Related papers: Time-optimal control of a two-peakon collision
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
An optimal control problem described by the Hamilton-Jacobi-Bellman equation can be developed into a problem that can be solved by general computational fluid dynamics packages. We describe how this formulation would allow a classical…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
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 consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
Optimal control theory aims to find an optimal protocol to steer a system between assigned boundary conditions while minimizing a given cost functional in finite time. Equations arising from these types of problems are often non-linear and…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
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…
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…
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…
The paper deals with a class of time-inconsistent control problems for McKean-Vlasov dynamics. By solving a backward time-inconsistent Hamilton-Jacobi-Bellman (HJB for short) equation coupled with a forward distribution-dependent stochastic…
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…