Local coefficients of Walsh functions and their applications to model reference adaptive control

In the existing method of Walsh functions (WF), a major disadvantage is that the process signals need to be recorded prior to obtaining their Walsh spectral expansions. This paper proposes a novel method of local coefficients of WF to overcome this shortcoming. An approximate algorithm of local coefficients is developed. Several properties of local coefficients and error analysis of the method are also investigated. By introducing a new delay operational matrix, recursive integral equations based on the local coefficients of WF are formulated. Using the new method to deal with process signals, it is shown that an integral equation can be directly solved in recursion with process data by WF. This method has successfully been used to update controller parameters for model reference adaptive control of a first-order system.