An efficient hp spectral collocation method for nonsmooth optimal control problems

Title:

An efficient hp spectral collocation method for nonsmooth optimal control problems

Creator:

Hedayati, Mehrnoosh, Ahsani Tehrani, Hojjat, Fakharzadeh Jahromi, Alireza, Noori Skandari, Mohammad Hadi, and Baleanu, Dumitru

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8070a1a8-ba38-4aba-8cb3-0428b502ffc4
uuid:8070a1a8-ba38-4aba-8cb3-0428b502ffc4
doi:10.14736/kyb-2022-6-0843

Subject:

nonsmooth optimal control, hp-method, Lagrange interpolating polynomials, and Legendre-Gauss-Lobatto points

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

One of the most challenging problems in the optimal control theory consists of solving the nonsmooth optimal control problems where several discontinuities may be present in the control variable and derivative of the state variable. Recently some extended spectral collocation methods have been introduced for solving such problems, and a matrix of differentiation is usually used to discretize and to approximate the derivative of the state variable in the particular collocation points. In such methods, there is typically no condition for the continuity of the state variable at the switching points. In this article, we propose an efficient hp spectral collocation method for the general form of nonsmooth optimal control problems based on the operational integration matrix. The time interval of the problem is first partitioned into several variable subintervals, and the problem is then discretized by considering the Legendre-Gauss-Lobatto collocation points. Here, the switching points are unknown parameters, and having solved the final discretized problem, we achieve some approximations for the optimal solutions and the switching points. We solve some comparative numerical test problems to support of the performance of the suggested approach.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

843-862

Source:

Kybernetika | 2022 Volume:58 | Number:6

Harvested from:

CDK

Metadata only:

false