Adaptive learning control for a class of nonlinearly parameterized uncertain systems

Fang, Yongchun; Xiao, Xi; Ma, Bin; Lu, Guizhang

doi:10.1109/acc.2005.1469931

Cited by 5 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, it arises naturally in physical systems such as biochemical processes and machines with friction. Furthermore, the existing adaptive methods for nonlinearly parameterized systems are abundant, such as those in previous works [30][31][32]. However, few results about the problem of safety control have been reported, especially for time-varying state constraints.…”

Section: Introductionmentioning

confidence: 99%

Model reference safety‐critical adaptive control for a class of nonlinearly parameterized systems

Zhang

Long

2021

Asian Journal of Control

View full text Add to dashboard Cite

Safety is the most fundamental problem of safety‐critical systems. Safety control addresses the problem whether a given unsafe region of the state space can be avoided by a specific control‐input. Moreover, linearly parameterized dynamical system is a general assumption in most safety‐critical adaptive control literature; however, unknown parameters in real systems are usually nonlinear. The control problem of nonlinearly parameterized systems is really difficult without linear‐in‐the‐parameters (LIP) assumptions, which tends to be complicated and computationally intensive. In this paper, a novel model reference safety‐critical adaptive control (MRAC) approach is proposed for a class of nonlinearly parameterized systems. The proposed approach involves a novel controller architecture with a modified update law, which specifically filters out the unsafe behavior (the system is in a state which the system cannot operate normally, i.e., the given unsafe region), while preserving favorable tracking capability and robustness. The novelty of this paper is that the nonlinearly parameterized systems can be enforced safety, without LIP assumptions and complex calculations. Most importantly, this approach is effective for nonlinearly parameterized systems as well as linearly parameterized systems. Finally, three illustrative numerical examples are presented to demonstrate the effectiveness of the proposed design approach.

show abstract

Section: Introductionmentioning

confidence: 99%

Model reference safety‐critical adaptive control for a class of nonlinearly parameterized systems

Zhang

Long

2021

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…Ye et al in [3] designed an adaptive learning control law for a class of feed-forward nonlinear systems to asymptotically regulate the system errors. In [4], Fang et al designed a global adaptive controller to deal with a class of nonlinearly parameterized uncertain systems in which the uncertainty can be separated into an unknown parameter vector with a periodic signal. In [5], Ma et al proposed a switching logic-based adaptive robust control for a class of nonlinearly parameterized systems.…”

Section: Introductionmentioning

confidence: 99%

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

Sun

Cai

Zhao

2013

J. of Syst. Eng. Electron.

View full text Add to dashboard Cite

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network (FBFN). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

show abstract

“…Ye et al in [3] designed an adaptive learning control law for a class of feedforward nonlinear systems to asymptotically regulate the system errors. In [4], Fang et al designed a global adaptive controller to deal with a class of nonlinearly parameterized uncertain systems in which the uncertainty can be separated into an unknown parameter vector multiplying a periodic signal. In [5], Ma et al proposed a switching logic-based adaptive robust control for a class of nonlinearly parameterized systems which enabled a global uniformly ultimate boundedness result for the system errors.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Repetitive Control of Nonlinearly Parameterized Systems Based on Fuzzy Basis Function Networks

Sun

Cai

Zhao

2012

AMR

View full text Add to dashboard Cite

In this note, an adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on fuzzy basis function networks (FBFNs). The parameters of the fuzzy rules are tuned with adaptive schemes. The adaptive repetitive control law is derived by using Lyapunov synthesis method to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, the controller singularity problem is solved as it avoids the nonlinear parameterization from entering into the adaptive control and repetitive control. The proposed approach has the added advantage that it does not require an exact structure of the system dynamics. The proposed controller is applied to control a model of permanent-magnet linear synchronous motor (PMLSM) subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method in terms of significant reduction in chattering while maintaining asymptotic convergence.

show abstract

Adaptive learning control for a class of nonlinearly parameterized uncertain systems

Cited by 5 publications

References 25 publications

Model reference safety‐critical adaptive control for a class of nonlinearly parameterized systems

Model reference safety‐critical adaptive control for a class of nonlinearly parameterized systems

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

Adaptive Repetitive Control of Nonlinearly Parameterized Systems Based on Fuzzy Basis Function Networks

Contact Info

Product

Resources

About