Adaptive Post-Linearization of Dynamic Nonlinear Systems With Artificial Neural Networks

Abstract

We have applied tailor-made neural networks to the post-linearization of nonlinear systems containing memory. The problems we address involve tracking systems that contain linear dynamics together with memoryless, nonlinear sensors and amplifiers. In general, the goal is to accurately infer a system’s inputs based only on the system’s outputs, which have been corrupted by nonlinear components. The linearizing neural network is trained to emulate the inverse of the Volterra operator which describes the nonlinear system. In implementation, the network estimates the original input signal from the system’s output sequence. The post-linearizing network architecture is determined from an approximate model of the system to be linearized. The network is trained with test signals that excite the tracking system over its domain of operation and expose much of its nonlinear behavior. Network weights and biases are adjusted using a novel algorithm, batch backpropagation-through-time (BBTT). This paper presents a test case involving a sensor with an input-output relation similar to that of a scaled dc SQUID. The sensor and amplifier nonlinearities are embedded within a fourth-order dynamic system with negative feedback. The problem is generally formulated and we discuss the application of our methodology to a variety of nonlinear sensing and amplification systems.