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This paper presents a controller design and optimization framework fornonlinear dynamic systems to track a given reference signal in the presence ofdisturbances when the task is repeated over a finite-time interval. This novelframework mainly consists of two steps. The first step is to design a robustlinear quadratic tracking controller based on the existing control structurewith a Youla-type filter $\tilde Q$. Secondly, an extra degree of freedom: aparameterization in terms of $\tilde Q$, is added to this design framework.This extra design parameter is tuned iteratively from measured tracking costfunction with the given disturbances and modeling uncertainties to achieve thebest transient performance. The proposed method is validated with simulationplaced on a Furuta inverted pendulum, showing significant tracking performanceimprovement.

Robust Tracking Control for Nonlinear Systems: Performance optimization via extremum seeking