Related papers: A Pontryagin Maximum Principle in Wasserstein Spac…
In this article we present a geometric discrete-time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the controls in addition to pointwise constraints on the states and control actions…
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all…
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…
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…
We consider in this paper, mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this…
A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…
This article considers a discrete-time robust optimal control problem on matrix Lie groups. The underlying system is assumed to be perturbed by exogenous unmeasured bounded disturbances, and the control problem is posed as a min-max optimal…
We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably,…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle---such as the separating hyperplanes, costate, necessary condition, and normal/abnormal…
We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the…
In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical…
This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalised by the relative entropy. We identify suitable metric space on which we construct a gradient flow for the…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid version of Pontryagin's maximum principle is presented. This…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results.…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
In this research, we consider the commercial aircraft trajectory optimization problem for a general cruise model with arbitrary spatial wind fields to be solved using the Pontryagin maximum principle. The model features two fundamental…