Backstepping design of nonlinear control systems and its applications to vehicle lateral control in automated highway systems

In this dissertation the effort is to explore new aspects of recursive backstepping design methodology from both theoretical and application point of view. Three main topics are investigated in this dissertation from a backstepping perspective: control of multivariable nonlinear systems whose vector relative degrees are not well defined, steering control of light passenger vehicles on automated highways, and coordinated steering and braking control of commercial heavy vehicles on automated highways.; For a class of affine multivariable nonlinear systems with an equal number of inputs and outputs, if the decoupling matrix is singular, the vector relative degree is not well defined. If the multivariable nonlinear system is strongly invertible and strongly accessible, the vector relative degree of the system can be achieved by adding chains of integrators to the input channels. Several versions of dynamic extension algorithms have been proposed to identify the input channels where dynamic compensators (or integrators) are needed to achieve the nonsingularity of the decoupling matrix. In this dissertation, instead of decoupling the nonlinear system by adding chains of integrators in the input channels, we modify the dynamic extension algorithm by incorporating backstepping design methods to partially close the loop in each design step. The resulting control law by this new approach is a static state feedback law.; Backstepping design methodology is utilized for lateral control of light passenger vehicles and commercial heavy vehicles in Automated Highway Systems (AHS). The steering control algorithm for light passenger vehicles is designed by utilizing the robust backstepping technique, whereas the coordinated steering and braking control algorithm for commercial heavy vehicles is designed by applying the backstepping technique for multivariable nonlinear systems without vector relative degrees.; For lateral control of light passenger vehicles, the lateral tracking error is affected by the relative yaw angle of the vehicle with respect to the road centerline. Then the relative yaw angle is controlled by the front wheel steering command. Intuitively, this backstepping control procedure resembles the human driver behavior. Another advantage of the backstepping controller is that the road disturbance, which does not satisfy the matching condition, can be attenuated effectively. Thus the backstepping design effectively utilizes the feedforward information of the road curvature to generate the feedforward part of the steering command. To satisfy both the ride comfort and safety requirements, we introduce a nonlinear spring term (nonlinear position feedback) which exhibits lower gains at small tracking errors and higher gains at larger tracking errors.; For lateral control of commercial heavy vehicles, a control oriented dynamic modeling approach for articulated vehicles is proposed. A generalized coordinate system is introduced to describe the kinematics of the vehicle. Equations of motion of a tractor-semitrailer vehicle are derived based on the Lagrange mechanics. Experimental studies are conducted to validate the effectiveness of this modeling approach. Two nonlinear lateral control algorithms are designed for a tractor-semitrailer vehicle. The baseline steering control algorithm is designed utilizing input-output linearization. To prevent jackknifing and furthermore reduce tracking errors of the trailer, braking forces are independently controlled on the inner and outer wheels of the trailer. The coordinated steering and braking control algorithm is designed based on the multivariable backstepping technique. Simulations show that the trailer yaw errors under coordinated steering and independent braking force control are smaller than those without independent braking force control. (Abstract shortened by UMI.)...