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In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent…
In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
We present a method for collisionless multi-agent path planning using the Hamilton-Jacobi-Bellman equation. Because the method is rooted in optimal control theory and partial differential equations, it avoids the need for hierarchical…
A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
Real-world autonomous systems often employ probabilistic predictive models of human behavior during planning to reason about their future motion. Since accurately modeling human behavior a priori is challenging, such models are often…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value…
This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling…
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…
We consider the problem of optimal path planning on a manifold which is the image of a smooth function. Optimal path-planning is of crucial importance for motion planning, image processing, and statistical data analysis. In this work, we…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…
The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems…
In standard treatments of stochastic filtering one first has to estimate the values of the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
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 is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
Sailboat path-planning is a natural hybrid control problem (due to continuous steering and occasional "tack-switching" maneuvers), with the actual path-to-target greatly affected by stochastically evolving wind conditions. Previous studies…