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In this paper, the authors study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a…
Aerial manipulators undergo rapid, configuration-dependent changes in inertial coupling forces and aerodynamic forces, making accurate dynamics modeling a core challenge for reliable control. Analytical models lose fidelity under these…
We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…
We consider a continuous-time Bienaym\'e-Galton-Watson process with logistic competition in a regime of weak competition, or equivalently of a large carrying capacity. Individuals reproduce at random times independently of each other but…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…
In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form $\dot{x} = f_0(x) + f_1(x)$, where $f_0$ encodes non-reversible dynamics, motivating schemes…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…
We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…
Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their…
This paper presents an observer-based event-triggered boundary control strategy for a class of reaction-diffusion PDEs with Robin actuation. The observer only requires boundary measurements. The control approach consists of a backstepping…
Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in…
In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using time- and space-dependent velocity fields as the control parameters. This partial differential equation (PDE)…