Local Adaptive Observer for Linear Time-Varying Systems with Parameter-Dependent State Matrices

Abstract

We present an adaptive observer for linear timevarying systems whose state matrix depends on unknown parameters. We first assume that the state matrix is affine in these parameters. In this case, the proposed observer generates state and parameter estimates, which exponentially converge to the plant state and the true parameter, respectively, provided a persistence of excitation condition holds and the unknown parameters lie in a neighborhood of some known nominal values. Hence, some prior knowledge on the unknown parameters is required, but not on the state. We then modify the adaptive observer and its convergence analysis to systems whose state matrix is smooth, instead of being affine, in the unknown parameters. The convergence is approximate, and no longer exponential, in this case. An example is provided to illustrate the results, for which the required distance between the unknown parameters and their nominal values is investigated numerically.

Novel Adaptive Extended State Observer for Dynamic Parameter Identification with Asymptotic Convergence

“…Among others, adaptive observers, which support simultaneous estimation of the system parameters and their state, can be distinguished as a separate category. Solutions have been proposed for linear time-invariant [11][12][13], linear time-varying systems [14][15][16], state-affine [17], or fully nonlinear systems [18][19][20][21].…”