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Summary In this paper, a novel adaptive control scheme is proposed based on radial basis function neural network (RBFNN). The considered system is deduced by the structure of RBFNN with nonzero time‐varying parameter that installed in the fore‐end and terminal of RBFNN. With this structure and the Taylor expansion of any smooth continuous nonlinear function, a universal approximation of RBFNN is addressed according to the analysis of the character of continuous homogenous function and the Euler's theorem. The approximation accuracies can be adjusted online by the nonzero time‐varying parameter in the device with the degree of continuous homogenous function, which expand the semiglobally stability to global stability over conventional neural controller design approaches. Based on the theory analysis of barrier Lyapunov function, the violation of time‐varying constraints can be subjugated without wrecked. Finally, simulation results are carried out to verify the effectiveness by the design methods.

A novel fuzzy control scheme with adaptation algorithms is developed for robot manipulators' system. At the beginning, one adjustable parameter is introduced in the fuzzy logic system, the robot manipulators system with uncertain nonlinear terms as the master device and a reference model dynamic system as the slave robot system. To overcome the limitations such as online learning computation burden and logic structure in conventional fuzzy logic systems, a parameter should be used in fuzzy logic system, which composes fuzzy logic system with updated parameter laws, and can be formed for a new fashioned adaptation algorithms controller. The error closed-loop dynamical system can be stabilized based on Lyapunov analysis, the number of online learning computation burdens can be reduced greatly, and the different kinds of fuzzy logic systems with fuzzy rules or without any fuzzy rules are also suited. Finally, effectiveness of the proposed approach has been shown in simulation example.

One of the amazing abilities of fuzzy logic systems or neural networks is their ability to approximate unknown certainties. When nonlinear systems possess multiple variables, however, the process of the adaptive fuzzy or neural network online control becomes difficult. In this paper, we will introduce the extended partition of unity (EPU), composed of scalars and saturators, to address this problem. The merit of the suggested design scheme is that the construction of the partition of unity and the design of adaptive laws are separate. This means the proposed design method only adjusts the outputs of EPU and one update law, even in nonlinear systems with multiple variables. Therefore, this new method of EPU leads to easier selection of basis functions, reduces the number of adaptive laws, has greater robustness, and is suitable for different kinds of universal approximators. Finally, a numerical example is given to illustrate the effectiveness of the approach.

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