Related papers: Distributional Hamilton-Jacobi-Bellman Equations f…
This paper deals with a family of stochastic control problems in Hilbert spaces which arises in typical applications (such as boundary control and control of delay equations with delay in the control) and for which is difficult to apply the…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult.…
This work presents a distributed algorithm for resolving cooperative multi-vehicle conflicts in highly constrained spaces. By formulating the conflict resolution problem as a Multi-Agent Reinforcement Learning (RL) problem, we can train a…
This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with…
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…
Existing reinforcement learning (RL) methods struggle with complex dynamical systems that demand interactions at high frequencies or irregular time intervals. Continuous-time RL (CTRL) has emerged as a promising alternative by replacing…
We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow…
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…
In this manuscript, we investigate importance sampling methods for rare-event simulation in diffusion processes. We show, from a large-deviation perspective, that the resulting importance sampling estimator is log-efficient. This connection…
We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
We study the problem of predicting the future, though only in the probabilistic sense of estimating a future state of a time-varying probability distribution. This is not only an interesting academic problem, but solving this extrapolation…
This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…
CASL-HJX is a computational framework designed for solving deterministic and stochastic Hamilton-Jacobi equations in two spatial dimensions. It provides a flexible and efficient approach to modeling front propagation problems, optimal…
We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By…
Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit…