Adaptive Control of Vehicleposition 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 control that could appear for complicated maneuvers are investigated. In such motion the determinant of the matrix of kinematics may be equal to zero. This fact does not allow to set the desired dynamics of the closed-loop system in the form of linear equations. In other words the system cannot be linearized by feedback. The problem is solved by applying adaptive control systems with a reference model. A procedure for the synthesis of the basic position-trajectory control is proposed. Asymptotic 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 adaptive 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 reference models, the vehicle, and the adaptation subsystem. Modeling results are presented.