Stabilization for a class of nonholonomic perturbed systems via robust adaptive sliding mode control

Robust stabilizing control of nonholonomic systems with uncertainties via adaptive integral sliding mode

“…The control problem becomes further complicated whenever various uncertainties influence the nonholonomic mechanical systems. [22][23][24] A simple, rather useful, approach to control nonholonomic uncertain systems is the sliding mode control (SMC). The SMC has attracted the attention of many researchers due to its simplicity, fast response, and robustness to external noise and parameter variations.…”

“…The SMC has attracted the attention of many researchers due to its simplicity, fast response, and robustness to external noise and parameter variations. [24][25][26][27][28][29] The properties of SMC just depend upon the design of the switching surface and have nothing to do with the external interferences. 29 Some recent practical applications of SMC include control of steerable needles, 30 nonlinear control of an unmanned agricultural tractor, 31 and impedance control of a piezoelectric microgripper.…”

“…Also, backstepping techniques are difficult to implement on nonholonomic mechanical systems, whereas the adaptive technique in combination with ISMC guarantees the robustness of system trajectory in the whole state space. 24,26 This article presents a robust method for stabilization of nonholonomic AUVs affected with uncertainties. The methodology is based on adaptive ISMC.…”

“…where g 1 ðÞ ¼ ½ 1 tan À sec tan 0 0 0 T g 2 ðÞ ¼ ½ 0 0 0 1 0 0 T g 3 ðÞ ¼ ½ 0 0 0 sin' tan cos' sin' sec T g 4 ðÞ ¼ ½ 0 0 0 cos' tan À sin' cos' sec T and pð; tÞ 2 spanf g 1 ðÞ ; g 2 ðÞ; g 3 ðÞ ; g 4 ðÞ g; 8 t According to Liang and Jianying, 24 if pð; tÞ 2 spanf g 1 ðÞ ; g 2 ðÞ; g 3 ðÞ ; g 4 ðÞ g is in matched form, then under coordinate change and state feedback (11) can be locally or globally transformed into…”