Related papers: Optimality conditions for a controlled sweeping pr…
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
In the present paper we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
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…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…
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…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
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…
Motivated by the control of invasive biological populations, we consider a class of optimization problems for moving sets $t\mapsto \Omega(t)\subset\mathbb{R}^2$. Given an initial set $\Omega_0$, the goal is to minimize the area of the…
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 a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical…
The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems…
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…