Wavelets as a tool for systems analysis and control

This survey presents the broad range of research on using wavelets in the analysis and design of dynamic systems. Though wavelets have been used with all types of systems, the major focus of this survey is mechanical and electromechanical systems in addition to their controls. However, the techniques presented can be applied to any category of dynamic systems such as economic, biological, and social systems. Wavelets can be classified into three different types: orthogonal, biorthogonal, and pseudo, all of which are employed in dynamic systems engineering. Wavelets-based methods for dynamic systems applications can be divided into vibrations analysis and systems and control analysis. Wavelets applications in vibrations extend to oscillatory response solutions and vibrations-based systems identification. Also, their applications in systems and control extend to time–frequency representation and modeling, nonlinear systems linearization and model reduction, and control design and control law computation. There are serious efforts within systems and control theory to establish time–frequency and wavelets-based Frequency Response Functions (FRFs) parallel to the Fourier-based FRFs, which will pave the road for time-varying FRFs. Moreover, the natural similarity of wavelets to the representation of neural networks allows them to slip into neural-networks-based and fuzzy-neural-networks-based controllers. Additionally, wavelets have been considered for applications in feedforward and feedback control loops for computation, analysis, and synthesis of control laws.