Related papers: Presymplectic high order maximum principle
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization,…
The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…
A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously…
We introduce the MAGICARP algorithm, a numerical optimization method for quantum optimal control problems that combines the structure provided by Pontryagin's Maximum Principle (PMP) and the robustness of gradient ascent techniques, such as…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the…
This paper is devoted to the study of a class of optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems, which are based on a phase-field model of grain boundary motion, proposed by [Kobayashi et al, Physica D, 140,…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
We study the selective and robust time-optimal rotation control of several spin-1/2 particles with different offset terms. For that purpose, the Pontryagin Maximum Principle is applied to a model of two spins, which is simple enough for…
Nesterov's accelerated gradient algorithm is derived from first principles. The first principles are founded on the recently-developed optimal control theory for optimization. This theory frames an optimization problem as an optimal control…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
An optimal guidance law for impact time control with field-of-view constraint is presented. The guidance law is derived by first converting the inequality-constrained nonlinear optimal control problem into an equality-constrained one…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Optimal control remains as one of the most versatile frameworks in systems theory, enabling applications ranging from classical robust control to real-time safe operation of fleets of vehicles. While some optimal control problems can be…
In many resource-limited optimal control problems, multiple constraints may be enforced that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we…