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Adaptive robust control of nonholonomic systems with stochastic disturbances. (English) Zbl 1117.93027
Summary: This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances. The objective is to design the almost global adaptive asymptotical controllers in probability $u_0$ and $u_1$ for the systems by using discontinuous control. A switching control law $u_0$ is designed to almost globally asymptotically stabilize the state $x_0$ in both the singular $x_0(t_0)=0$ case and the non-singular $x_0(t_0)\ne0$ case. Then the state scaling technique is introduced for the discontinuous feedback into the $(x_1,x_2,\dots,x_n)$-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law $u_1$ has been presented for $(x_1,x_2,\dots,x_n)$-subsystem for both different $u_0$ in non-singular $x_0(t_0)\ne0$ case and the singular case $x_0(t_0)=0$. The control algorithm validity is proved by simulation.

93B35Sensitivity (robustness) of control systems
93C42Fuzzy control systems
93E03General theory of stochastic systems
93E15Stochastic stability
Full Text: DOI
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