Robust model reference adaptive control for transient performance enhancement

Abstract

To circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L 2-norm and Cauchy-Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high-gain adaptation. In addition, the frequency-domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high-gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.

A Sigmoid-plane adaptive control algorithm for unmanned surface vessel considering marine environment interference

“…The adaptive control algorithm was studied in this paper. According to the structure of the adaptive control system, it can usually be divided into model reference adaptive control (Yang et al, 2020), self-tuning control (Filip et al, 2019), and other new types of adaptive control (Yu¨ksel, 2019). Self-tuning control is to modify the parameters of the controller itself by identifying the parameters of the mathematical model of the controlled system in real-time so that the controlled system can work under the specified performance index.…”

Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

“…Robust model reference control techniques are applied to different types of systems, such as multivariable linear systems with parameter uncertainties (Duan et al, 2001; Gerardo et al, 2016; Huang and Jia 2017), descriptor linear systems with parametric uncertainties (Duan and Zhang, 2007), linear parameter-varying systems (Abdullah, 2018; Abdullah and Zribi, 2009), Markov jump systems with unknown transition probabilities (Boukas, 2009; Zhang and Boukas, 2009), non-linear systems (Zhang et al, 2018; Qin et al 2018) and uncertain network-based control systems (Gao and Chen, 2008). To improve the transient response caused by uncertain dynamics, a robust model reference control design is proposed in Yang et al (2020). Furthermore, a new model reference control architecture to guarantee transient and steady-state system performance is also proposed in Gerardo et al (2016).…”

Finite‐time adaptive output synchronization of uncertain nonlinear heterogeneous multi‐agent systems

“…To partially bridge the gap, synchronization of follower agents with parametric uncertainty is considered in References 27‐29. However, only asymptotic convergence under restrictive persistence of excitation (PE) condition 30,31 can be guaranteed. To relax this restrictive PE condition, Reference 32 leverages an adaptive law based on the experience‐replay technique to guarantee asymptotic convergence for dynamic identification of single‐agent nonlinear systems.…”