Frequency domain synthesis of optimal inputs for online identification and adaptive control

The authors formulate an input design problem for choosing proper inputs for use in single-input-single-output (SISO) online identification and model reference adaptive control algorithms. When the convergence rate divided by the adaptation gain is optimized for this adaptation gain going to zero, characterization of the optimal inputs is given in the frequency domain and is arrived at through the use of averaging theory. An expression for what is termed the average information matrix is derived and its properties are studied. To solve the input design problem, the authors recast the design problem in the form of an optimization which maximizes the smallest eigenvalue of the average information matrix over power constrained signals. A convergent numerical algorithm is provided to obtain the optimal solution