MechE PhD Prospectus Defense: Sadra Sadraddini

Title: "Safety Control of Discrete-time Systems" Committee: Prof. Calin Belta (ME) (advisor),Prof. Christos Cassandras (ECE/SE),Prof. Sean Andersson (ME/SE) Abstract: "Safe and reliable control is a central problem in automation of cyber-physical systems. Safety specifications are typically stated as constraints that should never be violated. These constraints may be described using reference points or trajectories, regions in the state space or be more widely expressed using tools from formal methods such as temporal logics. In this dissertation, we describe safety specifications using the safety fragment of signal temporal logic (STL), which is rich and powerful enough to describe a wide range of properties such as stability, persistence, and response. We develop a robust model predictive control (MPC) algorithm to plan controls optimally in a receding horizon manner for discrete-time piecewise affine systems, while the constraints are met for all allowable uncertainties. In case satisfying the specification is not possible, we exploit STL quantitative semantics to minimize a type of "distance to satisfaction" for the specification. While finite horizon predictive control schemes are a popular method to handle constraints, they are typically unable to guarantee infinite horizon safe execu-tions. In other words, a predictive control strategy may encounter a "dead end" , where any further action may violate the specification. We study how to guarantee infinite horizon safety using tools from set-invariance theories. The computational issues for this approach are discussed for general piecewise affine systems. Next, we turn our focus to a special type of systems where the state evolution has a monotonicity law. Such systems are widely common in models of transportation networks and biological systems. We propose a computationally efficient approach to set-invariance computations of monotone systems, which is used for guaranteeing infinite horizon safety in the robust MPC. Application to vehicular traffic management is thor-oughly discussed, where the primary safety objective is avoiding traffic jams. We also show how our methods can be used to develop a distributed control scheme for traffic management, while controls decisions are made using the local information. An assume-guarantee method specifies global coordination between the local controllers such that the overall specification is guaranteed to be satisfied."