Related papers: Numerical Solution of the Dynamic Programming Equa…
In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…
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…
In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…
In this paper, we propose and study the stochastic path-dependent Hamilton-Jacobi-Bellman (SPHJB) equation that arises naturally from the optimal stochastic control problem of stochastic differential equations with path-dependence and…
This paper presents the optimal control and synchronization problem of a multilevel network of R\"ossler chaotic oscillators. Using the Hamilton-Jacobi-Bellman (HJB) technique, the optimal control law with three-state variables feedback is…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
This work investigates the optimal control problem for reflected McKean-Vlasov SDEs and the viscosity solutions to Hamilton-Jacobi-Bellman(HJB) equations on the Wasserstein space in terms of intrinsic derivative. It follows from the flow…
In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman…
This paper studies the stochastic optimal control of jump-diffusion processes and the associated fully nonlinear backward stochastic Hamilton--Jacobi--Bellman (BSHJB) equations. We establish the dynamic programming principle (DPP) via…
This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in…
In this paper, we study the existence and uniqueness of viscosity solutions to a kind of Hamilton-Jacobi-Bellman (HJB) equations combined with algebra equations. This HJB equation is related to a stochastic optimal control problem for which…
The Hamilton-Jacobi-Bellman equation arising from the optimal portfolio selection problem is studied by means of the maximal monotone operator method. The existence and uniqueness of a solution to the Cauchy problem for the nonlinear…
We formulate and analyze a new method for solving optimal control problems for systems governed by Volterra integral equations. Our method utilizes discretization of the original Volterra controlled system and a novel type of dynamic…
This paper presents a mathematical formulation to perform temporal parallelisation of continuous-time optimal control problems, which can be solved via the Hamilton--Jacobi--Bellman (HJB) equation. We divide the time interval of the control…
We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation in [12] by means of control…