2018 Volume 11 Issue 6 Pages 477-485
A generic control method is proposed for the non-square systems where the number of system inputs is not equal to that of the states. The non-square system to be controlled is first restructured in form of the combination of a square system and the variation from the original non-square system. This variation term is treated as a time-varying uncertainty to the restructured square system. Thus the stabilization for a non-square system is reformulated as an adaptive control problem for a square system. In this paper we address this adaptive control problem by applying the function approximation technique. Specifically, we can parameterize the variation with a chosen basis function weighted by unknown constant parameters. Then we define an update law such that the parameters of the weighted basis function can be automatically determined and the variation between the auxiliary square system and the original non-square system can then be eliminated. The asymptotic stability is established for the closed loop system formulated by the non-square system and the constructed controller. The feasibility of the proposed control method is verified under simulations for linear system, nonlinear underactuated system, and nonholonomic system.