Frequency Domain Synthesis of Optimal Inputs for Adaptive Identification and Control

In this paper, we precisely formulate the input design problem of choosing proper inputs for use in SISO Adaptive Identification and Model Reference Adaptive Conrol algorithms. 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 we call the average information matrix is derived and its properties are studied. To solve the input design problem, we recast the design problem in the form of an optimization problem which maximizes the smallest eigenvalue of the average information matrix over power constrained signals. A convergent numerical algorithm is provided to obtain the global optimal solution. In the case where the plant has unmodelled dynamics, a careful study of the robustness of both Adaptive Identification and Model Reference Adaptive Control algorithms is performed using averaging theory. With these results, we derive a bound on the frequency search range required in the design algorithm in terms of the desired performance.