Adaptive λ-tracking-control for relative degree two systems with application to bio-inspired sensors

This paper deals with the (adaptive) control of a sensory system, which is inspired by biological ideas concerning the behaviour of a tactile hair or sensillum. The cells for reception of vibrations adjust their sensibility to a continuing excitement, such that this permanent excitation of the whole system tends to the rest position. Hence, this biological paradigm demonstrates a fundamental principle: adaption. In general, one cannot expect to have complete information about a sophisticated mechanical or biological system, but instead only structural properties (e.g. minimum phase condition, strict relative degree) are known. Therefore, the method of adaptive control is chosen in this paper. The aim is to design a universal adaptive controller, which learns from the behaviour of the system, so automatically adjusts its parameters and achieves a pre-specified control objective. Since we deal with a non-linearly perturbed multi-input, multi-output system, which is not necessarily autonomous, particular attention is paid to the lambda-tracking control objective. Simple adaptive servomechanisms, which achieve tracking of a given reference signal for any pre-specified accuracy (tracking-error) lambda, are introduced. We stress that the introduced adaptive controllers consist of very simple feedback mechanisms and adaptation rules. These controllers are only based on information about the output of the system - no knowledge of system parameters is required.