Many of the physical phenomena, like friction, backlash, drag, and etc., which appear in mechanical systems are inherently nonlinear and have destructive effects on the control systems behavior. Generally, they are modeled by hard nonlinearities. In this paper, two different methods are proposed to cope with the effects of hard nonlinearities which exist in friction various models. Simple inver...

This thesis looks at a few different approaches to solving stochastic optimal control problems with state constraints. The motivating problem is optimal control of an energy buffer in a hybrid vehicle, although applications are abundant in a number of areas. Stochastic optimal control problems can be solved via the socalled Hamilton-Jacobi-Bellman (HJB) equation. State constraints result in bou...

We give a short introduction to the stochastic calculus for ItôLévy processes and review briefly the two main methods of optimal control of systems described by such processes: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated backward stochastic differential equation (BSDE). The two methods are illustrated by applica...

This paper is concerned with Sobolev weak solution of Hamilton-Jacobi-Bellman (HJB) equation. This equation is derived from the dynamic programming principle in the study of the stochastic optimal control problem. Adopting Doob-Meyer decomposition theorem as one of main tool, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. For the ...

This paper is concerned with Sobolev weak solution of Hamilton-Jacobi-Bellman (HJB) equation. This equation is derived from the dynamic programming principle in the study of the stochastic optimal control problem. Adopting Doob-Meyer decomposition theorem as one of main tool, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. For the ...

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...

the aim of the present paper is the investigation of some problems which can be reduced to thegoursat problem for a third order equation. some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.

We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to build, see [1, 2, 25]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infin...