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Fault-Tolerant Funnel Control for Uncertain Linear Systems

We study adaptive fault-tolerant tracking control for uncertain linear systems. Based on recent results in funnel control, and the time-varying Byrnes–Isidori form, we develop a low-complexity model-free controller that achieves prescribed performance of the tracking error for any given sufficiently smooth reference signal. Within the considered system class, we allow for more inputs than outputs as long as a certain redundancy of the actuators is satisfied. An important role in the controller design is played by the controller weight matrix. This is a rectangular input transformation chosen such that in the resulting system, the zero dynamics, which are assumed to be uniformly exponentially stable, are independent of the new input. We illustrate the fault-tolerant funnel controller by an example of a linearized model for the lateral motion of a Boeing 737 aircraft.