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We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the…
This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…
We consider discrete-time infinite horizon deterministic optimal control problems with nonnegative cost per stage, and a destination that is cost-free and absorbing. The classical linear-quadratic regulator problem is a special case. Our…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in…
We consider control strategies for large-scale interacting agent systems under uncertainty. The particular focus is on the design of robust controls that allow to bound the variance of the controlled system over time. To this end we…
We provide a technique to obtain provably optimal control sequences for quantum systems under the influence of time-correlated multiplicative control noise. Utilizing the circuit-level noise model introduced in [Phys. Rev. Research 3,…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
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…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
We propose and analyze a framework for discrete-time robust mean-field control problems under common noise uncertainty. In this framework, the mean-field interaction describes the collective behavior of infinitely many cooperative agents'…
We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop…
In this paper, we introduce an optimal control problem for multi-agent systems with non-local cost which favors simultaneous aggregation of particles. This is done introducing a time-dependent notion of multiplicity whose intrinsic…
We investigate the problem of persistently monitoring a finite set of targets with internal states that evolve with linear stochastic dynamics using a finite set of mobile agents. We approach the problem from the infinite-horizon…
This paper investigates the robustness of a novel high-dimensional continuification control method for complex multi-agent systems. We begin by formulating a partial differential equation describing the spatio-temporal density dynamics of…
In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike effect persists in the presence of noise…
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…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…