We present a mathematical programming-based method for model predictive control of discrete-time cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a model predictive control framework. We present experimental results for controller synthesis for building energy and climate control.

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Model predictive control with signal temporal logic specifications

We present a counterexample-guided inductive synthesis approach to controller synthesis for cyber-physical systems subject to signal temporal logic (STL) specifications, operating in potentially adversarial nondeterministic environments. We encode STL specifications as mixed integer-linear constraints on the variables of a discrete-time model of the system and environment dynamics, and solve a series of optimization problems to yield a satisfying control sequence. We demonstrate how the scheme can be used in a receding horizon fashion to fulfill properties over unbounded horizons, and present experimental results for reactive controller synthesis for case studies in building climate control and autonomous driving.

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Reactive synthesis from signal temporal logic specifications

Reliability engineering dates back to reliability studies in the 20th century; since then, various models have been defined and used. Software engineering plays a key role from several viewpoints, but the main concern is that we're moving toward a more connected world, including enterprises and mobile devices. The three articles in this special issue illustrate current trends in this domain.

Reliability Engineering

The term Cyber-Physical Systems (CPS) typically refers to engineered, physical and biological systems monitored and/or controlled by an embedded computational core. The behaviour of a CPS over time is generally characterised by the evolution of physical quantities, and discrete software and hardware states. In general, these can be mathematically modelled by the evolution of continuous state variables for the physical components interleaved with discrete events. Despite large effort and progress in the exhaustive verification of such hybrid systems, the complexity of CPS models limits formal verification of safety of their behaviour only to small instances. An alternative approach, closer to the practice of simulation and testing, is to monitor and to predict CPS behaviours at simulation-time or at runtime. In this chapter, we summarise the state-of-the-art techniques for qualitative and quantitative monitoring of CPS behaviours. We present an overview of some of the important applications and, finally, we describe the tools supporting CPS monitoring and compare their main features.

Specification-Based Monitoring of Cyber-Physical Systems: A Survey on Theory, Tools and Applications

Formal verification of a control system can be performed by checking if a model of its dynamical behavior conforms to temporal requirements. Unfortunately, adoption of formal verification in an industrial setting is a formidable challenge as design requirements are often vague, nonmodular, evolving, or sometimes simply unknown. We propose a framework to mine requirements from a closed-loop model of an industrial-scale control system, such as one specified in Simulink. The input to our algorithm is a requirement template expressed in parametric signal temporal logic: a logical formula in which concrete signal or time values are replaced with parameters. Given a set of simulation traces of the model, our method infers values for the template parameters to obtain the strongest candidate requirement satisfied by the traces. It then tries to falsify the candidate requirement using a falsification tool. If a counterexample is found, it is added to the existing set of traces and these steps are repeated; otherwise, it terminates with the synthesized requirement. Requirement mining has several usage scenarios: mined requirements can be used to formally validate future modifications of the model, they can be used to gain better understanding of legacy models or code, and can also help enhancing the process of bug finding through simulations. We demonstrate the scalability and utility of our technique on three complex case studies in the domain of automotive powertrain systems: a simple automatic transmission controller, an air-fuel controller with a mean-value model of the engine dynamics, and an industrial-size prototype airpath controller for a diesel engine. We include results on a bug found in the prototype controller by our method.

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Mining Requirements From Closed-Loop Control Models

Formal Methods for Discrete-Time Dynamical Systems

This paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system properties (e.g. "the car successfully stops before hitting an obstruction"). A temporal logic formula that can discriminate between the desirable behaviors and the undesirable ones is constructed. The formulae also indicate possible causes for each set of behaviors (e.g. "If the speed of the car is greater than 15 m/s within 0.5s of brake application, the obstruction will be struck") which can be used to tune designs or to perform on-line monitoring to ensure the desired behavior. We introduce reactive parameter signal temporal logic (rPSTL), a fragment of parameter signal temporal logic (PSTL) that is expressive enough to capture causal, spatial, and temporal relationships in data. We define a partial order over the set of rPSTL formulae that is based on language inclusion. This order enables a directed search over this set, i.e. given a candidate rPSTL formula that does not adequately match the observed data, we can automatically construct a formula that will fit the data at least as well. Two case studies, one involving a cattle herding scenario and one involving a stochastic hybrid gene circuit model, are presented to illustrate our approach.

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Temporal logic inference for classification and prediction from data

We propose a framework for generating a signal control policy for a traffic network of signalized intersections to accomplish control objectives expressible using linear temporal logic. By applying techniques from model checking and formal methods, we obtain a correct-by-construction controller that is guaranteed to satisfy complex specifications. To apply these tools, we identify and exploit structural properties particular to traffic networks that allow for efficient computation of a finite-state abstraction. In particular, traffic networks exhibit a componentwise monotonicity property which enables reaching set computations that scale linearly with the dimension of the continuous state space.

Traffic Network Control From Temporal Logic Specifications

We propose a framework for generating a signal control policy for a traffic network of signalized intersections to accomplish control objectives expressible using linear temporal logic. By applying techniques from model checking and formal methods, we obtain a correct-by-construction controller that is guaranteed to satisfy complex specifications. To apply these tools, we identify and exploit structural properties particular to traffic networks that allow for efficient computation of a finite state abstraction. In particular, traffic networks exhibit a componentwise monotonicity property which allows reach set computations that scale linearly with the dimension of the continuous state space.

Traffic Network Control from Temporal Logic Specifications

This paper considers the problem of controlling discrete-time linear systems from specifications given as formulas of syntactically co-safe linear temporal logic over linear predicates in the state variables. A systematic procedure is developed for the automatic computation of sets of initial states and feedback controllers such that all the resulting trajectories of the closed-loop system satisfy the given specifications. The procedure is based on the iterative construction and refinement of an automaton that enforces the satisfaction of the formula. Linear programming based approaches are proposed to compute the polytope-to-polytope controllers that label the transitions of the automaton. Extensions to discrete-time piecewise affine systems and specifications given as formulas of full linear temporal logic are included. The algorithms developed in this paper were implemented as a software package that is available for download. Their application and effectiveness are demonstrated for several case studies.

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Ebru Aydin Gol

Papers

Formal Methods for Discrete-Time Dynamical Systems

Temporal logic inference for classification and prediction from data

Traffic Network Control From Temporal Logic Specifications

Traffic Network Control from Temporal Logic Specifications

Language-Guided Controller Synthesis for Linear Systems