Stability (learning theory)

Physics

Control engineering

Settling time

Nonlinear system

Mathematics

Mathematical optimization

Machine learning

Engineering

Step response

Mathematical analysis

Artificial intelligence

Fuzzy control system

Control (management)

Computer science

Fixed point

Quantum mechanics

Control theory (sociology)

Fuzzy logic

Upper and lower bounds

IEEE Transactions on Cybernetics

Fixed-time tracking control is considered for a class of nonlinear systems in this article. Different from the conventional literature on fixed-time control studies, in this article, the nonlinearities of systems are all completely unknown. Fuzzy-logic systems are utilized to model these unknown nonlinearities. To deal with the fixed-time control under the approximation errors, three steps are taken. First, a new criterion of fixed-time stability is developed; second, a new fixed-time control scheme is proposed, which is different from the existing adaptive design method; and third, to analyze the fixed-time stability of the system, two novel inequalities are established. It shows that the proposed fuzzy control scheme can guarantee system performance in a fixed time, and the upper bound of the settling time only depends on the design parameters.

Fixed-Time Fuzzy Control for a Class of Nonlinear Systems