This paper addresses the problem of data-driven computation of controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. With a focus on continuous-space stochastic systems with parametric uncertainty, we propose a two-stage approach that decomposes the problem into a learning stage and a robust formal controller synthesis stage. The first stage utilizes available Bayesian regression results to compute robust credible sets for the true parameters of the system. For the second stage, we introduce methods for systems subject to both stochastic and parametric uncertainties. We provide simulation relations for enabling correct-by-design control refinement that are founded on coupling uncertainties of stochastic systems via sub-probability measures. The presented relations are essential for constructing abstract models that are related to not only one model but to a set of parameterized models. The results are demonstrated on three case studies, including a nonlinear and a high-dimensional system.
As the complexity of control systems increases, safety becomes an increasingly important property since safety violations can damage the plant and put the system operator in danger. When the system dynamics are unknown, safety-critical synthesis becomes more challenging. Additionally, modern systems are controlled digitally and hence behave as sampled-data systems, i.e., the system dynamics evolve continuously while the control input is applied at discrete time steps. In this paper, we study the problem of control synthesis for safety-critical sampled-data systems with unknown dynamics. We ove…
In this work, we address the problem of synthesis of covert attackers in the setup where the model of the plant is available, but the model of the supervisor is unknown, to the adversary. To compensate the lack of knowledge on the supervisor, we assume that the adversary has recorded a (prefix-closed) finite set of observations of the runs of the closed-loop system, which can be used for assisting the synthesis. We present a heuristic algorithm for the synthesis of covert damage-reachable attackers, based on the model of the plant and the (finite) set of observations, by a transformation into …
In this paper, we consider the problem of synthesis of maximally permissive covert damage-reachable attackers in the setup where the model of the supervisor is unknown to the adversary but the adversary has recorded a (prefix-closed) finite set of observations of the runs of the closed-loop system. The synthesized attacker needs to ensure both the damage-reachability and the covertness against all the supervisors which are consistent with the given set of observations. There is a gap between the de facto maximal permissiveness, assuming the model of the supervisor is known, and the maximal per…
In this paper, we consider the problem of synthesizing the supremal covert damage-reachable attacker, in the setup where the model of the supervisor is unknown to the adversary but the adversary has recorded a (prefix-closed) finite set of observations of the runs of the closed-loop system. The synthesized attacker needs to ensure both the damage-reachability and the covertness against all the supervisors which are consistent with the given set of observations. There is a gap between the de facto supremality, assuming the model of the supervisor is known, and the supremality that can be attain…
In this work, we propose a data-driven approach for the construction of finite abstractions (a.k.a., symbolic models) for discrete-time deterministic control systems with unknown dynamics. We leverage notions of so-called alternating bisimulation functions (ABF), as a relation between each unknown system and its symbolic model, to quantify the mismatch between state behaviors of two systems. Accordingly, one can employ our proposed results to perform formal verification and synthesis over symbolic models and then carry the results back over unknown original systems. In our data-driven setting,…
Recent employments of SMT solvers within the Lyapunov function synthesis provided effective tools for automated construction of Lyapunov functions alongside with sound computer-assisted certificates. The main benefit of the suggested approach is the formal correctness and elimination of the numerical uncertainty. In the present work, we extend the SMT-based synthesis approach for wider classes of continuous and discrete-time systems. Additionally, we address constructions of Lyapunov functions for state-dependent switching systems. We illustrate our approach by means of various examples from t…
In this paper, we propose a formal controller synthesis approach for integrating a population of plug-in electric vehicles in frequency regulation of power systems. This approach is the first application of formal methods to the smart grids in particular to the frequency regulation of power systems. We design and simulate a novel symbolic controller for the Great Britain power system. The proposed controller enhances the frequency response behaviour of the system when encountered with a large outage event. The symbolic controller guarantees the settlement of the after-event's frequency in the …
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but lack of formal soundness. Symbolic computational methods for Lyapunov functions, which are in between, give formal guarantees but are typically semi-automatic because they rely on the user to provide appropriate function templates. We propose a method that finds Lyapunov functions fully automatically$-$using machine learning$-$while also providing formal guara…
This paper proposes a framework for automatic formal controller synthesis for general hybrid systems with a subset of safety and reachability specifications. The framework uses genetic programming to automatically co-synthesize controllers and candidate Lyapunov-like functions. These candidate Lyapunov-like functions are used to formally verify the control specification, and their correctness is proven using a Satisfiability Modulo Theories solver. The advantages of this approach are: no restriction is made to polynomial systems, the synthesized controllers are expressed as compact expressions…
This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available methods critically rely on a precise knowledge of the system dynamics (thus requiring off-line system identification and model refinement). To this aim, in this paper we first show that the steady-state transfer function of a linear system can be computed directly from control experiments, bypassing explicit model identification. Then, we leverage the estimated …
We introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. The approach is underpinned by an inductive framework: this is structured as a sequential loop between a learner, which manipulates a candidate BC structured as a neural network, and a sound verifier, which either certifies the candidate's validity or generates counter-examples to further guide the learner. We compare the approach against state-of-the-art techniques, over polynomial and non-polynomial dynamical models: t…
We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet STL specifications over finite-time trajectories. Rather than stating the STL specification for a single initial condition, we consider an (infinite and bounded) set of initial conditions. Candidate solutions are proposed using genetic programming, which evolves controllers based on a finite number of simulations. Subsequently, the best candidate is verified using reachability analysis; if the candidate solution does not satisfy the spe…
Technical University of Munich（慕尼黑工业大学）；University of Pennsylvania（宾夕法尼亚大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；LMU Munich（慕尼黑大学）
This paper focuses on the controller synthesis for unknown, nonlinear systems while ensuring safety constraints. Our approach consists of two steps, a learning step that uses Gaussian processes and a controller synthesis step that is based on control barrier functions. In the learning step, we use a data-driven approach utilizing Gaussian processes to learn the unknown control affine nonlinear dynamics together with a statistical bound on the accuracy of the learned model. In the second controller synthesis steps, we develop a systematic approach to compute control barrier functions that expli…
We consider the problem of securing a given control loop implementation of a cyber-physical system (CPS) in the presence of Man-in-the-Middle attacks on data exchange between plant and controller over a compromised network. To this end, there exist various detection schemes that provide mathematical guarantees against such attacks for the theoretical control model. However, such guarantees may not hold for the actual control software implementation. In this article, we propose a formal approach towards synthesizing attack detectors with varying thresholds which can prevent performance degradin…
This paper aims to synthesize a reachability controller for an unknown dynamical system. We first learn the unknown system using Gaussian processes and the (probabilistic) guarantee on the learned model. Then we use the funnel-based controller synthesis approach using this approximated dynamical system to design the controller for a reachability specification. Finally, the merits of the proposed method are shown using a numerical example.
