Adaptive Output Feedback Control of Nonlinear Systems: A Dynamic-Gain Scaling Approach.

In this technical note, the problem of global asymptotical state regulation is considered for a class of nonlinear systems with unknown measurement sensitivity and polynomial growth constraint. A new dynamic output feedback controller with dual nonidentification adaptive gains is proposed by means of a novel constructive solution of a pair of matrix inequalities including an unknown time-varying parameter. It mainly reduces the conservatism of the existing results from two aspects: 1) the unknown measurement sensitivity is allowed to be nondifferentiable with its upper bound unknown; 2) in the presence of a large measurement error, the growth rate of nonlinearities is relaxed to be x(1)-polynomial containing an unknown parameter. Furthermore, the initial value and increasing rate of dynamic gains can be set to any small positive real number, which avoids somewhat the peaking phenomenon of classical high-gain observer. Notably, the control approach of this note is nonbackstepping with the design parameters determined easily by a set of explicit constrained conditions.