A neural-network based technique for modelling and LPV control of an arm-driven inverted pendulum

This paper presents a generalization of a recurrent neural-networks (RNNs) approach which was proposed previously in [1], together with stability and identifiability proofs based on the contraction mapping theorem and the concept of sign-permutation equivalence, respectively. A slight simplification of the generalized RNN approach is also proposed that facilitates practical application. To use the RNN for linear parameter-varying (LPV) controller synthesis, a method is presented of transforming it into a discrete-time quasi LPV model in polytopic and linear fractional transformation (LFT) representations. A novel indirect technique for closed-loop identification with RNNs is proposed here to identify a black box model for an arm-driven inverted pendulum (ADIP). The identified RNN model is then transformed into a quasi-LPV model. Based on such LPV models, two discrete-time LPV controllers are synthesized to control the ADIP. The first one is a full-order standard polytopic LPV controller and the second one is a fixed-structure LPV controller in LFT form based on the quadratic separator concept. Experimental results illustrate the practicality of the proposed methods.