Generalized-inverse approach to model following control for nonlinear mechanical systems and its extensions

Extensions of the results of the model reference adaptive control (MRAC) to nonlinear systems have been attempted. In particular, designs of MRAC for nonlinear mechanical systems, such as a manipulator and or an inverted pendulum, have been studied with much interest. For this purpose, we propose a design method for model following control systems (MFCS) as a first step towards MRACS for nonlinear mechanical systems affine in the control. First, we consider Hirschorn´s algorithm concerning the invertibility of nonlinear control systems. However, it is difficult to apply the algorithm directly to the control objective with the small number of inputs. Secondly, we propose an alternative MFCS design, based on a kind of generalized-inverse technique which makes it possible to assign any following characteristics. Thirdly, we consider an example of the application to the inverted pendulum to demonstrate the feasibility and efficiency of the proposed control design strategy. Finally, we discuss two extensions of the present method to both cases of modeling error and of non-affine type control