Parameter Convergence for Adaptive Control in Nonlinear System

Shadab, S.; Hozefa, J.; Wagh, Sushama; Singh, Navdeep

doi:10.1109/anzcc50923.2020.9318333

Cited by 15 publications

(4 citation statements)

References 14 publications

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“…Furthermore, the approximate feedback linearization-based MRAC (AMI-MRAC) [22] enables adaptive controllers to be designed for a broader class of nonlinear systems [23]. In the literature, different MRAC models with parametric approaches such as CL-based [24], DREM-based MRAC [25], [26], and composite learning-based MRAC [27] have been proposed. However, when control is applied to very complex systems, these MRAC models based on the parametric approaches become more challenging, especially when the dynamics cannot be determined using the first principle methods.…”

Section: B Literature Review On Stabilization and Control Of The Part...mentioning

confidence: 99%

“…Remark 2: An inverted pendulum [24], [25], [29], wing rock dynamics [22], Van der Pol equation [32] and an adapted pendulum system with a sigmoidal function [23] are examples of systems in normal form. This paper focuses on the control and stabilization of systems with feedback linearizable structures (1).…”

Section: Problem Formulationmentioning

confidence: 99%

“…11. The MRAC is designed for comparative purposes and the specifications (gains and reference model) are directly taken from [25], [29]. From Fig.…”

Section: Control Via Proposed Pandi and Comparison Analysismentioning

confidence: 99%

“…11, it is clearly seen that the convergence time of the P&I is 1.2 sec and 7.5 sec for MRAC to track the reference one. A complete comparative analysis of MRAC with different parametric (Concurrent Learning [24], DREM [40]) and nonparametric approaches (Neural networks, GP) for estimation of ψ(x 1 , x 3 ) is already carried out by the authors in [25], [29] (refer Fig. 6 of [29]).…”

Section: Control Via Proposed Pandi and Comparison Analysismentioning

confidence: 99%

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Passivity and Immersion (P&I) Approach With Gaussian Process for Stabilization and Control of Nonlinear Systems

Nayyer¹,

Hozefa

Revati³

et al. 2022

IEEE Access

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The virtual derivatives computation and successive derivations of virtual inputs in an adaptive backstepping controller cause the explosion of complexity. Moreover, the feedback linearization has poor robustness features and necessitates exact estimation of the feedback control law's coefficients. Due to measurement noise, the model-based estimation techniques for identifying uncertainties result in inaccurate gradient and Hessian calculations. Such limitations lead to model and measurement uncertainties that prevent effective stabilization and control of nonlinear systems. Machine learning-based data-driven approaches offer effective tools for identifying dynamical systems and uncertainties with minimal prior knowledge of the model structure. Therefore, the contribution of this research is two-fold: First, the general controller design theory is proposed which utilizes the idea of an invariant target manifold giving rise to a non-degenerate two form, through which the definition of certain passive outputs and storage functions leads to a generation of control law for stabilizing the system. Since the above concepts are linked with the Immersion and Invariance (I&I) design policy and the passivity theory of controller design, the proposed methodology is labeled as the "Passivity and Immersion (P&I) based approach". Second, the proposed P&I approach is integrated with a Bayesian nonparametric approach, particularly the Gaussian Process for stabilization and control of the partially unknown nonlinear systems. The effectiveness of the proposed methodologies has been evaluated on an inverted pendulum using MATLAB in the presence of input-output uncertainties.

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Section: B Literature Review On Stabilization and Control Of The Part...mentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

“…11. The MRAC is designed for comparative purposes and the specifications (gains and reference model) are directly taken from [25], [29]. From Fig.…”

Section: Control Via Proposed Pandi and Comparison Analysismentioning

confidence: 99%