Safety Controller Synthesis Research Articles

Formal Synthesis of Safety Controllers via $k$-Inductive Control Barrier Certificates

Formal Synthesis of Safety Controllers via $k$-Inductive Control Barrier Certificates

Distributed Safety Controller Synthesis for Unknown Interconnected Systems via Graph Neural Networks

This paper focuses on distributed controller synthesis for ensuring the safety of large-scale systems with unknown dynamics and known interconnection structures, employing control barrier certificates. Our approach centers on a distributed framework tailored to create control barrier certificates for safety, utilizing the interconnections within large-scale systems. We introduce a novel application of graph neural networks to synthesize these certificates and distributed controllers in a data-driven fashion. The formal correctness of trained networks is subsequently validated through data-driven techniques involving the solution of a sampling-based optimization problem. To illustrate the effectiveness of our methodology, we conduct experiments on a complex interconnected system comprising as many as 1000 components.

Compositional Construction of Safety Controllers for Networks of Continuous-Space POMDPs

In this article, we propose a compositional framework for the synthesis of safety controllers for networks of partially observable discrete-time stochastic control systems (also known as continuous-space partially observable Markov decision processes (POMDPs)). Given an estimator, we utilize a discretization-free approach to synthesize controllers ensuring safety specifications over finite-time horizons. The proposed framework is based on a notion of so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local control barrier functions</i> computed for subsystems in two different ways. In the first scheme, no prior knowledge of estimation accuracy is needed. The second framework utilizes a probability bound on the estimation accuracy using a notion of so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stochastic simulation functions</i> . In both proposed schemes, we derive sufficient small-gain-type conditions in order to compositionally construct control barrier functions for interconnected POMDPs using local barrier functions computed for subsystems. The constructed control barrier functions for the overall networks enable us to compute lower bounds on the probabilities that the interconnected POMDPs avoid certain unsafe regions in finite-time horizons. We demonstrate the effectiveness of our proposed approaches by applying them to an adaptive cruise control problem.

Safety Verification and Controller Synthesis for Systems with Input Constraints

In this paper we consider the safety verification and safe controller synthesis for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the barrier certificates approach. Our approach can be used to characterize control invariance of a given set in terms of safety of a general nonlinear control system subject to input constraints. From the point of view of controller design, the proposed method provides an approach to synthesize a safe control law that guarantees that the trajectories of the system starting from a given initial set do not enter an unsafe set. Unlike the related control barrier functions formulations, our formulation only considers the vector field within the tangent cone of the zero level set defined by the certificates, and is shown to be less conservative by means of numerical evidence. For polynomial systems with semi-algebraic initial and safe sets, CBCs and safe control laws can be synthesized using sum-of-squares decomposition and semi-definite programming. Numerical examples demonstrate the efficacy of our approach.

Formal Synthesis of Safety Controllers for Unknown Systems Using Gaussian Process Transfer Learning

Formal Synthesis of Safety Controllers for Unknown Systems Using Gaussian Process Transfer Learning

Synthesis of Controllers for Partially-Observable Systems: A Data-Driven Approach

This paper is concerned with the formal synthesis of safety controllers for partially-observable continuous-time polynomial-type systems with unknown dynamics. Given a continuous-time polynomial-type estimator with a partially-unknown dynamic and a known upper bound on the estimation accuracy, we propose a data-driven approach to compute a polynomial-type controller ensuring safety of the system. The proposed framework is based on a notion of so-called control barrier functions and only requires a single output trajectory collected from the system and a single state trajectory collected from its estimator. We show the application of our technique by synthesizing a safety controller for a partially-observable jet engine with unknown dynamics.

Data-Driven Synthesis of Safety Controllers via Multiple Control Barrier Certificates

This work proposes a data-driven framework to synthesize safety controllers for nonlinear systems with finite input sets and unknown mathematical models. The proposed scheme leverages new notions of multiple control barrier certificates (M-CBC) and provides controllers ensuring the safety of systems with confidence 1. While there may not exist a common control barrier certificate with a fixed template, our proposed technique adaptively partitions the state set to potentially find M-CBC of the same template for different regions. In the proposed data-driven framework, we first cast our proposed conditions of M-CBC as a robust optimization program (ROP). Given that the unknown model appears in some of the constraints of the ROP, we propose a sampling approach for collecting data and provide a scenario optimization program (SOP) associated with the proposed ROP. We solve the resulted SOP and construct M-CBC together with safety controllers for the unknown system with 100% correctness guarantee. We apply our results to a nonlinear jet engine compressor with unknown dynamics to illustrate the efficacy of our data-driven approach. In the case study, we show that while there exists no common polynomial-type control barrier certificate of a given degree, there exist polynomial-type M-CBC of the same degree by partitioning the state set to different regions.

