Parallel algorithms for LQ optimal control of discrete-time periodic linear systems
type: Item
instance of: scholarly article
title: Parallel algorithms for LQ optimal control of discrete-time periodic linear systems
zbMATH Open document ID: 1008.93035
author: P. Benner
author: Ralph Byers
author: Rafael Mayo
author: Enrique S. Quintana-Ortí
author: V. Hernández
published in: Journal of Parallel and Distributed Computing
publication date: 2002-07-04T00:00:00Z
review text: Consider the periodic linear quadratic optimization problem \(\sum^\infty_{i=0} y^\top_iQ_iy_i+u_i^\top R_iu_i \to\min\) under the constraints \(x_{k+1}= A_kx_k+B_ku_k\), \(y_k=C_kx_k\), where \(x_k\in\mathbb{R}^n\), \(u_k\in \mathbb{R}^m\) and the involved matrices are \(p\)-periodic in the sense that \(A_k=A_{k+p}\), etc. Under standard assumptions the optimal control \(u^*_k\) is a periodic feedback defined by a discrete-time periodic Riccati equation (DPRE). The paper deals with the parallelizations of two DPRE solvers proposed earlier by the first two authors. The performance of the two parallel algorithms is analyzed. Experimental results are presented which show high performance and scalability of the proposed parallelizations.
reviewed by: Mihail M. Konstantinov
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 68W10
zbMATH DE Number: 1763510
zbMATH Keywords: periodic linear quadratic optimization
zbMATH Keywords: periodic feedback
zbMATH Keywords: discrete-time periodic Riccati equation
zbMATH Keywords: parallel algorithms
describes a project that uses: ScaLAPACK
describes a project that uses: SLICOT
describes a project that uses: LAPACK
describes a project that uses: BLAS
describes a project that uses: PLAPACK
MaRDI profile type: Publication
OpenAlex ID: W2159670073
DOI: 10.1006/JPDC.2001.1790
description: scientific article; zbMATH DE number 1763510