Fig 1

Graphical presentation of ${{\overset{\smile} {{y}}}_{{i}}}$ "

Fig 2

Zoom graphical presentation of ${{\overset{\smile} {{y}}}_{{i}}}$ "

Fig 3

Comparison results of states ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ in system (28) between controller ${{{v}}_{{{n1}}}}$ and the controller in [25] "

Fig 4

Comparison results of states ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ in system (28) between controller ${{{v}}_{{{n1}}}}$ and the controller in [33] "

Fig 5

Comparison results of states ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ in system (28) under ${{{v}}_{{{n1}}}}$ and ${{{v}}_{{{naf}}}}$ "

Fig 6

Control input ${{{v}}_{{{naf}}}}$ "

Fig 7

Adaptive gain ${{\overset{\smile} {{k}}}_{{1}}}({{t}}),{{\overset{\smile} {{k}}}_{{2}}}({{t}}),{{\overset{\smile} {{k}}}_{{3}}}({{t}})$ "

Fig 8

States ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ of the system (28) under controller ${{{v}}_{{{naf}}}}$ with uncertainties "

Fig 9

Kinematic car model"

Fig 10

Trajectories of ${{{x}}_{{2}}}$ and ${{{x}}_{{{2c}}}}$ under controller (35) "

Fig 11

States ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ in system (33) under controller (35) and sliding variable ${{s}}$ "

Fig 12

Control input ${{u}}$ (35) "

Fig 13

Adaptive gain $\tilde {{k}}({{t}})$ and ${{\overset{\smile} {{k}}}_{{1}}}({{t}}),{{\overset{\smile} {{k}}}_{{2}}}({{t}}),{{\overset{\smile} {{k}}}_{{3}}}({{t}})$ "

Fig 14

"

Fig 14

Comparison results of states ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ in system (33) between our controller (35) and the method in [25] "

Fig 15

Comparison results of states ${{{z}}_{{1}}},{{{z}}_{{2}}},{{{z}}_{{3}}}$ in system (33) between our controller (35) and the method in [33] "