Adaptive Control of Vehicle Position with Non-linearizable Feedback

Abstract – The problem of vehicle control is considered in the paper. The model of vehicle is represented by the equations of kinematics and dynamics of a rigid body. The features of con-trol that could appear for complicated maneuvers are investi-gated. In such motion the determinant of the matrix of kine-matics may be equal to zero. This fact does not allow to set the desired dynamics of the closed-loop system in the form of line-ar equations. In other words the system cannot be linearized by feedback. The problem is solved by applying adaptive con-trol systems with a reference model. A procedure for the syn-thesis of the basic position-trajectory control is proposed. As-ymptotic stability analysis on base of the method of Lyapunov functions is considered. Adaptation of control is carried out by proportional and integral algorithms. The block-diagram of the closed-loop system is presented. The stability of the adap-tive control system is proved. It is shown that in the linear approximation, the characteristic equation of the closed-loop system is a product of the characteristic equation of the refer-ence models, the vehicle, and the adaptation subsystem. Mod-eling results are presented. Keywords-position-path control, adaptive control, vehicle, reference model, function of Lyapunov. I