Adaptive control systems with augmented errors
A survey on the following problem is presented. Consider the class of time-invariant, linear, single-input single-output systems \[ A\bigl({\textstyle{d\over dt}}\bigr)y(t)=k B\bigl( {\textstyle{d\over dt}}\bigr)u(t), \] where \(A(\cdot)\) and \(B(\cdot)\) are monic polynomials with real coefficients and \({d\over dt}\) denotes the usual differential operator. The coefficients of the polynomials are unknown, the only assumptions made are: \(B(s)\) is Hurwitz, \(k\) is positive, and the degrees of the polynomials \(A(s)\) and \(B(s)\) are known. The control objective is to find an adpative controller such that \(y(t)-y_m(t)\) tends to 0 as \(t\to\infty\). Here \(y_m(t)\) denotes the output of the reference model \[ A_m\bigl({\textstyle{d\over dt}}\bigr)y_m(t)= k_mB_m\bigl({\textstyle{d\over dt}}\bigr)u(t), \] where \(A_m(\cdot)\) and \(B_m(\cdot)\) are monic polynomials with the same degree as \(A\) and \(B\). Attention is given to the augmentation of the tracking error and improvements of identification properties and the rate of convergence of adaptation algorithms.
scientific article; zbMATH DE number 922170
scientific article