CONTROL OF SYSTEMS WITH INPUT NONLINEARITIES AND UNCERTAINTIES: AN ADAPTIVE APPROACH

Although many of today’s nonlinear control design algorithms assume the system dynamics to be affine in the control input, this often does not hold in practice. A remedy for this is to instead design a control law in terms of some other entity that satisfies the structural assumptions of the design method. In this contribution we discuss how to realize such a virtual con-trol law in terms of the actual control variable. Given a nomi-nal static invertible model of the mapping between the two, the true mapping is assumed to differ from the model by a con-stant bias. Two ways of how to estimate this bias on-line and use it for feedback are proposed. One of them corresponds to adaptive backstepping, the other one is an observer based ap-proach. In both cases we investigate how to guarantee closed loop stability when the estimate is used for feedback.