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 control law in terms of the actual control variable. Given a nominal static invertible model of the mapping between the two, the true mapping is assumed to differ from the model by a constant 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 approach. In both cases we investigate how to guarantee closed loop stability when the estimate is used for feedback.