A data-driven method to design reference tracking controllers for nonlinear systems is presented. The technique does not derive explicitly a model of the system, rather it delivers directly a time-varying state-feedback controller by combining an on-line and an off-line scheme. Like in other on-line algorithms, the measurements collected in closed-loop operation are exploited to modify the controller in order to improve the tracking performance over time. At the same time, a predictable closed-loop behavior is guaranteed by making use of a batch of available data, which is a feature of off-line algorithms. The feedback controller is parameterized with kernel functions and the design approach exploits results in set membership identification and learning by projections. Under the assumptions of Lipschitz continuity and stabilizability of the system's dynamics, it is shown that if the initial batch of data is informative enough, then the resulting closed-loop system is guaranteed to be finite gain stable. In addition to the main theoretical properties of the approach, the design algorithm is demonstrated experimentally on a water tank system.
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