Empirical Model Reduction of Controlled Nonlinear Systems

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-Lo`eve 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

Model reduction, centering, and the Karhunen-Loeve expansion

We propose a new computationally efficient modeling method that captures a given translation symmetry in a system. To obtain a low order approximate system of ODEs, prior to performing a 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

Controlled hybrid system safety verification: advanced life support system testbed

In this paper we demonstrate the use of Barrier Certificates as a method to verify safe performance of a hybrid Variable Configuration CO_2 Removal (VCCR) system. We designed a simple nonlinear feedback controller that tracks a desired CO_2 profile, while ensuring that the CO_2 and O_2 concentrations stay within acceptable limits. Though the controller and its switching rules are simple, we do not have a closed form expression for the equilibrium sets of the closed loop hybrid system, and hence Lyapunov stability analysis and computation of region of attraction are impossible. We used Sum-Of-Squares programming approach to construct and verify that our control law provides safe functionality of VCCR system

A subspace approach to balanced truncation for model reduction of nonlinear control systems

In 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