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Adaptive Estimation for a Class of nonlinearly parameterized dynamical systems

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2014年第10期59卷 2818-2824页

作者： Adetola, Veronica Guay, Martin Lehrer, Devon United Technol Res Ctr E Hartford CT 06118 USA Queens Univ Dept Chem Engn Kingston ON K7L 3N6 Canada

The technical note presents a new technique for the adaptive parameter estimation in nonlinear parameterized dynamical systems. The technique proposes an uncertainty set-update approach that guarantees forward invariance of the true value of the parameters. In addition, it is shown that in the presence of sufficiently exciting state trajectories, the parameter estimates converge to the true values and the uncertainty set vanishes around the true value of the parameters. The set-based approach is also shown to identify when the parameter estimates are biased. Two simulation examples are presented that demonstrate the effectiveness of the technique.

关键词： nonlinear parameterized dynamical systems

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A-Posteriori Error Estimation for parameterized Kernel-Based systems

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IFAC Proceedings Volumes 2012年第2期45卷 763-768页

作者： Daniel Wirtz Bernard Haasdonk Institute for Applied Analysis and Numerical Simulation University of Stuttgart 70569 Stuttgart Pfaffenwaldegger 57 – Germany

Abstract This work is concerned with derivation of fully offline/online decomposable efficient a-posteriori error estimators for reduced parameterized nonlinear kernel-based systems. The dynamical systems under consideration consist of a nonlinear, time- and parameter-dependent kernel expansion representing the system's inner dynamics as well as time- and parameter-affine inputs, initial conditions and outputs. The estimators are established for a reduction technique originally proposed in Phillips et al. (2003) and are an extension of the estimators derived in Wirtz and Haasdonk (2012) to the fully time-dependent, parameterized setting. Key features for the efficient error estimation are to use local Lipschitz constants provided by a certain class of kernels and an iterative scheme to balance computation cost against estimation sharpness. Together with the affinely time/parameter-dependent system components a full offline/online decomposition for both the reduction process and the error estimators is possible. Some experimental results for synthetic systems illustrate the efficient evaluation of the derived error estimators for different parameters.

关键词： nonlinear parameterized dynamical systems model reduction kernel methods a-posteriori error estimates offline/online decomposition subspace projection

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