Trajectory tracking control of chained systems: A new approach (Q2705707)

The authors investigate the trajectory tracking problem of the chained control system NEWLINE\[NEWLINE\left\{ \begin{aligned} \dot x_1&=v_1,\\ \dot x_2&=x_3v_1,\\ &\phantom{a}\vdots \\ \dot x_{n-1}&=x_{n}v_1,\\ \dot x_n&=v_2, \\ \end{aligned}\right. \tag{1}NEWLINE\]NEWLINE where \(x=[x_1,\dots,x_n]^T\) is the state and \(v=[v_1, v_2]^{\text{T}}\) is the control input. A new tracking approach is presented. The proposed static tracking can globally design the state of the system which asymptotically track the given trajectory \(y\) which is the solution to a system similar to the system (1). Tracking control of multi-chained system is also considered. An application to a wheeled mobile robot is given. Simulation results show the efficiency of this approach.