Issues on Robust Adaptive Feedback Control

Abstract

We discuss recent progress in the field of robust adaptive control with special emphasis on methodologies that use multiple-model architectures. We emphasize that the selection of the number of models, estimators and compensators in such architectures must be based on precise definition of the robust performance requirements. We illustrate some of the concepts and outstanding issues for a new methodology that blends robust nonadaptive mixed µ-synthesis and stochastic hypothesis-testing concepts leading to the so-called RMMAC architecture. A numerical example is used to illustrate the RMMAC design methodology.

A multi-model approach to Saint-Venant equations: A stability study by LMIs

“…This degree is a function of the system inputs, outputs and time. The multimodel approach has often been used for the modelling and control of nonlinear systems (Porfirio et al, 2003;Athans et al, 2005) and for fault diagnosis (Bhagwat et al, 2003;Gatzke and Doyle, 2002;Rodrigues et al, 2008). Some authors refer to it as a gain scheduling strategy (Leith and Leithead, 2000), or Linear Parameter Varying (LPV) systems with the same formalism (Hamdi et al, 2011), or interpolated controllers (Banerjee et al, 1995) and switching controllers (Narendra et al, 1995).…”

Multiple‐Model Adaptive Estimation with A New Weighting Algorithm

“…According to [25], we have the following convergence result of the weighting algorithm (13), (14), (15), (16), (17), and (18). For more details on the proof of the theorem, see Lemma A.2 in the appendix.…”

“…Then, the state estimates of MMAE with the weighting algorithm (13), (14), (15), (16), (17), and (18) will converge to the optimal estimates given by the jth KF corresponding to M j , that is,x k →x j k 28…”

“…Since the late 1990s, MMAC is an important research direction in the adaptive control area, including switching MMAC [9][10][11][12][13][14] and weighted MMAC [15][16][17][18][19][20]. With MMAC, it is expected that the limitations of classical adaptive control (mainly self-tuning control and model reference adaptive control), such as poor transient performance and stabilizability of an online estimated model, could be overcome.…”

Model Weight and State Estimation for Multiple Model Systems Applied to Fault Detection and Identification

“…This algorithm can be used in the same manner as the classical multiple model algorithms for other applications. Examples of such applications are, but not limited to, multiple model adaptive control (Athans et al, 2005), fault-tolerant control (Zhang and Jiang, 2001) and approximation of nonlinear systems with multiple models (Banerjee et al, 1997). This paper is organized as follows.…”