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Adaptive decentralized finite-time output tracking control for MIMO interconnected nonlinear systems with output constraints and actuator faults. (English) Zbl 1390.93044
Summary: In this work, we present a novel adaptive decentralized finite-time fault-tolerant control algorithm for a class of multi-input-multi-output interconnected nonlinear systems with output constraint requirements for each vertex. The actuator for each system can be subject to unknown multiplicative and additive faults. Parametric system uncertainties that model the system dynamics for each vertex can be effectively dealt with by the proposed control scheme. The control input gain functions of the nonlinear systems can be not fully known and state dependent. Backstepping design with a $$tan$$-type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, with the use of graph theory, finite-time convergence of the system output tracking error into a small set around zero is guaranteed for each vertex, while the time-varying constraint requirement on the system output tracking error for each vertex will not be violated during operation. An illustrative example on 2 interacting 2-degree-of-freedom robot manipulators is presented in the end to further demonstrate the effectiveness of the proposed control scheme.

##### MSC:
 93A14 Decentralized systems 93C40 Adaptive control/observation systems 93C35 Multivariable systems, multidimensional control systems 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations
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