwind finite-difference numerical scheme for the Hamilton–Jacobi–Bellman Equation arising in optimal control. This effective scheme has been well-adapted and successfully applied to many examples. Nevertheless, its convergence has remained open until now. In this note, we show that the solution from this finite-difference scheme converges to the value function of the associated optimal control problem.

  • Numerical solution to the optimal feedback control of continuous casting process
    Journal of Global Optimization, 2007
    Co-Authors: Bao-zhu Guo, Bing Sun
    Abstract:

    Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton---Jacobi---Bellman Equation satisfied by the value function. It is shown that the value function is the viscosity solution of the Hamilton---Jacobi---Bellman Equation. The optimal feedback control is found numerically by solving the associated Hamilton---Jacobi---Bellman Equation through a designed finite difference scheme. The validity of the optimality of the obtained control is experimented numerically through comparisons with different admissible controls. Detailed study of a low-carbon billet caster is presented.

George N Saridis - One of the best experts on this subject based on the ideXlab platform.

  • approximate solutions to the time invariant hamilton jacobi Bellman Equation
    Journal of Optimization Theory and Applications, 1998
    Co-Authors: Randal W Beard, George N Saridis
    Abstract:

    In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) Equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB Equation to a sequence of linear partial differential Equations. These Equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.

  • galerkin approximations of the generalized hamilton jacobi Bellman Equation
    Automatica, 1997
    Co-Authors: Randal W Beard, George N Saridis
    Abstract:

    In this paper we study the convergence of the Galerkin approximation method applied to the generalized Hamilton-Jacobi-Bellman (GHJB) Equation over a compact set containing the origin. The GHJB Equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB Equation can also be used to successively approximate the Hamilton-Jacobi-Bellman Equation. We state sufficient conditions that guarantee that the Galerkin approximation converges to the solution of the GHJB Equation and that the resulting approximate control is stabilizing on the same region as the initial control. The method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the LQR design method.