Implicit Controller for Classes of Nonlinear Systems

In this paper, implicit controls are investigated for nonaffine systems in pure-feedback form and affine systems in strict-feedback form. While control system design for general unknown nonaffine nonlinear systems needs further investigation, elegant control designs are presented for known systems and systems with unknown scalar parametrization. For affine nonlinear systems, though it can be shown that the resulting control laws are equivalent to that obtainable based on feedback linearization control, the approaches are fundamentally different. The most important differences/features are that (i) the implicit control is a function of both states and control signals, rather than states alone, and (ii) the resulting sampled-data systems are different, subsequently, their stability results are different. Simulation studies are carried out to show the validity of the proposed design method.