This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of ...This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.展开更多
In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are de...In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed.展开更多
This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergenc...This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.展开更多
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the me...In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.展开更多
Abstract--In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman （GHJB） equation through successively approximate it. Firstly, the GHJB equation is converted to an algebra...Abstract--In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman （GHJB） equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems. Index Terms--Generalized Hamilton-Jacobi-Bellman （HJB） equation, iterative method, nonlinear dynamic system, optimal control.展开更多
文摘This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.
文摘In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed.
文摘This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.
文摘In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.
基金supported by the National Natural Science Foundation of China(U1601202,U1134004,91648108)the Natural Science Foundation of Guangdong Province(2015A030313497,2015A030312008)the Project of Science and Technology of Guangdong Province(2015B010102014,2015B010124001,2015B010104006,2018A030313505)
文摘Abstract--In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman （GHJB） equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems. Index Terms--Generalized Hamilton-Jacobi-Bellman （HJB） equation, iterative method, nonlinear dynamic system, optimal control.
