Related papers: Hamilton-Jacobi equations for optimal control on m…
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
We study an optimal stopping problem when the state process is governed by a general Feller process. In particular, we examine viscosity properties of the associated value function with no a priori assumption on the stochastic differential…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
In this paper we establish H\"older continuity estimates for viscosity solutions to first order Hamilton-Jacobi equations linked to linear control systems satisfying the Kalman rank condition. Our model Hamiltonians are non-convex in the…
We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…
We study the well-posedness of an infinite-dimensional Hamilton-Jacobi equation posed on the set of non-negative measures and with a monotonic non-linearity. Our results will be used in a companion work to propose a conjecture and prove…
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…
In this article, we are concerned about the velocity tracking optimal control problem for 3D critical convective Brinkman-Forchheimer equations defined on a simply connected bounded domain $\mathbb{D}\subset\mathbb{R}^3$ with…
Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…
We consider the well-posedness and numerical approximation of a Hamilton--Jacobi equation on an evolving hypersurface in $\mathbb R^3$. Definitions of viscosity sub- and supersolutions are extended in a natural way to evolving hypersurfaces…
For an optimal control problem of an It\^o's type stochastic differential equation, the control process could be taken as open-loop or closed-loop forms. In the standard literature, provided appropriate regularity, the value functions under…
In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…
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…
We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory spatial dependence and rough time dependence. The time dependence is in the form of the derivative of a continuous path that converges to a possibly…
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…
In this note, we formulate and study a Hamilton-Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation.…