Performance Enhancement of Parameter Estimators via Dynamic Regressor Extension and Mixing
TL;DR: A new procedure to design parameter estimators with enhanced performance is proposed, which yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation.
Abstract: A new procedure to design parameter estimators with enhanced performance is proposed in the technical note. For classical linear regression forms, it yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation. The technique is also applied to nonlinear regressions with “partially” monotonic parameter dependence—giving rise again to estimators with enhanced performance. Simulation results illustrate the advantages of the proposed procedure in both scenarios.
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TL;DR: A novel integral concurrent learning method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties.
Abstract: Concurrent learning is a recently developed adaptive update scheme that can be used to guarantee parameter convergence without requiring persistent excitation. However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. A novel integral concurrent learning method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties. A Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation.
82 citations
Cites background from "Performance Enhancement of Paramete..."
...(27) Similarly, taking the time derivative of (20) and substituting the parameter estimate update law from (26) result in the following closed-loop parameter estimation error dynamics:...
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TL;DR: In this article, a novel integral concurrent learning method is developed that removes the need to estimate state derivatives while maintaining parameter convergence properties, and a Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation.
Abstract: Concurrent learning is a recently developed adaptive update scheme that can be used to guarantee parameter convergence without requiring persistent excitation. However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. A novel integral concurrent learning method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties. A Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation.
74 citations
TL;DR: In this article, an online inertia estimation algorithm is proposed for transmission system operators to be able to monitor the system inertia in real time in a highly deregulated and uncertain environment, and the estimator is derived using the recently proposed dynamic regressor and mixing procedure.
Abstract: The increasing penetration of power-electronic-interfaced devices is expected to have a significant effect on the overall system inertia and a crucial impact on the system dynamics. In future, the reduction of inertia will have drastic consequences on protection and real-time control and will play a crucial role in the system operation. Therefore, in a highly deregulated and uncertain environment, it is necessary for transmission system operators to be able to monitor the system inertia in real time. We address this problem by developing and validating an online inertia estimation algorithm. The estimator is derived using the recently proposed dynamic regressor and mixing procedure. The performance of the estimator is demonstrated via several test cases using the 1013-machine ENTSO-E dynamic model.
70 citations
TL;DR: This paper provides a unified framework for the analysis and design of parameter estimators and shows that they lie at the core of some modified schemes recently proposed in the literature, and uses this framework to propose some new schemes with relaxed conditions for convergence and improved transient performance.
70 citations
TL;DR: In this paper, a unified treatment of the continuous and the discrete-time cases is presented, and two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation.
Abstract: We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include the following, first, a unified treatment of the continuous and the discrete-time cases; second, the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement , and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and, third, an alternative estimator ensuring convergence in finite-time whose adaptation gain, in contrast with the existing one, does not converge to zero. Simulations that illustrate our results are also presented.
64 citations
References
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Book•
01 Jan 1987
TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.
Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...
20,436 citations
"Performance Enhancement of Paramete..." refers background in this paper
...It is well known that standard parameter estimation algorithms applied to linear regressions give rise to a linear time-varying system, which is exponentially stable if and only if a certain PE condition is imposed—this fundamental result constitutes one of the main building blocks of identification and adaptive control theories [1], [2]....
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...It is well-known [1], [2] that the zero equilibrium of the linear time-varying system (3)...
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Book•
01 Jan 1989TL;DR: In this paper, the deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers, with a focus on basic AC approaches, notation and fundamental theorems, identification problem, model-reference AC, parameter convergence using averaging techniques, and robustness.
Abstract: The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.
2,914 citations
"Performance Enhancement of Paramete..." refers background in this paper
...It is well known that standard parameter estimation algorithms applied to linear regressions give rise to a linear time-varying system, which is exponentially stable if and only if a certain PE condition is imposed—this fundamental result constitutes one of the main building blocks of identification and adaptive control theories [1], [2]....
[...]
...It is well-known [1], [2] that the zero equilibrium of the linear time-varying system (3)...
[...]
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01 Jan 1985
TL;DR: A survey of Scalar Polynomials can be found in this article, where the Jordan Canonical Form is used to define the normal form of matrix polynomials and normal forms.
Abstract: Maxtrix Algebra. Determinants, Inverse Matrices, and Rank. Linear, Euclidean, and Unitary Spaces. Linear Transformations and Matrices. Linear Transformations in Unitary Spaces and Simple Matrices. The Jordan Canonical Form: A Geometric Approach. Matrix Polynomials and Normal Forms. The Variational Method. Functions of Matrices. Norms and Bounds for Eigenvalues. Perturbation Theory. Linear Matrix Equations and Generalized Inverses. Stability Problems. Matrix Polynomials. Nonnegative Matrices. Appendix 1. A Survey of Scalar Polynomials. Appendix 2. Some Theorems and Notions from Analysis. Appendix 3. Suggestions for Further Reading. Index.
748 citations
"Performance Enhancement of Paramete..." refers background in this paper
...Remark 2: It is important to underscore that for any matrix A ∈ Rq×q , we have that adj{A}A = det{A}Iq , even if A is not full rank [14]....
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Book•
01 Jan 2008
TL;DR: In this article, the authors provide a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties, based on the ideas of system immersion and manifold invariance.
Abstract: "Nonlinear and Adaptive Control with Applications" provides a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties. The authors employ a new tool based on the ideas of system immersion and manifold invariance. Departing, in part, from the Lyapunov-function approach of classical control, new algorithms are delivered for the construction of robust asymptotically-stabilising and adaptive control laws for nonlinear systems. The methods proposed lead to modular schemes. These algorithms cater for nonlinear systems with both parametric and dynamic uncertainties. This innovative strategy is illustrated with several examples and case studies from real applications. Power converters, electrical machines, mechanical systems, autonomous aircraft and computer vision are among the practical systems dealt with. Researchers working on adaptive and nonlinear control theory or on control applications will find this monograph of conspicuous interest while graduate students in control systems and control engineers working with electrical, mechanical or electromechanical systems can also gain much insight and assistance from the methods and algorithms detailed.
586 citations
"Performance Enhancement of Paramete..." refers background in this paper
...As shown in [10], [11] it is possible to design parameter estimators directly for the system (39) using immersion and invariance techniques [18]....
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01 Jan 2010
TL;DR: It is shown that for an adaptive controller that uses recorded and instantaneous data concurrently for adaptation, a verifiable condition on linear independence of the recorded data is sufficient to guarantee exponential tracking error and parameter error convergence.
Abstract: We show that for an adaptive controller that uses recorded and instantaneous data concurrently for adaptation, a verifiable condition on linear independence of the recorded data is sufficient to guarantee exponential tracking error and parameter error convergence. This condition is found to be less restrictive and easier to monitor than a condition on persistently exciting exogenous input signal required by traditional adaptive laws that use only instantaneous data for adaptation.
338 citations