Concurrent Learning Based Finite-Time Parameter Estimation in Adaptive Control of Uncertain Switched Nonlinear Systems
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Concurrent Learning Based Finite-Time Parameter Estimation in Adaptive Control of Uncertain Switched Nonlinear Systems Saeede Nazari Goldar1 · Mojtaba Yazdani2 · Behzad Sinafar3
Received: 5 August 2015 / Revised: 18 October 2016 / Accepted: 29 March 2017 © Brazilian Society for Automatics–SBA 2017
Abstract In this paper, We develop concurrent learning adaptive controller, which uses recorded and current data concurrently for adaptation, to model reference adaptive control (MRAC) of uncertain switched nonlinear systems. In standard MRAC architecture for switched systems, the adaptive update laws are derived based on the gradient descent scheme, but here we developed two novel parameter estimation schemes by using modification terms in adaptation laws in which recorded data are used simultaneously with current data and a triggering time is considered in which a sufficient condition on the linear independence of the recorded data is obtained to guarantee the exponential convergence of tracking error and parameter estimation error to zero for the uncertain switched system under all admissible switching strategy. The convergence of the parameters to the ideal values makes an online learned model of the system available. This sufficient condition is easily verifiable in comparison with the restrictive persistence of excitation condition of the standard MRAC structures in practical applications. Finally, a simulation example is given to illustrate the efficacy of the proposed method.
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Behzad Sinafar [email protected] Saeede Nazari Goldar [email protected] Mojtaba Yazdani [email protected]
1
Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran
2
Department of Control Engineering, Faculty of Electronics, Semnan University, Semnan, Iran
3
Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran
Keywords Uncertain nonlinear switched systems · Model reference adaptive control (MRAC) · Concurrent learning adaptation · Finite-time parameter estimation · Persistence of excitation
1 Introduction In the past decades, hybrid and switched systems have attracted much attention as a new area in the control theory since it can be used widely in engineering and applied science to model a multitude of devices, such as networked control systems (Zhao et al. 2009), near space vehicle control systems (Bao et al. 2010), circuit and power systems (Homaee et al. 2014). A switched system is a dynamical system that consists of a finite number of subsystems and a logic rule that orchestrates switching between these subsystems which are usually described by a collection of indexed differential or difference equations (Lin and Antsaklis 2009). Research on the switching systems is mainly focused on the fields of identification (Kersting and Buss 2014; Yang et al. 2015), control (Sinafar et al. 2014; Zhao et al. 2015), stability analysis (Aleksandrov et al. 2011; Gonzaga et al. 2012; Liberzon and Morse 1999) and state estimation (He et al. 2012; di Berna
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