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Adaptive tracking-control synthesis for functionally uncertain systems via modified backstepping

The paper is concerned with a problem of adaptive tracking system control synthesis. It is assumed that a nonlinear object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that a nonlinear state feedback plus parameter adaptation are able to ensure its asymptotic stability. The proposed controller design is based on modified adaptive backstepping method. In this approach, as opposite to the standard backstepping, the design process has been reduced to a single iteration, which enables avoiding complicated recursive procedure. An extra task here is to find a control synthesis of linear-like, chained system. The solution of the last problem in general framework is also presented. The obtained thereby controller has several attractive features of both the feedback linearization and backstepping schemes.