This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that financial market consists of risk-free asset and risky asset, where subject to Ornstein–Uhlenbeck (O-U) process, stochastic income inflation risk were also considered in model. firstly derived Hamilton–Jacobi–Bellman (HJB) equation through control method. Secondly, under lo...

Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton–Jacobi–Bellman equation satisfied by the value function. It is shown that the value function is the viscosity so...

Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving associated non-local Hamilton-Jacobi-Bellman (HJB) equation having effective Hamiltonian. Focusing on sediment storage as modern engineering problem, we formulate, analyze, and compute new under discrete observations: simple but non-trivial mathematical problem. We ...

This paper considers a class of optimization problems arising in wireless communication systems. We analyze the optimal control and the associated Hamilton–Jacobi–Bellman (HJB) equations. It turns out that the value function is a unique viscosity solution of the HJB equation in a certain function class. To deal with the fast growth condition of the value function in establishing uniqueness, we ...

We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this repor...

We formulate a new two-variable river environmental restoration problem based on jump stochastic differential equations (SDEs) governing the sediment storage and nuisance benthic algae population dynamics in dam-downstream river. Controlling is carried out through impulsive replenishment with discrete random observation/intervention to avoid depletion thick growth. consider cost-efficient manag...

A novel approach for online design of optimal control systems based on QRtuning, state and action-dependent heuristic dynamic programming, and approximate-LS solutions of the Hamilton-Jacobi-Bellman (HJB) equation is the main concern of this paper. The QR-tuning for optimal control systems takes into account heuristic variations in the weighting matrices Q and R of the discrete linear quadratic...

We propose multigrid methods for solving Hamilton-Jacobi-Bellman (HJB) and HamiltonJacobi-Bellman-Isaacs (HJBI) equations. The methods are based on the full approximation scheme. We propose a damped-relaxation method as smoother for multigrid. In contrast with policy iteration, the relaxation scheme is convergent for both HJB and HJBI equations. We show by local Fourier analysis that the damped...

The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimizing a cost functional, while satisfying hard constraints on the input. For linear systems the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems the “shape” of the optima...

We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper. The adverse player (nature) chooses open-loop controls that represent the so-called Knightian uncertainty, i.e., misspecifications of the model. The (half) ...