Hands-off Control for Discrete-time Linear Systems subject to Polytopic Uncertainties ⁎⁎This work was supported in part by the JSPS KAKENHI Grant Numbers JP15H02668 and JP16KK0134, the Ministry of Internal Affairs and Communications of Japan under the Strategic Information and Communications R&D Promotion Programme, 2017-2019, No. 3620, and JST-Mirai Program Grant Number JPMJMI17B4, Japan

• Published in: IFAC-PapersOnLine Vol. 51; no. 23; pp. 355 - 360
• Main Authors: Kishida, Masako, Barforooshan, Mohsen, Nagahara, Masaaki
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2018
• Subjects: Convex programming; Discrete-time systems; Linear optimal control; Robust control; Uncertainty; Robust control; Discrete-time systems; Uncertainty; Linear optimal control; Convex programming
• ISSN: 2405-8963
• DOI: 10.1016/j.ifacol.2018.12.061

This paper develops approaches to the hands-off control problem subject to performance constraints for discrete-time linear systems. The approaches minimize the l1-norm of the control input to acquire the hands-off property, while satisfying the performance constraints that are given in terms of the quadratic cost of states and inputs with respect to the optimal solution to the finite-horizon linear quadratic regulator problem. We consider three kinds of the input and state matrices for the system; 1) known, 2) uncertain but contained in a known discrete set, and 3) uncertain but contained in a known polytopic uncertainty set. For the first two cases, we show that each problem is formulated as an l1 optimization that is expressed as a second-order cone programming. We also show that the last case leads to a second-order cone programming after relaxations. A numerical example is included to illustrate the validity of the proposed approach.