A dynamical adaptation algorithm for time-variant systems (Q1881931)

The authors propose a dynamic adaptation method for time-invariant systems with linear models of residual and parametric drift. The control system as designed includes a combined control law and adaptation algorithm. Unlike many approaches to adaptation, the authors allow the possibility of fast parameter variation. To illustrate their approach, they restrict their attention to the simplest case of a time-invariant system with an unknown parameter. They assume that the control problem is reduced to the stabilization of the model of signal residuals of the form \(\dot e=Ae+b(u+z\theta)\) where \(e\in\mathbb{R}^n\) is the vector of residuals, \(u\) is a scalar control input, \(z=z(t)\) is some unknown excitation function, \(\theta=\theta(t)\) is the unknown parameter whose dynamics are described by a parameter drift model, and \(A\) and \(b\) are matrices of appropriate dimensions. In the absence of additional perturbations, the authors' approach produces stable models of signal and parameter residuals with a relatively simple dynamic algorithm. Simulation results illustrate the authors' methods with parameter variation as either a linear or a sinusoidal function of time.