Composite Model Reference Adaptive Control with Parameter Convergence Under Finite Excitation

Abstract

A new parameter estimation method is proposed in the framework of composite model reference adaptive control for improved parameter convergence without persistent excitation. The regressor filtering scheme is adopted to perform the parameter estimation with signals that can be obtained easily. A new framework for residual signal construction is proposed. The incoming data is first accumulated to build the information matrix, and then its quality is evaluated with respect to a chosen measure to select and store the best one. The information matrix is built to have full rank after sufficient but not persistent excitation. In this way, the exponential convergence of both tracking error and parameter estimation error can be guaranteed without persistent oscillation in the external command which drives the system. Numerical simulations are performed to verify the theoretical findings and to demonstrate the advantages of the proposed adaptation law over the standard direct adaptation law.

Integral concurrent learning: Adaptive control with parameter convergence using finite excitation

“…However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. Recently, results in other works 14-18 have shown convergence using an interval or finite excitation condition, although they either require measurements of state derivatives (see, eg, the work of Pan and Yu 15 ), require determining the analytical Jacobian of the regressor (see, eg, the work of Pan et al 14 ), or are developed in a model reference adaptive control context, 16,17,[19][20][21] which essentially assume that desired trajectories are generated from an LTI system and may rely on a matching condition, rather than the general nonlinear systems considered here without such assumptions. Data recorded online is exploited in the adaptive update law, and numerical integration is used to circumvent the need for state derivatives.…”

Composite adaptive control with fast convergence for multilayer neural network

“…Remark Apart from experience replay, several other techniques can be used to relax the PE condition, such as concurrent learning and composite learning . These methods apply historical data to update the weights.…”

“…Furthermore, the condition of persistent excitation (PE) needs to be satisfied to guarantee parameter convergence in CAC, but this requirement is very strict and often infeasible in the online monitoring of practical control systems . The PE condition can be attenuated by employing concurrent learning and composite learning . However, given the characteristics of the nonlinear model, the techniques are difficult to apply due to the complicated computing of the Fisher information matrix of the nonlinear approximator.…”

On the almost sure central limit theorem for ARX processes in adaptive tracking

“…We now focus our attention on the average costs and estimation errors sequences (C n (m)) and (G n (m)), respectively given by (7) and (8). First of all, it was proven in lemma 3 in the work of Bercu and Vázquez 15 that matrix L is positive definite.…”

“…Recently, Cho et al 8 proposed a new parameter estimation method in the framework of composite model reference adaptive control to improve parameter estimation without persistent excitation. Recently, Cho et al 8 proposed a new parameter estimation method in the framework of composite model reference adaptive control to improve parameter estimation without persistent excitation.…”