This project considers the control of combined longitudinal and lateral
motion of individual vehicles with partial state measurements, which are
longitudinal and lateral deviations, longitudinal velocity and yaw rate.
We have developed, an eighth order nonlinear state-space model to describe the
combined lateral and longitudinal vehicle motion, where both coupling terms
arising from the velocities and from the controls are included. Linearization
around circular motion with arbitrary constant velocity and radius is
characterized, and is approximated by a linear model with linear or multilinear
perturbations of some simple functions of the scheduling variables ---
longitudinal velocity, yaw rate, cornering stiffness and the vehicle load. The
operating range is determined by a hypercube in the space of these four
variables. After redefining the scheduling variables without introducing
excessive conservativeness, a group of linear systems are obtained, which
correspond to the vertices of the whole linearized system family in the new
For each of the extremal linear systems, LQG-type controllers are designed
through an optimization problem with LMI (linear matrix inequality) constraints.
Upon solution, a common quadratic Lyapunov function is obtained for the whole
family of the linearized closed-loop systems. This guarantees the stability and
some related performance of the final gain scheduled control system, which is
nonlinear. A compensator is reconstructed from the solution of the optimization
problem and the schedulinging variables. Combining the information of road
geometry and reference velocity profile, a gain-scheduled feedback-feedforward
controller is obtained. Since the cornering stiffness and vehicle load are not
measured, they are estimated using least square method.
Simulation results show that controllers obtained with this method are very
robust to parameter variations, and perform well in the presence of measurement
noise and initial deviations.
Current research in this project is directed towards designing
H-infinity-type gain-scheduled controllers with guaranteed performance in an