Discontinuous control of high-order generalized chained systems

Bounded control of a general extended chained form systems

“…For these reasons, system (1) has attracted much attention during recent years in the nonlinear control community. In [7], a discontinuous control to exponentially stabilize the generalized version of system (1) is presented. It was also the subject of study in [12] where the exponential stability is guaranteed by applying a continuous control law variable over time.…”

Backstepping for nonsmooth systems

“…This paper was recommended for publication in revised form by Associate Editor Zhihua Qu under the direction of Editor Hassan Khalil.Stabilization of dynamic models for nonholonomic systems has also been addressed in Campion, d'Andrea Novel, and Bastin (1991), Reyhanoglu and McClamroch (1992), Jiang (2000), Lin, Pongvuthithum, and Quian (2002), Laiou and Astolÿ (1999), Kolmanovsky and McClamroch (1995b), M'Closkey and Murray (1994). A common problem in discontinuous strategies is unboundedness of inputs around the discontinuity manifold and possible appearance of chattering, both of which are treated with various techniques (Astolÿ, 1996;Luo & Tsiotras, 2000;Tsiotras & Luo, 1997;Jiang, 2000).…”

Robust Point Stabilization of Underactuated Mechanical Systems via the Extended Chained Form

“…However, no definitive unifying notation seems to exist as yet for the family of "chained systems." In [11], for instance, a two-input control system is introduced which is referred to as an n-dimensional, high-order generalized chained system. On the other hand, chained systems having more than two inputs have also been studied under the denomination multi-input chained systems, e.g., in [29].…”