In this work we deal with the numerical solution of a Hamilton-Jacobi-Bellman (HJB) equation with infinitely many solutions. To compute the maximal solution – the optimal cost of the original optimal control problem – we present a complete discrete method based on the use of some finite elements and penalization techniques. Mathematics Subject Classification. 49L20, 49L99, 93C15, 65L70. Receive...

This paper introduces an optimal tracking controller for robot manipulators with saturation torques. The model is presented as a strict-feedback nonlinear system. Firstly, the position control problem transformed into problem. Subsequently, saturated law designed. determined through solution of Hamilton-Jacobi-Bellman (HJB) equation. We use reinforcement learning algorithm only one neural netwo...

We provide an approximation scheme for the maximal expected utility and optimal investment policies for the portfolio choice problem in an incomplete market. Incompleteness stems from the presence of a stochastic factor which affects the dynamics of the correlated stock price. The scheme is built on the Trotter-Kato approximation and is based on an intuitively pleasing splitting of the Hamilton...

In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the beha...

We show the existence of a local solution to a Hamilton–Jacobi–Bellman (HJB) PDE around a critical point where the corresponding Hamiltonian ODE is not hyperbolic, i.e., it has eigenvalues on the imaginary axis. Such problems arise in nonlinear regulation, disturbance rejection, gain scheduling, and linear parameter varying control. The proof is based on an extension of the center manifold theo...

In this paper we use a reference trajectory computed by a model predictive method to shrink the computational domain where we set the Hamilton-Jacobi Bellman (HJB) equation. Via a reduced-order approach based on proper orthogonal decomposition(POD), this procedure allows for an efficient computation of feedback laws for systems driven by parabolic equations. Some numerical examples illustrate t...

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...

This paper studies the problem of target control and how a virtual ellipsoid can avoid static obstacle. During motion to set, achieve under collision avoidance by keeping distance between We present solutions this in class closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify validity effectiveness our algorithm.

The valuation of a gas storage facility is characterized as a stochastic control problem, resulting in a Hamilton-Jacobi-Bellman (HJB) equation. In this paper, we present a semi-Lagrangian method for solving the HJB equation for a typical gas storage valuation problem. The method is able to handle a wide class of spot price models that exhibit mean-reverting, seasonality dynamics and price jump...

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...