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 ...

A new fast algorithm for reinforcement learning (RL) in continuous state and action spaces is proposed. Unlike algorithms based on dynamic programming, the proposed algorithm uses neither temporal nor spatial diierencing. Instead, it couples the solution of the Hamilton-Jacobi-Bellman (HJB) partial diierential equation with the structure of the function approximators that are commonly used toge...

Water management in agriculture is a key issue due to the increasing problem of water scarcity worldwide. Based on the recent progress in the dynamic modeling of plant growth in interaction with the water resource, our objective is to study the optimal control problem of crop irrigation. For this purpose, we first describe the LNAS model for sugar beet growth, driving the dynamics of both plant...

5 We determine the optimal dynamic investment policy for a mean quadratic variation ob6 jective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial 7 differential equation (PDE). We compare the efficient frontiers and optimal investment poli8 cies for three mean variance like strategies: pre-commitment mean variance, time-consistent 9 mean variance, and mean quad...

In this paper we consider a semi-Lagrangian scheme for minimum time problems with L-penalization. The minimum time function of the penalized control problem can be characterized as the solution of a Hamilton-Jacobi Bellman (HJB) equation. Furthermore, the minimum time converges with respect to the penalization parameter to the minimum time of the non-penalized problem. To solve the control prob...

Successive Galerkin Approximation (SGA) provides a means for approximating solutions to the Hamilton-Jacobi-Bellman (HJB) equation. The SGA strategy is applied to the development of optimal control laws for an electro-hydraulic positioning system (EHPS) having nonlinear dynamics. The theory underlying the SGA strategy is developed. Equations of motion for an EHPS are presented and validated exp...

We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to build, see [1, 2, 25]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infin...

We study a class of optimal control problems with state constraints, where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to build, see [1, 2, 26]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infi...

We determine the optimal dynamic investment policy for a mean quadratic variation objective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We compare the efficient frontiers and optimal investment policies for three mean variance like strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic vari...

We propose a Hamilton-Jacobi equation approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton-Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins’ and Reeds-Shepp’s cars, and gives further generalizations. We show that the value function of the control problem so...