TRUST is an open-source software tool developed for data-driven controller synthesis of dynamical systems with unknown mathematical models, ensuring either stability or safety properties. By collecting only a single input-state trajectory from the unknown system and satisfying a rank condition that ensures the system is persistently excited according to the Willems et al.'s fundamental lemma, TRUST aims to design either control Lyapunov functions (CLF) or control barrier certificates (CBC), along with their corresponding stability or safety controllers. The tool implements sum-of-squares (SOS) optimization programs solely based on data to enforce stability or safety properties across four system classes: (i) continuous-time nonlinear polynomial systems, (ii) continuous-time linear systems, (iii) discrete-time nonlinear polynomial systems, and (iv) discrete-time linear systems. TRUST is a Python-based web application featuring an intuitive, reactive graphic user interface (GUI) built with web technologies. It can be accessed at https://trust.tgo.dev or installed locally, and supports both manual data entry and data file uploads. Leveraging the power of the Python backend and a JavaScript frontend, TRUST is designed to be highly user-friendly and accessible across desktop, laptop, tablet, and mobile devices. We apply TRUST to a set of physical benchmarks with unknown dynamics, ensuring either stability or safety properties across the four supported classes of models.

Synthesizing safety controllers for general nonlinear systems is a highly challenging task, particularly when the system models are unknown, and input constraints are present. While some recent efforts have explored data-driven safety controller design for nonlinear systems, these approaches are primarily limited to specific classes of nonlinear dynamics (e.g., polynomials) and are not applicable to general nonlinear systems. This paper develops a direct data-driven approach for discrete-time general nonlinear systems, facilitating the simultaneous learning of control barrier certificates (CBCs) and dynamic controllers to ensure safety properties under input constraints. Specifically, by leveraging the adding-one-integrator approach, we incorporate the controller's dynamics into the system dynamics to synthesize a virtual static-feedback controller for the augmented system, resulting in a dynamic safety controller for the actual dynamics. We collect input-state data from the augmented system during a finite-time experiment, referred to as a single trajectory. Using this data, we learn augmented CBCs and the corresponding virtual safety controllers, ensuring the safety of the actual system and adherence to input constraints over a finite time horizon. We demonstrate that our proposed conditions boil down to some data-dependent linear matrix inequalities (LMIs), which are easy to satisfy. We showcase the effectiveness of our data-driven approach through two case studies: one exhibiting significant nonlinearity and the other featuring high dimensionality.

This work is concerned with a data-driven scheme to construct reduced-order models (ROMs) of dynamical systems with unknown mathematical models. Our methodology leverages data and establishes similarity relations between output trajectories of unknown systems and their data-driven ROMs via the notion of simulation functions (SFs), capable of formally quantifying their closeness. To achieve this, under a rank condition readily fulfillable using data, we collect only two input-output trajectories from unknown systems to construct both ROMs and SFs, while offering correctness guarantees. We demonstrate that the proposed ROMs derived from data can be leveraged for controller synthesis endeavors while effectively ensuring high-level logic properties over unknown dynamical models. We showcase our data-driven findings across a range of benchmark scenarios involving various unknown physical systems, demonstrating the enforcement of diverse complex properties.

We offer a compositional data-driven scheme for synthesizing controllers that ensure global asymptotic stability (GAS) across large-scale interconnected networks, characterized by unknown mathematical models. In light of each network's configuration composed of numerous subsystems with smaller dimensions, our proposed framework gathers data from each subsystem's trajectory, enabling the design of local controllers that ensure input-to-state stability (ISS) properties over subsystems, signified by ISS Lyapunov functions. To accomplish this, we require only a single input-state trajectory from each unknown subsystem up to a specified time horizon, fulfilling certain rank conditions. Subsequently, under small-gain compositional reasoning, we leverage ISS Lyapunov functions derived from data to offer a control Lyapunov function (CLF) for the interconnected network, ensuring GAS certificate over the network. We demonstrate that while the computational complexity for designing a CLF increases polynomially with the network dimension using sum-of-squares (SOS) optimization, our compositional data-driven approach significantly mitigates it to linear with respect to the number of subsystems. We showcase the efficacy of our data-driven approach over a set of benchmarks, involving physical networks with diverse interconnection topologies.

