Adaptive Control of Nonlinear Systems: Parametric and Non-Parametric Approach

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

doi:10.1109/med51440.2021.9480230

Cited by 14 publications

(8 citation statements)

References 14 publications

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“…Moreover, the RBFN-based MRAC is only locally effective as the approximation holds within the estimated operating domain. The ANN-based MRAC, which utilizes feedforward networks to approximate unknown functions, exhibits a poor transient response [29]. The GP as a Bayesian nonparametric regression…”

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%

“…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]). The estimation performance of unknown term ψ(x 1 , x 3 ) via GP-MRAC and RBFN-MRAC is shown in [22].…”

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%

Section: Control Via Proposed Pandi and Comparison Analysismentioning

confidence: 99%

Section: Control Via Proposed Pandi and Comparison Analysismentioning

confidence: 99%

See 3 more Smart Citations

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

Nayyer¹,

Hozefa

Revati³

et al. 2022

IEEE Access

Self Cite

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Multiple models for decentralised adaptive control of discrete‐time systems

Makam,

George

2024

Adaptive Control & Signal

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This paper investigates decentralised adaptive control of discrete‐time systems consisting of linear time‐invariant systems and a class of nonlinear systems. The parameters of the subsystems and the interconnection strengths between the subsystems are assumed unknown. Multiple adaptive prediction models with switching are used in this paper to address the relatively poor transient performance that typically results from a single prediction model. However, the application of this methodology requires indirect model reference discrete‐time adaptive control, and there appears to be very little focus in the literature on this. The principal contribution of this paper is to fill this void by arriving at proof of global stability of such decentralised adaptive systems using the theory of Lyapunov and properties of square‐summable sequences. The chosen representation of the system enables the same results to be directly applicable to both linear time‐invariant and linear‐in‐the‐parameters nonlinear subsystems. We consider two parametric update algorithms, one of which has a normalisation factor. Simulation studies included in this paper demonstrate the improvement in transient performance.

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