Exponentially Stable MRAC of MIMO Switched Systems with Matched Uncertainty and Completely Unknown Control Matrix

Abstract

In this paper an attempt is made to extend the concept of the exponentially stable adaptive control to one class of multi-input-multi-output (MIMO) plants with matched nonlinearity and unknown piecewise constant parameters. Within the intervals between two consecutive parameter switches, the proposed adaptive control system ensures: 1) exponential convergence to zero of the parameter and reference model tracking errors, 2) the monotonicity of the control law adjustable parameters. Both properties are guaranteed in case the regressor is finitely exciting somewhere inside each of such intervals. Compared to the existing methods, the proposed one is applicable to systems with unknown switching signal function and completely unknown control matrix. The theoretical results are supported by the numerical experiments.

Sensorless Adaptive Vibration Suppression in Two-Mass Systems via Joint Estimation of Controller Parameters and System States

“…The elements of the sequence can be defined in different ways. In [32], using a special detection scheme, it is proposed to reset the filter states to zero at time instants of the system parameters switch. In [33] it is proposed to reset the filters when the reference value is changed.…”

“…Based on the results of Lemma 1 and equation ( 32), the solution of the stated problem can be divided into two main steps. At the first one, in order to implement additional feedback K x (θ) x p (t), it is necessary to obtain estimates of states x p (t) with the help of the measurable regression equation (32). At the second step, it is necessary to transform the regression equation w.r.t.…”

“…Thus, both the states x p (t) observer and the law of controller parameters κ (θ) identification will be derived on the basis of the measurable regression equation (32) w.r.t. parameters θ, which is obtained by transformations ( 23)-( 26), ( 31), (32) and has a bounded from zero scalar regressor M θ (t) for all t ≥ t e .…”