Related papers: Absolute Extrema of Invariant Optimal Control Prob…
In this paper we consider an optimal control problem for the coupled system of a nonlinear monotone Dirichlet problem with anisotropic p-Laplacian and matrix-valued nonsmooth controls in its coefficients and a nonlinear equation of…
We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form…
We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the…
In optimal control theory, infimum gap means that there is a gap between the infimum values of a given minimum problem and an extended problem, obtained by enlarging the set of original solutions and controls. The gap phenomenon is somewhat…
In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are…
We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results…
This work develops a control-centric framework for a custom 4-DOF rigid-body manipulator by coupling a reduced-order Pontryagin's Maximum Principle (PMP) controller with a physics-informed Gradient Descent stage. The reduced PMP model…
We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-agent path finding. Our approach yields controls in a feedback…
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal…
Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresses this challenge by precomputing optimal…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…
We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This…
Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
We establish Pontryagin principles for a Mayer's optimal control problem governed by a functional differential equation. The control functions are piecewise continuous and the state functions are piecewise continuously differentiable. To do…
Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schroedinger bridges to the case of inertial particles with losses and general, possibly singular diffusion…
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…
We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of…
In this work we refer to motivations, applications, and relations of control theory with other areas of mathematics. We present a brief historical review of optimal control theory, from its roots in the calculus of variations and the…
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains…