Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on the model representation. To this end, this work considers the linear fractional representation framework. In a linear fractional representation the linear dynamics and the system nonlinearities are modeled by two separate blocks that are interconnected with one another. This results in a structured, yet flexible model structure. Estimating such a model directly from input-output data is not a trivial task as the involved optimization is nonlinear in nature. This paper proposes an initialization scheme for the model parameters based on the best linear approximation of the system and shows that this approach results in high quality models on a set of benchmark data sets.
This paper describes the LPVcore software package for MATLAB developed to model, simulate, estimate and control systems via linear parameter-varying (LPV) input-output (IO), state-space (SS) and linear fractional (LFR) representations. In the LPVcore toolbox, basis affine parameter-varying matrix functions are implemented to enable users to represent LPV systems in a global setting, i.e., for time-varying scheduling trajectories. This is a key difference compared to other software suites that use a grid or only LFR-based representations. The paper contains an overview of functions in the toolb…
The identification of black-box nonlinear state-space models requires a flexible representation of the state and output equation. Artificial neural networks have proven to provide such a representation. However, as in many identification problems, a nonlinear optimization problem needs to be solved to obtain the model parameters (layer weights and biases). A well-thought initialization of these model parameters can often avoid that the nonlinear optimization algorithm converges to a poorly performing local minimum of the considered cost function. This paper introduces an improved initializatio…
ReLU (rectified linear units) neural network has received significant attention since its emergence. In this paper, a univariate ReLU (UReLU) neural network is proposed to both modelling the nonlinear dynamic system and revealing insights about the system. Specifically, the neural network consists of neurons with linear and UReLU activation functions, and the UReLU functions are defined as the ReLU functions respect to each dimension. The UReLU neural network is a single hidden layer neural network, and the structure is relatively simple. The initialization of the neural network employs the de…
Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data
Department of Computer Science and Engineering, The Chinese University of Hong Kong（香港中文大学计算机科学与工程系）；School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电气与计算机工程学院）；School of Mechanical Engineering, Purdue University（帕克大学机械工程系）；Elmore Family School of Electrical and Computer Engineering, Purdue University（帕克大学埃尔莫家族电气与计算机工程学院）
System identification uses measurements of a dynamic system's input and output to reconstruct a mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most of the systems around us exhibit some form of nonlinear behavior, nonlinear system identification techniques are the tools that will help us gain a better understanding of our surroundings and potentially let us improve their performance. One model that is often used to represent nonlinear systems is the polynomial NARX model, an equation error model where the output is a polynomial funct…
Identification of parameterized gray-box state-space systems: from a black-box linear time-invariant representation to a structured one: detailed derivation of the gradients involved in the cost functions
