Stability analysis for mobile robots with different time-scales based on unsupervised competitive neural networks

The dynamics of complex neural networks modelling self-organized process in cortical maps, like unsupervised competitive neural networks (UCNN), are based on the standard competitive learning law to determine the best-matching representant among all neurons for a given input. However, UCNNs include aspects of long and short-term memory, which are characterized by an equation of neural activity as fast part and an equation of neural synaptic modification as a slow part. For close-loop systems of mobile robots with different time-scales UCNNs can be used to represent the violation of kinematic constraints (like neural activity) and generalized coordinates (like synaptic modifications). Furthermore, UCNNs can act as powerful preprocessors of other neural networks with supervised learning because the unsupervised learning part usually has low computational effort. In this way, the overall computational effort will be considerably reduced. The present work uses the mutual interference between neuron and unsupervised learning of an UCNN in order to analyse the local and global asymptotic stability of mobile robots that not exactly satisfying kinematic constraints. To validate the proposed analysis the equilibrium point of UCNN model will be mathematically analysed by using quadratic-type Lyapunov functions and compared with a model based on a fully supervised learning rule. The results shows that the model based on UCNN converges toward a small ball of the origin with a better performance than the model based on a fully supervised learning rule.