A switched second-order sliding mode control algorithm for non-affine systems with saturations

In control systems design, the problem of managing dynamical systems affected by uncertainties that are different in different region of the state space, or with closed-loop specification that should be adjusted to the current operating condition must be often faced. To adapt the controller performance to these spatially-varying phenomena, switched solutions proved to be effective and more easily manageable than conventional adaptive ones. Within this context, this paper addresses the problem of designing a switched sliding mode controller for a class of nonlinear non-affine systems with saturating actuators. The original system is first reduced to an affine form, thus defining a new system which is assumed to be affected by unknown, yet bounded, uncertainties that are different in different regions of the state space. For such system, a switched second order sliding mode control algorithm is designed which can cope with saturating actuators present in the original non-affine system. The control law is proved to ensure finite-time convergence to the origin of the closed-loop trajectory, and a simulation example is given to assess the performance of the proposed approach.