Distributed Strategies for Nonlinear System Identification

Abstract

Nonlinear systems, existing in almost all industrial processes, can be customarily classified into lumped parameter systems (LPSs) and distributed parameter systems (DPSs). Modeling of these systems plays a vital role in the modern development of industrial technologies. Therefore, the study of nonlinear systems and modeling their dynamical behavior are important for prediction, control, and optimization.
This dissertation is concerned with the development of distributed modeling for LPSs and DPSs to embrace the benefits of distributed signal processing. It is worth revealing
that the distributed estimation, an application of wireless sensor network (WSN), promises to administer a large volume of data movement among sources, data centers, or processing elements. It can precisely estimate the required parameters using the discrete data samples collected across the wireless sensor nodes. When it comes to distributed modeling of nonlinear systems, it is a bit difficult task due to the presence of nonlinear dynamics. The modeling even becomes more difficult especially for nonlinear DPSs because of their spatio-temporally coupled dynamics and infinite dimensionality. But, it is primarily required for real-time prediction, control, and optimization. Volterra-Laguerre model and Wiener block-structured model are two among the extensively used nonlinear models that are solicitously considered in this dissertation due to their well-established methodology and ease of understanding. Traditional Volterra model limits its practical usage due to high parameter complexity. Hence, it poses an illconditioned problem while modeling highly nonlinear systems. To overcome this limitation, Volterra kernels are approximated using Laguerre functions giving rise to Volterra-Laguerre model. The distributed algorithms are developed to identify Volterra-Laguerre and Wiener models that are used for distributed modeling of LPSs. A simple yet powerful optimization method called alternating direction method of multipliers (ADMM) is employed to address the problem of distributed optimization. In distributed optimization, the global objective function is collaboratively optimized by the nodes of the network through operating on their local objective functions and communicating with their neighboring nodes. The algorithms developed to model LPSs are successfully applied to a causal second-order nonlinear system. These algorithms are then extended to identify DPSs that lead to distributed spatio-temporal Volterra-Laguerre modeling and Wiener modeling. These approaches involve distributed optimization of global objective function containing the sum of two cost functions, where one represents the KL decomposition or PCA problem for time-space separation and other represents the temporal modeling problem. The global problem is reformulated as a multiple constrained separable optimization problem. Then, the problem is optimized in a distributed fashion using coordinate descent in coalescing with ADMM. Simulation studies are carried-out to demonstrate the potential of the proposed algorithms.