This paper offers a formal data-driven scheme for constructing control barrier certificates (CBC) and synthesizing safety controllers for discrete-time control systems. Our framework accommodates scenarios where the mathematical model is unknown, while also considering the presence of wireless communication networks between sensor-controller and controller-actuator links. While existing literature extensively addresses the design of CBC, there has been a notable lack of attention in incorporating wireless communication networks to tackle potential packet losses. This gap poses a greater challenge when considering the absence of knowledge about the system’s model, a crucial aspect in real-world applications. Given a particular rank condition for unknown wirelessly-connected systems, our method provides a linear matrix inequality, constructed based on two input-output trajectories of the system, offering a probabilistic safety assurance across an infinite time horizon. We showcase the efficacy of our data-driven approach over a wirelessly-connected synchronous motor with an unknown model.

In this work, we propose a formal framework for safety controller synthesis of stochastic control systems with both process and measurement noises while considering wireless communication networks between sensors, controllers, and actuators. The proposed scheme relies on the utilization of control barrier certificates (CBC), enabling us to offer probabilistic safety certifications for wirelessly connected stochastic systems. Despite the existing literature on designing control barrier certificates, wireless communication networks have not been taken into account to address potential packet losses and end-to-end delays, a critical consideration for safety-critical real-world applications. In our proposed scenario, the primary aim is to construct a control barrier certificate alongside a safety controller, ensuring a lower bound on the probability of satisfying the safety property within a finite time horizon. We showcase the efficacy of our approach through multiple physical case studies involving communication networks, including a permanent magnet synchronous motor, vehicle lane-keeping system, and Moore-Greitzer jet engine with nonlinear dynamics.

In this work, we develop a framework for formally constructing finite abstractions, also known as finite Markov decision processes (MDPs), for continuous-space stochastic hybrid systems. These complex systems encompass both continuous dynamics, described by stochastic differential equations involving Brownian motions and Poisson processes, as well as instantaneous jumps governed by stochastic difference equations with additive noise components. Our approach is grounded in the concept of stochastic simulation functions, enabling us to employ finite MDPs as suitable substitutes for original hybrid systems in the controller design process. Our construction methodology offers an augmented framework capable of characterizing stochastic hybrid systems with both continuous evolutions and instantaneous jumps. This unified framework ensures that state trajectories of augmented systems exactly match those of original hybrid systems. Subsequently, we outline a systematic procedure for constructing finite MDPs from the general class of nonlinear stochastic hybrid systems exhibiting an incremental input-to-state stability property. Additionally, we focus on a linear class of stochastic hybrid systems and propose a construction scheme based on the satisfaction of certain matrix inequalities. We validate the efficacy of our proposed approaches through a case study.

In this work, we develop an open-source software tool, called IMPaCT, for the parallelized verification and controller synthesis of large-scale stochastic systems using interval Markov chains (IMCs) and interval Markov decision processes (IMDPs), respectively. The tool serves to (i) construct IMCs/IMDPs as finite abstractions of underlying original systems, and (ii) leverage interval iteration algorithms for formal verification and controller synthesis over infinite-horizon properties, including safety, reachability, and reach-avoid, while offering convergence guarantees. IMPaCT is developed in C++ and designed using AdaptiveCpp, an independent open-source implementation of SYCL, for adaptive parallelism over CPUs and GPUs of all hardware vendors, including Intel and NVIDIA. IMPaCT stands as the first software tool for the parallel construction of IMCs/IMDPs, empowered with the capability to leverage high-performance computing platforms and cloud computing services, while providing formal convergence guarantees. We benchmark IMPaCT on several physical case studies adopted from the ARCH tool competition for stochastic models.

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This work studies formal verification of continuous-time continuous-space systems with unknown dynamics against safety specifications. The proposed framework is based on a data-driven construction of barrier certificates using which the safety of unknown systems is verified via a finite set of data collected from trajectories of systems with a priori guaranteed confidence. In the proposed scheme, we first cast the original safety problem as a robust convex program (RCP). Since the unknown model appears in one of the constraints of the proposed RCP, we provide the scenario convex program (SCP) corresponding to the original RCP by collecting finite numbers of data from systems' evolutions. We then establish a probabilistic closeness between the optimal value of SCP and that of RCP. Accordingly, we formally quantify the safety guarantee of unknown systems based on the number of data and the required level of safety confidence.

