From Uncertainty Data to Robust Policies for Temporal Logic Planning

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving

A Theory of Sampling for Continuous-time Metric Temporal Logic

This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over continuous-time models and over discrete-time models is studied. It is shown to what extent discrete-time sequences obtained by sampling continuous-time signals capture the semantics of MTL formulas over the two time domains. The main results apply to "flat" formulas that do not nest temporal operators and can be applied to the problem of reducing the verification problem for MTL over continuous-time models to the same problem over discrete-time, resulting in an automated partial practically-efficient discretization technique.Comment: Revised version, 43 pages

Reactive synthesis from 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

Translating temporal logic to controller specifications

Abstract — The problem of designing hybrid controllers in order to satisfy safety or liveness specifications has received much attention in the past decade. Much more recently, there is an increased interest in designing hybrid controllers in order to achieve more sophisticated discrete specifications, such as those expressible in temporal logics. A great challenge is how to compose safety and liveness controllers in order to achieve more complex specifications. Existing approaches are predominantly bottom-up, in the sense that the overall control and composition (or switching) logic requires verification of the integrated closed-loop hybrid system. In this paper, we advocate and develop a top-down approach for this problem by synthesizing controllers which satisfy the specification by construction. Given a flat linear temporal logic specification as an input, we develop an algorithm that translates the temporal logic specification into a hybrid automaton where in each discrete mode we impose controller specifications for the continuous dynamics. In addition to achieving the desired specification by construction, our methodology provides a very natural interface between high level logic design and low level control design. I

On a Continuous Degree of Satisfaction of Temporal Logic Formulae with Applications to Systems Biology

Abstract. Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeller that techniques like model-checking help solving, in the qualitative but also in the quantitative case. In this article we propose to go one step further by defining a continuous degree of satisfaction of a temporal logic formula with constraints. We show how such a satisfaction measure can be used as a fitness function with state-of-the-art search methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some specification. These methods are evaluated on models of the cell cycle and of the MAPK signalling cascade.

Parameter Synthesis Through Temporal Logic Specifications

Parameters are often used to tune mathematical models and capture nondeterminism and uncertainty in physical and engineering systems. This paper is concerned with parametric nonlinear dynamical systems and the problem of determining the parameter values that are consistent with some expected properties. In our previous works, we proposed a parameter synthesis algorithm limited to safety properties and demonstrated its applications for biological systems. Here we consider more general properties specified by a fragment of STL (Signal Temporal Logic), which allows us to deal with complex behavioral patterns that biological processes exhibit. We propose an algorithm for parameter synthesis w.r.t. a property specified using the considered logic. It exploits reachable set computations and forward refinements. We instantiate our algorithm in the case of polynomial dynamical systems exploiting Bernstein coefficients and we illustrate it on an epidemic model

Symbolic Monitoring against Specifications Parametric in Time and Data

This is the author version of the manuscript of the same name published in the proceedings of the 31st International Conference on Computer-Aided Verification (CAV 2019).International audienceMonitoring consists in deciding whether a log meets a given specification. In this work, we propose an automata-based formalism to monitor logs in the form of actions associated with time stamps and arbitrarily data values over infinite domains. Our formalism uses both timing parameters and data parameters, and is able to output answers symbolic in these parameters and in the log segments where the property is satisfied or violated. We implemented our approach in an ad-hoc prototype SyMon, and experiments show that its high expressive power still allows for efficient online monitoring