This paper studies formal synthesis of controllers for continuous-space systems with unknown dynamics to satisfy requirements expressed as linear temporal logic formulas. Formal abstraction-based synthesis schemes rely on a precise mathematical model of the system to build a finite abstract model, which is then used to design a controller. The abstraction-based schemes are not applicable when the dynamics of the system are unknown. We propose a data-driven approach that computes the growth bound of the system using a finite number of trajectories. The growth bound together with the sampled tra…
Neural networks (NNs) are emerging as powerful tools to represent the dynamics of control systems with complicated physics or black-box components. Due to complexity of NNs, however, existing methods are unable to synthesize complex behaviors with guarantees for NN dynamic models (NNDMs). This work introduces a control synthesis framework for stochastic NNDMs with performance guarantees. The focus is on specifications expressed in linear temporal logic interpreted over finite traces (LTLf), and the approach is based on finite abstraction. Specifically, we leverage recent techniques for convex …
In the context of the linear programming (LP) approach to data-driven control, one assumes that the dynamical system is unknown but can be observed indirectly through data on its evolution. Both theoretical and empirical evidence suggest that a desired suboptimality gap is often only achieved with massive exploration of the state-space. In case of linear systems, we discuss how a relatively small but sufficiently rich dataset can be exploited to generate new constraints offline and without observing the corresponding transitions. Moreover, we show how to reconstruct the associated unknown stag…
Learning-based Formal Synthesis of Cooperative Multi-agent Systems
Unmanned Systems Research Institute (DU2SRI), Department of Electrical and Computer Engineering, University of Denver（丹佛大学电气与计算机工程学院无人系统研究所）；Department of Electrical Engineering, University of Notre Dame（圣母大学电气工程系）
In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of control policies by using a notation of control barrier functions without requiring any knowledge of the estimation accuracy. Our goal is to synthesize an offline control policy providing (potentially maximizing) a lower bound on the probability that the trajectories of the partially observed jump-diffusion system satisfy some complex specifications expressed by…
Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-Output Data
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb（机械与船舶工程学院，萨格勒布大学）；Electrical Engineering Faculty, Eindhoven University of Technology（电气工程学院，埃因霍温理工大学）
There exist various methods and tools to size solar photovoltaic systems; however, these tools rely on simulations, which do not cover all aspects of the design space during the search for optimal solution. In prior studies in optimal sizing, the focus was always on criteria or objectives. Here, we present a new sound and automated approach to obtain optimal sizing using an unprecedented program synthesis. Our variant of counterexample guided inductive synthesis (CEGIS) approach has two phases linking the technical and cost analysis: first we synthesize a feasible candidate based on power reli…
Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-State Data
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb（萨格勒布大学机械与船舶工程学院）；Electrical Engineering Faculty, Eindhoven University of Technology（埃因霍温理工大学电气工程学院）
In this paper, we study feedback dynamical systems with memoryless controllers under imperfect information. We develop an algorithm that searches for "adversarial scenarios", which can be thought of as the strategy for the adversary representing the noise and disturbances, that lead to safety violations. The main challenge is to analyze the closed-loop system's vulnerabilities with a potentially complex or even unknown controller in the loop. As opposed to commonly adopted approaches that treat the system under test as a black-box, we propose a synthesis-guided approach, which leverages the kn…
The problem of unknown input observer design is considered for coupled PDE/ODE systems subject to incremental sector bounded nonlinearities and unknown boundary inputs. Assuming available measurements at the boundary of the distributed domain, the synthesis of the unknown input observer is based on Lyapunov methods and convex optimization. Numerical simulations support and confirm the theoretical findings, illustrating the robust estimation performances of the proposed nonlinear unknown input observer.
Radboud University（拉德堡德大学）；University of Oxford（牛津大学）
Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based co…
The prolific rise in autonomous systems has led to questions regarding their safe instantiation in real-world scenarios. Failures in safety-critical contexts such as human-robot interactions or even autonomous driving can ultimately lead to loss of life. In this context, this paper aims to provide a method by which one can algorithmically test and evaluate an autonomous system. Given a black-box autonomous system with some operational specifications, we construct a minimax problem based on control barrier functions to generate a family of test parameters designed to optimally evaluate whether …
