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Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
This work establishes a crucial step toward advancing data-driven trajectory-based methods for stochastic systems with unknown mathematical dynamics. In contrast to scenario-based approaches that rely on independent and identically…
Discrete-time stochastic optimal control remains a challenging problem for general, nonlinear systems under significant uncertainty, with practical solvers typically relying on the certainty equivalence assumption, replanning and/or…
We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
We consider trajectory optimal control problems in which parameter uncertainty limits the applicability of control trajectories computed prior to travel. Hence, efficient trajectory adjustment is needed to ensure successful travel. However,…
A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…