Design of Luenberger state observers using fixed-structure H∞ optimization and its application to fault detection in lane-keeping control of automated vehicles

Lane-keeping control forms an integral part of fully automated intelligent vehicle highway systems (IVHS) and its reliable operation is critical to the operation of an automated highway. We present the design of a fault detection filter for the lane-keeping control systems onboard vehicles used by California-PATH, USA in its automated highways program. We use a Luenberger structure for the fault detection filters and tune the observer gains based on an H_∞-based cost. Such a choice of cost was motivated by the need to explicitly incorporate frequency-domain-based performance objectives. The linear matrix inequality (LMI)-based formulation of an H_∞ optimization problem of Luenberger state observers does not allow for the augmentation with dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We present an algorithm to locally solve the problem of the design of Luenberger state observers using H_∞ optimization by transforming the problem into an H_∞ static output feedback controller problem. Experimental results demonstrate the efficacy of the tuning methodology by comparing the fault detection performance of filters that use H_∞ Luenberger observers versus those that use Kalman filters. Implementation issues of the observers are also discussed.