Adaptive Regulation of Discrete-Time Nonaffine Systems With Parametric Uncertainty

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This article investigates the problem of global adaptive stabilization for discrete-time nonlinearly parameterized systems with nonaffine inputs. Using the notion of passivity and the idea of small bounded feedback, we present a discrete-time adaptive controller that globally adaptively stabilizes a class of nonaffine systems with unknown parameters, under the assumptions that the unforced dynamics are stable and the controllabilitylike rank conditions hold. The latter is shown to be characterizable by the vector fields $f(x,0,\theta)$ and $\frac{\partial f}{\partial u}(x, 0, \theta)$ , together with their “Lie derivatives” and “Lie brackets” in discrete time.