In this work, we propose a data-driven technique for a formal estimation of infinitesimal generators of continuous-time stochastic systems with unknown dynamics. In the proposed framework, we first approximate the infinitesimal generator of the solution process via a set of data collected from solution processes of unknown systems. We then put some proper assumptions on dynamics of systems and quantify the closeness between the infinitesimal generator and its approximation while providing a priori guaranteed confidence bound. We show that both the time discretization and the number of data play significant roles in providing a reasonable closeness precision.

In this paper, we propose a software tool, called AMYTISS , implemented in C++/OpenCL, for designing correct-by-construction controllers for large-scale discrete-time stochastic systems. This tool is employed to (i) build finite Markov decision processes (MDPs) as finite abstractions of given original systems, and (ii) synthesize controllers for the constructed finite MDPs satisfying bounded-time high-level properties including safety, reachability and reach-avoid specifications. In AMYTISS , scalable parallel algorithms are designed such that they support the parallel execution within CPUs, GPUs and hardware accelerators (HWAs). Unlike all existing tools for stochastic systems, AMYTISS can utilize high-performance computing (HPC) platforms and cloud-computing services to mitigate the effects of the state-explosion problem, which is always present in analyzing large-scale stochastic systems. We benchmark AMYTISS against the most recent tools in the literature using several physical case studies including robot examples, room temperature and road traffic networks. We also apply our algorithms to a 3-dimensional autonomous vehicle and 7-dimensional nonlinear model of a BMW 320i car by synthesizing an autonomous parking controller.

Large-scale stochastic systems have recently received significant attentions due to their broad applications in various safety-critical systems such as traffic networks and self-driving cars. In this poster, we describe the software tool AMYTISS, implemented in C++/OpenCL, for designing correct-by-construction controllers for large-scale discrete-time stochastic systems. This tool is employed to (i) build finite Markov decision processes (MDPs) as finite abstractions of given original systems, and (ii) synthesize controllers for the constructed finite MDPs satisfying bounded-time safety, reachability, and reach-avoid specifications. In AMYTISS, scalable parallel algorithms are designed such that they support the parallel execution within CPUs, GPUs and hardware accelerators (HWAs). Unlike all existing tools for stochastic systems, AMYTISS can utilize high-performance computing (HPC) platforms and cloud-computing services to mitigate the effects of the state-explosion problem, which is always present in analyzing large-scale stochastic systems. We benchmark AMYTISS against the most recent tools in the literature using several physical case studies including robot examples, room temperature and road traffic networks. We also apply our algorithms to a 3-dimensional autonomous vehicle and a 7-dimensional nonlinear model of a BMW 320i car by synthesizing autonomous parking controllers.

This paper is concerned with a compositional approach for constructing finite Markov decision processes of interconnected discrete-time stochastic control systems. The proposed approach leverages the interconnection topology and a notion of so-called stochastic storage functions describing joint dissipativity-type properties of subsystems and their abstractions. In the first part of the paper, we derive dissipativity-type compositional conditions for quantifying the error between the interconnection of stochastic control subsystems and that of their abstractions. In the second part of the paper, we propose an approach to construct finite Markov decision processes together with their corresponding stochastic storage functions for classes of discrete-time control systems satisfying some incremental passivablity property. Under this property, one can construct finite Markov decision processes by a suitable discretization of the input and state sets. Moreover, we show that for linear stochastic control systems, the aforementioned property can be readily checked by some matrix inequality. We apply our proposed results to the temperature regulation in a circular building by constructing compositionally a finite Markov decision process of a network containing 200 rooms in which the compositionality condition does not require any constraint on the number or gains of the subsystems. We employ the constructed finite Markov decision process as a substitute to synthesize policies regulating the temperature in each room for a bounded time horizon. We also illustrate the effectiveness of our results on an example of fully connected network.

No abstract available.