Fazal-ur-Rehman and N. Ahmed
Feedback stabilization, systems without drift, nonholonomic systems, nilpotent Lie algebra, Lyapunov function
This paper presents three different kinds of stabilizing feedback control strategies for the nonholonomic integrator known in literature as Brockett’s system. The first strategy presents piece-wise constant, states-dependent feedback control laws, and the method is based on the construction of a cost function V that is the sum of two semi-positive definite functions V1 and V2. The second strategy presents a time-varying feedback control law based on the model reference approach, where the trajectory of the extended system is chosen as the model reference trajectory. The controllers are designed in such a way that after each time period T, the trajectory of the nonholonomic integrator system intersects the trajectory of the model reference which can be made asymptotically stable. The third strategy presents a time-varying feedback control law based on the construction of a time-varying Lyapunov function.
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