Identification and adaptive multi-dimensional Taylor network control of single-input single-output non-linear uncertain time-varying systems with noise disturbances

In this paper, an adaptive control approach based on the multi-dimensional Taylor network (MTN) is proposed to control the non-linear uncertain time-varying systems with noise disturbances. MTNs are introduced to formulate adaptive filtering, non-linear identification and optimal control. First, an MTN filter is developed to eliminate the control interference and measurement noise, so that the model output without stochastic disturbance can be obtained. Then, an MTN identifier (MTNI) is so designed as to be capable of dynamic mapping and require fewer weights than traditional neural networks. On the basis of the above, the MTN controller (MTNC) is developed to realise the precise tracking control of the system. The non-linear uncertain time-varying system is identified by MTNI, which then provides sensitivity information of the plant to MTNC to make it adaptive. Furthermore, the skeletonisation algorithm is adopted to remove redundant inputs and redundant regression items from MTNI and MTNC for concise MTNs. Successful convergence and faster learning are guaranteed using the Lyapunov theorem, and the optimal learning rates are identified. Simulation results demonstrate that the proposed approach features its accurate identification, excellent tracking and better anti-interference capability for the adaptive real-time control of uncertain, stochastic and time-varying non-linear systems.