Smoothing switched control laws for uncertain nonlinear systems subject to actuator saturation

• Published in: International journal of adaptive control and signal processing Vol. 30; no. 8-10; pp. 1408 - 1433
• Main Authors: Alves, Uiliam Nelson L. T., Teixeira, Marcelo C. M., de Oliveira, Diogo R., Cardim, Rodrigo, Assunção, Edvaldo, de Souza, Wallysonn A.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.08.2016; Wiley Subscription Services, Inc
• Subjects: Actuators; control signal smoothing; Control systems; Design engineering; Dynamical systems; linear matrix inequalities (LMIs); Mathematical models; Nonlinear dynamics; Saturation; sliding mode control; switched control of uncertain nonlinear systems; Takagi-Sugeno fuzzy models; Variable structure control
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.2671

Summary This paper considers a class of uncertain nonlinear systems exactly described by Takagi–Sugeno (T‐S) fuzzy models, with or without matched uncertainties and/or disturbances, within an operating region in the state space. Considering the plant subject to actuator saturation is proposed, a switched control design method such that the equilibrium point of the controlled systems is locally asymptotically stable with an adequate decay rate, for all initial conditions in a region obtained in the design procedure, that is within a given operating region. Moreover, an exact representation of the minimum function using signal functions is presented. Therefore, it is offered a bridge between the switched control and variable structure control laws, because they are usually based on minimum and signal functions, respectively. Considering the well‐known approximation of the signal function by a sigmoid function, this paper introduces the ‘smooth minimum’ function. The smooth minimum function allowed the design of ‘smooth switched’ control laws, without chattering, for the aforementioned class of systems. The proposed smooth switched control laws guarantee the uniform ultimate boundedness of the controlled systems. Design examples and simulation results illustrate the control design procedures and the effectiveness of the proposed control laws. Future researches in this subject may explore the presented relationship between the switched control and variable structure control laws, in order to obtain new useful control laws. Copyright © 2016 John Wiley & Sons, Ltd.