Safety Control for Order Preserving Systems with Applications to Intelligent Transportation.

Abstract

In this thesis we develop computational tools for the safety control of multi-agent systems, with applications towards intersection collision avoidance within traffic networks. For multi-agent systems, the classical approach to the safety problem, or that of computing the maximal safe controlled invariant set, is computationally prohibitive in practice, where state information is imperfect (due to sensor and plant uncertainty) and controllers need be implemented in a distributed manner. We exploit the order preserving properties of the system under study to compute the capture set assuming imperfect state information in an efficient manner, which is used to construct the set-valued feedback map that renders the system safe. These results hold for the case of disturbance inputs, which can model plant uncertainty or competition amongst agents. Algorithms are developed to compute the capture set, which have linear complexity with respect to state dimension. Our methods are verified in simulation, and through experimentation on a mini-vehicle test-bed. The results are extended to a three-vehicle roundabout system, where a safety controller is developed using the conjunction of cooperative and competitive controllers. Safety can be verified by checking that the controllers are non-blocking for all possible states outside of the individual capture sets. Experimental results are provided for a three-vehicle roundabout system using a mini-vehicle test-bed. The problem is next addressed for a full-size vehicle test-bed. System identification is carried out using the disturbance modeling framework, which generates a model reflecting worst case disturbance inputs. A set-valued state estimator is developed to address the issue of communication delay. Distributed control is considered through the design of a handshake mechanism implementing logical disjunction between cooperating controllers. Comprehensive testing is carried out for this two-vehicle system, where safety was found to hold over all experimental trials. Design parameters are developed to allow for a tunable safety margin, which allows for more or less conservative behavior with respect to the capture set.