Robust nonlinear control design via convex optimization and its application to fault tolerant longitudinal control of vehicles

This dissertation presents a new analysis and design method for robust nonlinear control in the framework of Dynamic Surface Control (DSC), and its extension to fault tolerant control (FTC). The results are shown to apply to a class of nonlinear systems and in particular to automated longitudinal vehicle control. FTC has recently received significant attention in the design of large-scale systems such as automated highway systems due to a growing demand for reliability and an increase in complexity. A systematic procedure is needed to realize the ultimate benefits of a fault tolerant control system, thus leading to several interesting questions in the area of nonlinear control.; Before developing a full FTC design method, it is necessary to develop an analysis and design procedure for nonlinear systems under a no-fault assumption. The method developed in this thesis is the DSC method, which is a “synthetic input” method, similar to the integrator backstepping method. The investigation of augmented closed loop error dynamics leads us to derive convex optimization problems for testing the stability and performance of nonlinear systems via DSC. It results in the development of a systematic method to choose appropriate gains and filter time constants for DSC and to analyze both the stability and tracking performance. We extend this rigorous analytical framework to derive a separation principle for nonlinear compensators which combine a nonlinear observer with DSC. The principle enables us to design the observer and DSC independently if full state information is not available or faults occur in the sensor measurements. Moreover, an initial condition set which guarantees quadratic stability for the regulation problem with input constraints, as well as a region of attraction, are estimated numerically within the framework of convex optimization.; As motivated by the automated highway application, a hierarchical hybrid architecture for the FTC system has been proposed to allow hierarchical building of complex systems from simple systems and modular integration of components. Moreover, using the fact that DSC is a passive fault tolerant approach in the sense that it gives robust stabilization and tracking in the presence of model uncertainties and even a specific class of faults, we develop a hybrid structure using a combination of the passive and active FTC approaches. This structure leads to a fault classification scheme as a switching logic between the two approaches. Furthermore, a nonlinear compensator and a trajectory reconfiguration scheme are used as an active FTC approach to minimize performance losses as well as to maintain quadratic stability in the face of either sensor or actuator faults. Finally, we apply the DSC and FTC design methods to the automated longitudinal control of vehicles.