Summary In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.

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Purpose The purpose of this paper is to propose a new control strategy based on adaptive inverse control aiming at high performance control of permanent magnet synchronous motor (PMSM). Design/methodology/approach This scheme adopts the vector control with double closed-loop structure and introduces a multi-dimensional Taylor network (MTN) inverse control method into velocity-loop. First, the invertibility of PMSM’s mathematical model is proved. Second, a novel dynamic network (MTN) is presented, which has simple structure and faster computing speed. Besides, to realize the high-precision speed control, three MTNs are applied to achieve system modeling, inverse modeling and noise disturbance elimination which correspond to the function of the adaptive identifier, adaptive feed-forward controller and nonlinear adaptive filter, respectively. Findings This scheme is designed with the full consideration of the PMSM’s particularity. For the PMSM’s unknown dynamics and time-varying characteristics, the variable forgetting factor recursive least squares algorithm is adopted to improve identification ability, and the weight-elimination algorithm is used to remove redundant regression items in the MTN identifier and inverse controller. In addition, to reduce the influence arose from measurement noise and other stochastic factors, adaptive MTN filter is introduced to eliminate noise disturbance. The computational results show that the proposed scheme possesses excellent control performance and better robustness against the load disturbance. Originality/value The paper presents a new inverse control scheme with MTN which is practical and flexible, and the MTN-based control system is very promising for real-time applications.