SUMMARYIn this paper, we introduce a new method of model reduction for nonlinear control systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix computations, and we show that when it is applied to linear systems it results in the usual balanced truncation. For nonlinear systems, the method makes use of data from either simulation or experiment to identify the dynamics relevant to the input}output map of the system. An important feature of this approach is that the resulting reduced-order model is nonlinear, and has inputs and outputs suitable for control. We perform an example reduction for a nonlinear mechanical system.
In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems results in the usual balanced truncation. For nonlinear systems, the method makes used of the Karhunen-Loève decomposition of the state-space, and is an extension of the method of empirical eigenfunctions used in fluid dynamics. We show that the new method is equivalent to balanced-truncation in the linear case, and perform an example reduction for a nonlinear mechanical system.
The problem of making the Kalman filter robust is considered in the paper. Proceeding from the equivalence between the Kalman filter and the least squares regression problem, a statistical approach named M -estimation is suggested to resolve the regression problem robustly. Since the derived robust M -filters do not have an attractive recursive form, the possibility is proposed of designing real-time estimators based on the general formulation of the robust stochastic approximation algorithm and step-by-step optimization with respect to the weighting matrix combined with suitable approximations. Results of simulation demonstrating the robustness of the proposed estimators are also included.
We propose a new computationally efficient modeling method that captures existing translation symmetry in a system. To obtain a low order approximate system of ODEs prior to performing Karhunen Loeve expansion we process the available data set using a "centering" procedure. This approach has been shown to be efficient in nonlinear scalar wave equations.
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