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
Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path...Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.展开更多
In this work time independent damping systems are studied using Lagrangian and Hamiltonian for time independent damping, which are present through the factor e<sup>λq</sup>. The Hamilton Jacobi equation i...In this work time independent damping systems are studied using Lagrangian and Hamiltonian for time independent damping, which are present through the factor e<sup>λq</sup>. The Hamilton Jacobi equation is formulated to find the Hamilton Jacobi function S using separation of variables technique. We can form this function in compact form of two parts the first part as a function of coordinate q, and the second part as a function of time t. Finally, we find the ability of these systems to quantize through an illustrative example.展开更多
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.
文摘Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.
文摘In this work time independent damping systems are studied using Lagrangian and Hamiltonian for time independent damping, which are present through the factor e<sup>λq</sup>. The Hamilton Jacobi equation is formulated to find the Hamilton Jacobi function S using separation of variables technique. We can form this function in compact form of two parts the first part as a function of coordinate q, and the second part as a function of time t. Finally, we find the ability of these systems to quantize through an illustrative example.
