friction is a nonlinear phenomenon which has destructive effects on performance of control systems. to obviate these effects, friction compensation is an effectual solution. in this paper, an adaptive technique is proposed in order to eliminate limit cycles as one of the undesired behaviors due to presence of friction in control systems which happen frequently. the proposed approach works for n...

This paper draws on two sources of motivation: (1) The European Union Emission Trading Scheme (EU-ETS) aims at limiting the overall emissions of greenhouse gases. The optimal abatement strategy of companies for the use of emission permits can be described as the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is a question of general interest, how regulatory constraints can b...

The paper presents the design of nonlinear state feedback controller for a rigid manipulator. In order to obtain such controllers, a partial differential equation, HJB equation, should be solved, which is difficult to find a closed solution of that. In this paper, an efficient method using Taylor series expansion of nonlinear terms is used to tackle this problem. The tracking performance of the...

The purpose of this paper is to describe the application of the notion of viscosity solutions to solve the Hamilton–Jacobi–Bellman (HJB) equation associated with an important class of optimal control problems for quantum spin systems. The HJB equation that arises in the control problems of interest is a first-order nonlinear partial differential equation defined on a Lie group. Hence we employ ...

Abstract. In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem in a factor model [SIAM J. Fin. Math. 2 (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-differential equation (PIDE). We are able to show th...

In many applications (engineering, management, economy) one is led to control problems for stochastic systems : more precisely the state of the system is assumed to be described by the solution of stochastic differential equations and the control enters the coefficients of the equation. Using the dynamic programming principle E. Bellman [6] explained why, at least heuristically, the optimal cos...

This paper studies the numerical algorithm of stochastic control problems in investment optimization. Investors choose optimal to maximize expected return under uncertainty. The optimality condition, Hamilton–Jacobi–Bellman (HJB) equation, satisfied by value function and obtained dynamic programming method, is a partial differential equation coupled with One major computational difficulties irr...

We consider the Cauchy problem in R for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The line...

This paper treats a finite time horizon optimal control problem in which the controlled state dynamics is governed by a general system of stochastic functional differential equations with a bounded memory. An infinite-dimensional HJB equation is derived using a Bellman-type dynamic programming principle. It is shown that the value function is the unique viscosity solution of the HJB equation.

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTIMAL CONTROL OF UNCERTAIN EULER-LAGRANGE SYSTEMS By Keith Dupree May 2009 Chair: Warren E. Dixon Major: Mechanical Engineering Optimal control theory involves the design of controllers that can satisfy some tracking or regulation cont...