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...

5 We compare optimal liquidation policies in continuous time in the presence of trading impact using 6 numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In par7 ticular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent 8 (pre-commitment) mean-variance strategy. We show that the two different risk measures lead t...

We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the controlled process and an absolute value component for the control of the jump size of the process. We characterize the value function by a “polynomial” of degree two...

We consider the valuation of a block of perpetual ESOs and the optimal exercise decision for an employee endowed with them and with trading restrictions. A fluid model is proposed to characterize the exercise process. The objective is to maximize the overall discount returns for the employee through exercising the options over time. The optimal value function is defined as the grant-date fair v...

Lemma 17 Suppose that Θ(ā, h̄ ≥ θ > 0 for all ā > 0. (i) For any initial conditions F (w) and F ′(w) the HJB equation (3) has a unique solution F in any interval [w, w̄] ⊂ R. (ii) F is twice continuously differentiable and (F, F ′) depends continuously on the initial conditions. (iii) F ′ is monotone with respect to F ′(w). That is, if F1 and F2 are two solutions of the HJB equation in an interva...

Abstract. The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton–Jacobi– Bellman (HJB) equation. A nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analog of White’s ‘relative value iteration’ ...

This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The ENO methodology is originally intended for hyperbo...

The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniqu...

In this paper, we consider a joint dynamic pricing and production policy for stochastic inventory system with perishable products. The demand is dependent on the price level of on-hand inventory. Combined control, optimization model that maximizes total discounted profit built. Applying optimal control theory, formulate problem finding schedule as solving Hamilton-Jacobi-Bellman (HJB) equation....

Errata: Stochastic Optimal Control with Delay in the I: Solving HJB Equation through Partial Smoothing, and II: Verification Theorem Feedbacks