Sadra Sadraddini

Robust temporal logic model predictive control

Control synthesis from temporal logic specifications has gained popularity in recent years. In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to constraints given as formulas of signal temporal logic (STL). We introduce a (conservative) computationally efficient framework to synthesize control strategies based on mixed integer programs. The designed controllers satisfy the temporal logic requirements, are robust to all possible realizations of the disturbances, and optimal with respect to a cost function. In case the temporal logic constraint is infeasible, the controller satisfies a relaxed, minimally violating constraint. An illustrative case study is included.

Safety control of monotone systems with bounded uncertainties

Monotone systems are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control strategy for a discrete time positive monotone system with bounded uncertainties such that the evolution of the system is guaranteed to be confined to a safe set in the state space for all times. By exploiting monotonicity, we propose an approach to this problem which is based on constraint programming. We find control strategies that are based on repetitions of finite sequences of control actions. We show that, under assumptions made in the paper, safety control of monotone systems does not require state measurement. We demonstrate the results on a signalized urban traffic network, where the safety objective is to keep the traffic flow free of congestion.

A provably correct MPC approach to safety control of urban traffic networks

Model predictive control (MPC) is a popular strategy for urban traffic management that is able to incorporate physical and user defined constraints. However, the current MPC methods rely on finite horizon predictions that are unable to guarantee desirable behaviors over long periods of time. In this paper we design an MPC strategy that is guaranteed to keep the evolution of a network in a desirable yet arbitrary -safe- set, while optimizing a finite horizon cost function. Our approach relies on finding a robust controlled invariant set inside the safe set that provides an appropriate terminal constraint for the MPC optimization problem. An illustrative example is included.

Provably Safe Cruise Control of Vehicular Platoons

We synthesize performance-aware safe cruise control policies for longitudinal motion of platoons of autonomous vehicles. Using set-invariance theories, we guarantee infinite-time collision avoidance in the presence of bounded additive disturbances, while ensuring that the length and the cruise speed of the platoon are bounded within specified ranges. We propose: 1) a centralized control policy and 2) a distributed control policy, where each vehicle’s control decision depends solely on its relative kinematics with respect to the platoon leader. Numerical examples are included.

Robotic swarm control from spatio-temporal specifications

In this paper, we study the problem of controlling a two-dimensional robotic swarm with the purpose of achieving high level and complex spatio-temporal patterns. We use a rich spatio-temporal logic that is capable of describing a wide range of time varying and complex spatial configurations, and develop a method to encode such formal specifications as a set of mixed integer linear constraints, which are incorporated into a mixed integer linear programming problem. We plan trajectories for each individual robot such that the whole swarm satisfies the spatio-temporal requirements, while optimizing total robot movement and/or a metric that shows how strongly the swarm trajectory resembles given spatio-temporal behaviors. An illustrative case study is included.

Model predictive control of urban traffic networks with temporal logic constraints

Model predictive control (MPC) is a popular method for urban traffic management. Apart from physical constraints, traffic networks are amenable to an extra layer of objectives that uphold certain behaviors for the vehicular flow. In this presentation, we survey the recent results on developing MPC strategies from signal temporal logic (STL) specifications. A wide range of desirable behaviors in urban traffic networks such as avoidance of gridlocks, liveness of vehicular flows and sequentiality of traffic lights can be expressed by STL formulas. By translating STL specifications to mixed integer constraints, traffic network control synthesis is formulated as a mixed integer linear programming (MILP) problem. In addition, STL quantitative semantics (robustness) provides a numerical measure of the distance to satisfaction (violation) of the evolution of a traffic network. We will also discuss robustness maximization policies in the context of traffic control.

Formal synthesis of distributed optimal traffic control policies

We propose a formal methods approach to control traffic signals optimally from specifications described by metric temporal logic (MTL). Since real-time optimization is computationally infeasible beyond small-scale networks, we use a divide and conquer approach. We decompose the network into smaller subnetworks and synthesize assume-guarantee contracts for their interconnections. We show how to exploit mathematical properties of traffic dynamics to find time varying contracts by solving a constraint satisfaction problem. A model predictive control (MPC) approach is used to find local controls for each subnetwork to minimize induced delays, while assume-guarantee contracts and appropriately designed terminal constraints ensure the satisfaction of the specification all over the network. We present a case study on an urban traffic network.

Formal Guarantees in Data-Driven Model Identification and Control Synthesis

For many performance-critical control systems, an accurate (simple) model is not available in practice. Thus, designing controllers with formal performance guarantees is challenging. In this paper, we develop a framework to use input-output data from an unknown system to synthesize controllers from signal temporal logic (STL) specifications. First, by imposing mild assumptions on system continuity, we find a set-valued piecewise affine (PWA) model that contains all the possible behaviors of the concrete system. Next, we introduce a novel method for STL control of PWA systems with additive disturbances. By taking advantage of STL quantitative semantics, we provide lower-bound certificates on the degree of STL satisfaction of the closed-loop concrete system. Illustrative examples are presented.

Distributed control policies for localization of large disturbances in urban traffic networks

We present a distributed control strategy to localize and attenuate traffic jams caused by large disturbances in urban transportation networks. The control policy is distributed in the sense that it uses those traffic lights in the vicinity of the jammed area. We model urban traffic using a discrete fluid-like model which is then reduced to a hybrid dynamical system with binary control inputs. For this system, we define notions of local control and localizability of disturbances. We then present a control strategy that uses only local controllers to attenuate traffic jams. This control design is formulated as a mixed-integer linear program (MILP) whose solution provides traffic light schedules. We show that the feasibility of this MILP is both necessary and sufficient for localizability. Finally, we illustrate this design on a test urban transportation network.

Feasibility envelopes for metric temporal logic specifications

Designing control policies from complex specifications has drawn significant attention in recent years. Metric temporal logic (MTL) is a specification formalism for describing a wide range of temporal properties with specific timing constraints. In this paper, we focus on discrete time linear control systems and specifications given as MTL formulas over linear predicates in the states. We present a method based on polyhedral projection to find the set of all initial states from which all trajectories satisfying MTL formulas can be generated. An illustrative example is included.