Low complexity quantized controllers for LTI systems : peak-to-peak performance guarantees

Abstract

In this thesis, we propose a novel feedback control scheme for unstable LTI systems performing noise attenuation via a finite-rate digital channel. In the first part of the thesis, we introduce the structure of the control system as well as the encoder and decoder used to transmit the required control signals along the digital channel. The performances of the proposed algorithm are then evaluated by providing explicit bounds on the peak-to-peak noise attenuation, in regards to the induced l[subscript infinity symbol] gain of the closed loop . This result is obtained by constructing a new class of storage functions that can be employed to verify the dissipativity of the closed loop system with respect to a suitable supply rate function. In the second part of the thesis, we examine the trade-off between the closed loop performances and the required rate of the channel. While the digital channel imposes some limitations on the achievable induced l[subscript infinity symbol] gain, we show how the performances of the proposed scheme can still approximate those achievable without communication constraints provided that the rate of the channel is large enough. A numerical optimization problem is then devised to design the parameters of the control scheme in order to minimize the strain on the channel while matching some prescribed constraints on the closed loop induced l[subscript infinity symbol] gain.