Verifying the Unknown: Correct-by-Design Control Synthesis for Networks of Stochastic Uncertain Systems

In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems with additive stochastic noise and model parametric uncertainty. Such settings arise when multiple systems interact in an uncertain environment and only observational data is available. We address two limitations of existing approaches for formal synthesis of controllers for networks of uncertain systems satisfying complex temporal specifications. Firstly, whilst existing approaches rely on the stochasticity to be Gaussian, the heterogeneous nature of composed systems typically yields a more complex stochastic behavior. Secondly, exact models of the systems involved are generally not available or difficult to acquire. To address these challenges, we show how abstraction-based control synthesis for uncertain systems based on sub-probability couplings can be extended to networked systems. We design controllers based on parameter uncertainty sets identified from observational data and approximate possibly arbitrary noise distributions using Gaussian mixture models whilst quantifying the incurred stochastic coupling. Finally, we demonstrate the effectiveness of our approach on a nonlinear package delivery case study with a complex specification, and a platoon of cars.Comment: 9 pages, 4 figures, accepted to CDC 202

Direct data-driven signal temporal logic control of linear systems

Most control synthesis methods under temporal logic properties require a model of the system, however, identifying such a model can be a challenging task for complex systems. In this paper, we develop a direct data-driven controller synthesis method for linear systems subject to a temporal logic specification, which does not require this explicit modeling step. After collecting a single sequence of input-output data from the system, we construct a data-driven characterization of the system behavior. Using this data-driven characterization we show that we can synthesize a controller, such that the controlled system satisfies a signal temporal logic-based specification. The underlying optimization problem is solved by mixed-integer linear programming. We demonstrate applicability of the results through benchmark simulation examples.Comment: Submitted to the 62nd IEEE Conference on Decision and Control (CDC2023

Simulation data SySCoRe

<p>Simulation data corresponding to the paper </p><p>SySCoRe: Synthesis via Stochastic Coupling Relations<br>van Huijgevoort, Birgit; Schön, Oliver; Soudjani, Sadegh; Haesaert, Sofie<br>HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control</p&gt

Multi-Layered Simulation Relations for Linear Stochastic Systems

The design of provably correct controllers for continuous-state stochastic systems crucially depends on approximate finite-state abstractions and their accuracy quantification. For this quantification, one generally uses approximate stochastic simulation relations, whose constant precision limits the achievable guarantees on the control design. This limitation especially affects higher dimensional stochastic systems and complex formal specifications. This work allows for variable precision by defining a simulation relation that contains multiple precision layers. For bi-layered simulation relations, we develop a robust dynamic programming approach yielding a lower bound on the satisfaction probability of temporal logic specifications. We illustrate the benefit of bi-layered simulation relations for linear stochastic systems in an example

Similarity quantification for linear stochastic systems: A coupling compensator approach

For the formal verification and design of control systems, abstractions with quantified accuracy are crucial. This is especially the case when considering accurate deviation bounds between a stochastic continuous-state model and its finite (reduced-order) abstraction. In this work, we introduce a coupling compensator to parameterize the set of relevant couplings and we give a comprehensive computational approach and analysis for linear stochastic systems. More precisely, we develop a computational method that characterizes the set of possible simulation relations and gives a trade-off between the error contributions on the systems output and deviations in the transition probability. We show the effect of this error trade-off on the guaranteed satisfaction probability for case studies where a formal specification is given as a temporal logic formula

Temporal logic control of nonlinear stochastic systems using a piecewise-affine abstraction

Automatically synthesizing controllers for continuous-state nonlinear stochastic systems, while giving guarantees on the probability of satisfying (infinite-horizon) temporal logic specifications crucially depends on abstractions with a quantified accuracy. For this similarity quantification, approximate stochastic simulation relations are often used. To handle the nonlinearity of the system effectively, we use finite-state abstractions based on piecewise-affine approximations together with tailored simulation relations that leverage the local affine structure. In the end, we synthesize a robust controller for a nonlinear stochastic Van der Pol oscillator

Correct-by-Design Control of Parametric Stochastic Systems

This paper addresses the problem of computing controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. We develop new methods for models of systems subject to both stochastic and parametric uncertainties. We provide for the first time novel simulation relations for enabling correct-by-design control refinement, that are founded on coupling uncertainties of stochastic systems via sub-probability measures. Such new relations are essential for constructing abstract models that are related to not only one model but to a set of parameterized models. We provide theoretical results for establishing this new class of relations and the associated closeness guarantees for both linear and nonlinear parametric systems with additive Gaussian uncertainty. The results are demonstrated on a linear model and the nonlinear model of the Van der Pol Oscillator