A Stabilization Framework for the Output Regulation of Rational Nonlinear Systems

Abstract

A systematic stabilization approach is provided for systems whose regulation error dynamics is subject to rational nonlinearities given prior knowledge of the system zero-error steady-state condition and a proper internal model. The error dynamics is cast in a differential-algebraic form so as to address the synthesis of controller parameters by a numerical optimization problem subject to bilinear matrix inequality constraints. A particular case is also explored where the resulting constraints are linear matrix inequalities.

Controller and anti‐windup co‐design for the output regulation of rational systems subject to control saturation

“…More recently, the DAR method was proposed for the stability analysis of output regulation control loops subject to rational error dynamics 20 . This result was later generalized into a controller design framework for closed‐loop stabilization of rational nonlinear output regulation schemes with internal model stages 21 . In order to extend the scope of the aforementioned study, it is possible to address the control input saturation effect and to investigate the use anti‐windup compensation, which are the subject of the present work.…”

“…To systematically design a stabilizing controller in the form of (13), as considered in Reference 21, we first introduce an auxiliary proxy error signal which is defined by a steady‐state vanishing function of the available measurements y , that is This proxy error ε represents a steady‐state vanishing signal to be employed as a feedback component in the stabilizing controller. Note that whenever the original output error e is implementable with the measurements, that is, ∃ h( y ) : h( g ( x , w )) = h ( x , w ), then can be considered, in which case ε is equivalent to e .…”

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

“…The choice of the polyhedral set could be considered conservative. However, due to its characteristics of simplicity and convexity, this set is widely used 6,25,27,37,43 …”

“…The use of Differential and Difference‐Algebraic Representations in analysis and control of nonlinear systems has been investigated in the last decades, under several aspects in the context of local stability analysis, 28,31‐34 local stabilization and DOA estimation, 12,13,35‐37 local stabilization and output performance, 12,24 filters and observers, 26,38,39 anti‐windup design, 40,41 event‐triggered control, 42 and more recently for the output regulation problem 43 . In the context of stability analysis, less‐conservative results to nonlinear systems described in a DAR form were obtained by searching for polynomial and rational Lyapunov candidate functions 31,44,45 .…”

Controle Baseado em Quatérnio para Estabilização Simultânea da Orientação e Posição de Veículos Omnidirecionais

“…Oliveira et al (2012) introduzem em suas análises saturação na entrada do sistema, propondo um controle via realimentação de estados utilizando LMIs. Em Castro et al (2017)é introduzido um método sistemático de análise de estabilidade para sistemas não lineares racionais com controle de regulação de saída utilizando DAR e LMIs. E possível observar que o estado da arte mostra a busca de generalizações de análise e controle para uma classe de sistemas não lineares.…”