No abstract

Piecewise affine systems constitute a popular framework for the approximation of non-linear systems and the modelling of hybrid systems. This paper addresses the recursive subsystem estimation in continuoustime piecewise affine systems. Parameter identifiers are extended from continuous-time state-space models to piecewise linear and piecewise affine systems. The convergence rate of the presented identifiers is improved further using concurrent learning, which makes concurrent use of current and recorded measurements. In concurrent learning, assumptions on persistence of excitation are replaced by the less restrictive linear independence of the recorded data. The introduction of memory, however, reduces the tracking ability of concurrent learning because errors in the recorded measurements prevent convergence to the true parameters. In order to overcome this limitation, an algorithm is proposed to detect and remove erroneous measurements at run-time and thereby restore the tracking ability. Detailed examples are included to validate the proposed methods numerically.

In this paper, we enhance a recently proposed method for adaptive identification of piecewise affine systems by the use of concurrent learning. It is shown that the concurrent use of recorded and instantaneous data leads to exponential convergence of all subsystem parameters under verifiable conditions on the recorded data. A key advantage of the proposed method is that linear independence of the recorded data is sufficient, compared to the persistence of excitation assumed by previous adaptive parameter identifiers. Furthermore, the procedure tremendously improves the performance of adaptive identification for piecewise affine systems that previously suffered from slow convergence. 53rd IEEE Conference on Decision and Control