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We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is obtained by a careful limit procedure of the Pontryagin…

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…

The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…

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…

The article considers a two-level open quantum system whose dynamics is driven by a combination of coherent and incoherent controls. Coherent control enters into the Hamiltonian part of the dynamics whereas incoherent control enters into…

In this short communication, we first recall a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. This result was recently obtained in [L. Bourdin and E. Tr{\'e}lat ,…

In this paper we focus on regional deterministic optimal control problems, i.e., problems where the dynamics and the cost functional may be different in several regions of the state space and present discontinuities at their interface.…

We derive the explicit solution of the problem of time-optimal control by a common magnetic fields for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin Maximum Principle and a novel symmetry reduction…

We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessary and sufficient condition. Solutions are then computed for…

In this paper, we solve the problem of simultaneously driving in minimum time to arbitrary final conditions, N two level quantum systems subject to independent controls. The solution of this problem is obtained via an explicit description…

In this paper we summarize our results in infinite horizon optimal control. We present optimality conditions for weak local minimizer in the framework of weighted functions. Moreover we formulate the Pontryagin Maximum Principle for strong…

Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the…

We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…

We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…

This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order Pontryagin type maximal principle.

We consider the simplest optimal control problem with one nonregular mixed inequality constraint, i.e. when its gradient in the control can vanish on the zero surface. Using the Dubovitskii--Milyutin theorem on the approximate separation of…

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…

We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability…

The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…