Optimal Control with Sweeping Processes: Numerical Method

Pinho, Maria do Rosário de; Ferreira, M. M. A.; Smirnov, Georgi

doi:10.1007/s10957-020-01670-5

Cited by 11 publications

(27 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[1,3,6,7,8,9,10,11,12,13,16,17,18,19,30,42] and their extensive bibliographies therein. Recently, the authors in [26,27,34,35,42] have introduced and developed an innovative exponential penalization technique (also known as a continuous approximation approach as opposed to the method of discrete approximations) to obtain the existence of solution and derive a set of nonsmooth necessary optimality conditions in the form of Pontryagin maximum principle involving a controlled nonconvex sweeping process governed by a sublevel-sweeping set. This exponential penalization technique allows them to approximate the controlled sweeping differential inclusions by the sequence of standard smooth control systems and hence has successfully demonstrated to be an appropriate technique for developing a numerical algorithm to efficiently compute an approximate solution for certain forms of controlled sweeping processes with smooth data; see [26,27,34,35,42] for details.…”

Section: Introduction and Problem Formulationsmentioning

confidence: 99%

Optimal Control of Several Motion Models

Cao¹,

Chapagain²,

Cho³

et al. 2022

Preprint

View full text Add to dashboard Cite

This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping process with perturbations. A set of necessary optimality conditions for such optimal control problems involving the crowd motion models with multiple agents and obstacles is obtained and analyzed. Several effective algorithms based on such necessary optimality conditions are proposed and various nontrivial illustrative examples together with their simulations are also presented.

show abstract

Section: Introduction and Problem Formulationsmentioning

confidence: 99%

Optimal Control of Several Motion Models

Cao¹,

Chapagain²,

Cho³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…More precisely, for (BBO) we use the Nelder-Mead method, and for (DFO) we use the Model-Based Descent method. Our codes are then applied to the numerical examples of [1] and [2] and their efficiencies are discussed.…”

Section: Objectivesmentioning

confidence: 99%

“…In [1], Nour and Zeidan propose a numerical algorithm to solve the problem (P ), which improves in several directions the numerical method established in [2]. Indeed, in [2], the problem (P ) is considered with initial condition in the interior of the convex sweeping set C, which is not the case in [1]. More precisely, in [1], no convexity is assumed on the sweeping set C, and the initial state x 0 can be any point in C including the boundary.…”

Section: Introduction Backgroundmentioning

confidence: 99%

“…More precisely, in [1], no convexity is assumed on the sweeping set C, and the initial state x 0 can be any point in C including the boundary. Note that the numerical algorithm proposed in [1] and [2] is second of its kind for (P ) after the work done by Adam and Outrata in [8] where a different techniques are used.…”

Section: Introduction Backgroundmentioning

confidence: 99%

“…The method used in [1] and [2] consists of approximating (D) by a standard control system (D γ k ), obtained by replacing in (D) the set N C (x(t)) by the penalty term:…”

Section: Introduction Backgroundmentioning

confidence: 99%

See 2 more Smart Citations

A Micro-Perspective on Governance in Informal Tented Settlements. (c2022)

Zeghondy¹

View full text Add to dashboard Cite

In [1], Nour and Zeidan proposed a numerical algorithm to solve optimal control problems involving sweeping processes. In order to apply this algorithm to real life problems, two numerical methods need to be developed: A numerical method to solve nonlinear differential equations, and a numerical method to nd the minimum of an objective function (given only numerically) in fi nite dimensional spaces. The goal of this thesis is to develop two MATLAB codes for the numerical algorithm of [1]. To solve nonlinear differential equations we use Runge-Kutta method of fourth order, and for the minimization part, we use two different methods, namely Nelder-Mead and Model Based Descent methods. Our codes are then applied to several examples and their efficiencies are discussed.

show abstract

A Maximum Principle for Optimal Control Problems Involving Sweeping Processes with a Nonsmooth Set

Pinho,

Ferreira,

Smirnov

2023

J Optim Theory Appl

View full text Add to dashboard Cite

We generalize a maximum principle for optimal control problems involving sweeping systems previously derived in de Pinho et al. (Optimization 71(11):3363–3381, 2022, https://doi.org/10.1080/02331934.2022.2101111) to cover the case where the moving set may be nonsmooth. Noteworthy, we consider problems with constrained end point. A remarkable feature of our work is that we rely upon an ingenious smooth approximating family of standard differential equations in the vein of that used in de Pinho et al. (Set Valued Var Anal 27:523–548, 2019, https://doi.org/10.1007/s11228-018-0501-8).

show abstract

Optimal Control with Sweeping Processes: Numerical Method

Cited by 11 publications

References 7 publications

Optimal Control of Several Motion Models

Optimal Control of Several Motion Models

A Micro-Perspective on Governance in Informal Tented Settlements. (c2022)

A Maximum Principle for Optimal Control Problems Involving Sweeping Processes with a Nonsmooth Set

Contact Info

Product

Resources

About