Study on different Numerical Optimization Strategies to compute the D-optimal Input Design for a simple Wiener system

For linear system the problem of optimal input design is considered to be solved. However, the extension to nonlinear system is not trivial and till now, only finite short memory system can be handled. Since a theoretical framework to describe the optimal input for nonlinear systems with infinite memory is still lacking, we follow a more pragmatic approach and resort to numerical optimization. In this work we evaluate different optimization strategies in order to compute the D-optimal Input Design for a simple Wiener system that consists of a linear second order system and third order polynomial nonlinearity. Special attention will go two distinct strategies. The first, referred to a Brute Force Optimization, directly optimizes the time samples of the input sequence. For the considered class of systems this approach results in a nonlinear and non-convex optimization, which is sensitive to the parameters settings of the optimization. The second strategy is called the Optimal Naïve Dictionary Design and constructs an input sequence that consists out of a concatenation of ‘elementary’ designs from a predefined set of signals called the dictionary.