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We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…

Optimization and Control · Mathematics 2016-10-25 Ricardo Almeida , Delfim F. M. Torres

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…

Optimization and Control · Mathematics 2023-10-18 Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen , Trang Nguyen

The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…

Mathematical Physics · Physics 2017-01-18 Leonardo Colombo

The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…

Optimization and Control · Mathematics 2021-01-27 Qi Lü , Xu Zhang

The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary…

Optimization and Control · Mathematics 2016-11-15 Anthony M. Bloch , Melvin Leok , Jerrold E. Marsden , Dmitry V. Zenkov

This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…

Optimization and Control · Mathematics 2023-12-14 Gabriel Nicolosi , Terry Friesz , Christopher Griffin

This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…

Optimization and Control · Mathematics 2016-03-10 M. T. Hale , Y. Wardi , H. Jaleel , M. Egerstedt

Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…

Numerical Analysis · Mathematics 2017-10-05 Michael Kraus , Omar Maj

This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion…

Optimization and Control · Mathematics 2021-01-21 Radoslaw Pytlak , Damian Suski

This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…

Optimization and Control · Mathematics 2022-06-30 Roman Chertovskih , Nathalie T. Khalil , Dmitry Karamzin , Fernando Lobo Pereira

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Optimization and Control · Mathematics 2018-02-13 Laurent Pfeiffer

We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…

Quantum Physics · Physics 2009-11-07 Ilia Grigorenko , Martin E. Garcia , K. H. Bennemann

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action…

Optimization and Control · Mathematics 2012-03-13 M. Delgado-Tellez , A. Ibort , T. Rodriguez de la Peña

This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…

Optimization and Control · Mathematics 2014-05-19 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…

Systems and Control · Electrical Eng. & Systems 2019-11-22 Zeji Yi , Zhefeng Cao , Evangelos Theodorou , Yongxin Chen

This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…

Numerical Analysis · Mathematics 2016-01-20 Loïc Bourdin , Jacky Cresson , Isabelle Greff , Pierre Inizan

We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…

Optimization and Control · Mathematics 2018-09-24 George I. Boutselis , Evangelos Theodorou

In this paper we study numerically solving optimal control problems with bang-bang control functions. We present a formal Lagrangian approach for solving the optimal control problem, and address difficulties encountered when numerically…

Optimization and Control · Mathematics 2021-04-20 Ryan H. Vogt , Sarah Strikwerda

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler