Revisiting the LQR Problem of Singular Systems  

作　　者：Komeil Nosrati Juri Belikov Aleksei Tepljakov Eduard Petlenkov 

机构地区：[1]IEEE [2]the Department of Computer Systems,Tallinn University of Technology [3]the Department of Software Science,Tallinn University of Technology

出　　处：《IEEE/CAA Journal of Automatica Sinica》2024年第11期2236-2252,共17页自动化学报（英文版）

基　　金：supported by the European Union’s Horizon Europe research and innovation programme (101120657);project ENFIELD (European Lighthouse to Manifest Trustworthy and Green AI), the Estonian Research Council (PRG658, PRG1463);the Estonian Centre of Excellence in Energy Efficiency, ENER (TK230) funded by the Estonian Ministry of Education and Research。

摘　　要：In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attributes are applicable only to transformed singular systems, and the efficiency of the regulator may be undermined if constraints are violated in nonsingular versions. To address this gap, we introduce a direct approach to the LQR problem for linear singular systems, avoiding the need for any transformations and eliminating the need for regularity assumptions. To achieve this goal, we begin by formulating a quadratic cost function to derive the LQR algorithm through a penalized and weighted regression framework and then connect it to a constrained minimization problem using the Bellman's criterion. Then, we employ a dynamic programming strategy in a backward approach within a finite horizon to develop an LQR algorithm for the original system. To accomplish this, we address the stability and convergence analysis under the reachability and observability assumptions of a hypothetical system constructed by the pencil of augmented matrices and connected using the Hamiltonian diagonalization technique.

关 键 词：DC motor optimal control penalized weighted regression power system quadratic regulator singular system 

分 类 号：O231[理学—运筹学与控制论]