The design of new optimal nonlinear voltage regulator for power systems is considered. In the proposed approach, the Hamilto-Jacobi-Belman (HJB), a partial differential equation, is solved using Taylor series expansion of its nonlinear terms. The performance of the proposed controller in a single-machine infinite-bus power system is simulated and the advantages of the nonlinear feedback control...

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markovswitching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic progr...

Jonathan S. Bogan, Bradley R. Rubin, Chenfei Yu, Michael G. Löffler, Charisse M. Orme, Jonathan P. Belman, Leah J. McNally, Mingming Hao, and James A. Cresswell From the Section of Endocrinology and Metabolism, Department of Internal Medicine, and Department of Cell Biology, Yale University School of Medicine, New Haven, CT 06520-8020 Running head: TUG cleavage regulates GLUT4 translocation Add...

We introduce a Monte Carlo scheme for the approximation of the solutions of fully non–linear parabolic non–local PDEs. The method is the generalization of the method proposed by [Fahim-Touzi-Warin, 2011] for fully non–linear parabolic PDEs. As an independent result, we also introduce a Monte Carlo Quadrature method to approximate the integral with respect to Lévy measure which may appear inside...