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 ...

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observati...

Hysteresis in smart materials hinders their wider applicability in actuators. The low dimensional hysteresis models for these materials are hybrid systems with both controlled switching and autonomous switching. In particular, they belong to the class of Duhem hysteresis models and can be formulated as systems with both continuous and switching controls. In this paper, we study the control meth...

Private sector operators of response services such as ambulance, fire or police etc. are often regulated by targets on the distribution of response times. This may result in inefficient overstaffing to ensure those targets are met. In this paper, we use a network chain of M/M/K queues to model the arrival and completion of jobs on the system so that quantities such as the expected total time wa...

This paper proposes a tracking control method for a differential drive wheeled mobile robot with nonholonomic constraints with an inverse optimal neural controller. It is based on two techniques: first, an identifier using a discrete-time recurrent high-order neural network (RHONN) trained with an extended Kalman filter (EKF) algorithm is employed; second, an inverse optimal control is used to ...

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style an option price constructed as a difference certainty equivalents value functions solving HJB equations. We introduce transformation method for penalized nonlinear partial differential equation. transformed equation involves possibly non-constant risk aversi...

We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice Z. Let T (x) be the first-passage time from the origin to a point x in Z. The convergence of the scaled first-passage time T ([nx])/n to the time-constant as n → ∞ can be viewed as a problem of homogenization for a discrete Hamilton-Jacobi-Bellman (HJB) equation. We derive an exact variational ...

This paper focuses on the optimal investment problem for an insurer and a reinsurer. The insurer’s and reinsurer’s surplus processes are both approximated by a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. In addition, both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. We first study the optimiz...

This paper proposes an inverse optimality design method for nonlinear deterministic system and nonlinear stochastic system with multiplicative and additive noises. The new method is developed based on the general Hamilton-Jacobi-Bellman(HJB) equation, and it constructs an estimated cost function using a linear function approximator—Gaussian Radial Basis function, which can recover the original ...

Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian Hamilton-Jacobi theory, are founded on structures such as jets, symplectic contact ones. In this paper, we shall use a partly forgotten framework second-order (or stochastic) differential geometry, developed originally by L. Schwartz P.-A. Meyer, to construct counterparts those classical structures. The...