[논문 리뷰] Generalized Parameter Estimation-based Observers: Application to Power Systems and Chemical-Biological Reactors

Roméo Ortega, Alexey Bobtsov외 3명|arXiv (Cornell University)|2020. 03. 24.

Power System Optimization and Stability참고 문헌 32인용 수 87

한 줄 요약

The paper introduces Generalized PEBO (GPEBO), an observer design that avoids open-loop integration and uses the fundamental matrix of an LTV system with DREM to achieve asymptotic or finite-time convergence for nonlinear systems; it is applied to multimachine power systems and chemical-biological reactors.

ABSTRACT

In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular algebraic constraint. In contrast to the previous observer, the new one avoids the need of implementing an open loop integration that may stymie its practical application. We give two versions of this observer, one that ensures asymptotic convergence and the second one that achieves convergence in finite time. In both cases, the required excitation conditions are strictly weaker than the classical persistent of excitation assumption. It is shown that the proposed technique is applicable to the practically important examples of multimachine power systems and chemical-biological reactors.

연구 동기 및 목표

• Extend parameter estimation-based observers to a broader class of nonlinear systems beyond cascade form.
• Eliminate the need for open-loop integration intrinsic to PEBO to improve robustness in noisy environments.
• Achieve asymptotic and finite-time convergence under weaker excitation assumptions.
• Demonstrate applicability to multimachine power systems and chemical-biological reactors.

제안 방법

• Transform nonlinear systems to an affine-in-state form and introduce a copy dynamics to avoid open-loop integration.
• Use the fundamental matrix of an associated LTV system to inject excitation via the regressor.
• Derive a linear regressor for the unknown initial condition when the output map is affine in x.
• Combine PEBO with Dynamic Regressor Extension and Mixing (DREM) to obtain FCT under weak excitation.
• Provide two observer variants: one with asymptotic convergence and one with finite-time convergence (FCT).

실험 결과

연구 질문

• RQ1 Can GPEBO recover full system state for nonlinear systems under weaker excitation conditions?
• RQ2 Does replacing open-loop integration with a fundamental-matrix-based approach yield robust observers for noisy environments?
• RQ3 Can DREM enable finite-time convergence in GPEBO for practical systems?
• RQ4 Is the GPEBO framework applicable to real-world problems in power systems and chemical-biological reactors?

주요 결과

• GPEBO relaxes transformability requirements from cascade form to state-affine form and identifies an algebraic constraint that simplifies parameter estimation.
• The fundamental matrix-based approach injects excitation into the parameter estimator, enabling convergence under weaker excitation than classic persistent excitation.
• When output maps are affine in the state, the method yields a linear regressor for the unknown parameter, simplifying estimation.
• Combining GPEBO with DREM allows finite-time convergence (FCT) under weak excitation assumptions.
• Applied to multimachine power systems (with lossy lines) and chemical-biological reactors, GPEBO achieves state observation in cases where traditional methods struggle, including a globally convergent solution for certain power-system configurations.
• The paper demonstrates both asymptotic and finite-time observer designs, with proofs provided for convergence properties.