Learning-based symbolic abstractions for nonlinear control systems

Symbolic models or abstractions are known to be powerful tools for the control design of cyber–physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach to the construction of symbolic models for nonlinear control systems. In particular, the symbolic model is constructed based on learning the un-modeled part of the dynamics from training data based on state-space exploration, and the concept of an alternating simulation relation that represents behavioral relationships with respect to the original control system. Moreover, we aim at achieving safe exploration, meaning that the trajectory of the system is guaranteed to be in a safe region for all times while collecting the training data. In addition, we provide some techniques to reduce the computational load, in terms of memory and computation time,of constructing the symbolic models and the safety controller synthesis, so as to make our approach practical. Finally, a numerical simulation illustrates the effectiveness of the proposed approach.

Verified synthesis of optimal safety controllers for human-robot collaboration

We present a tool-supported approach for the synthesis, verification and validation of the control software responsible for the safety of the human-robot interaction in manufacturing processes that use collaborative robots. In human-robot collaboration, software-based safety controllers are used to improve operational safety, e.g., by triggering shutdown mechanisms or emergency stops to avoid accidents. Complex robotic tasks and increasingly close human-robot interaction pose new challenges to controller developers and certification authorities. Key among these challenges is the need to assure the correctness of safety controllers under explicit (and preferably weak) assumptions. Our controller synthesis, verification and validation approach is informed by the process, risk analysis, and relevant safety regulations for the target application. Controllers are selected from a design space of feasible controllers according to a set of optimality criteria, are formally verified against correctness criteria, and are translated into executable code and validated in a digital twin. The resulting controller can detect the occurrence of hazards, move the process into a safe state, and, in certain circumstances, return the process to an operational state from which it can resume its original task. We show the effectiveness of our software engineering approach through a case study involving the development of a safety controller for a manufacturing work cell equipped with a collaborative robot.

Safety Control Synthesis for Systems with Missing Measurements

Abstract We study the problem of synthesizing controllers that enforce hard state-constraints under occasionally missing state measurements. Although the problem can be solved as a partial information game via power set construction, it is undesired to do so because power set construction is computationally expensive. In this paper, we consider the instances where the missing data pattern can be specified by an automaton, and show that, for such cases, the synthesis problem admits a simpler solution. We introduce string automata and exploit the causality requirement to define the structure of the controller, and further use this structure to derive a product system. The synthesis problem then reduces to a full-information game on this product system. Two examples illustrate the efficacy of the proposed approach.

Lazy Symbolic Controller for Continuous-Time Systems Based on Safe Set Boundary Exploration

Abstract In this paper, we present an abstraction-based approach to robust safety controller synthesis for continuous-time nonlinear systems. To reduce the computational complexity associated with symbolic control approaches, we develop a lazy controller synthesis algorithm, which iteratively explores states on the boundary of controllable domain while avoiding exploration of internal states, supposing that they are safely controllable a priory. A closed-loop safety controller for the original problem is then defined as follows: we use the abstract controller to push the system from a boundary state back towards the interior, while for inner states, any admissible input is valid. We then compare the proposed approach with the classical safety synthesis algorithm and illustrate the advantages, in terms of run-time and memory efficiency, on an adaptive cruise control problem.

Lazy Safety Controller Synthesis with Multi-Scale Adaptive-Sampling Abstractions of Nonlinear Systems

Abstract In this paper, we present an abstraction-based approach to safety controller synthesis for continuous-time nonlinear systems. To reduce the computational burden associated with symbolic control approaches, we develop a lazy controller synthesis algorithm, which uses the incremental forward exploration of the symbolic dynamics, allowing us to restrict the controller synthesis computations to reachable states only. We propose using this algorithm with novel multi-scale abstractions, which also use adaptive time sampling. Transition duration is constrained by intervals that must contain the reachable set, which enables better control of the symbolic transitions as opposed to using transitions of predetermined duration. Implementation of the algorithm and controller refinement are discussed. We provide a simple example to illustrate these benefits of the approach.

Safety control, a quantitative approach

Safety control consists in maintaining the state of a given system inside a specified set of safe states. Traditionally, the problem is tackled using set-theoretic methods, which are mostly qualitative: states are partitioned between safety-controllable (i.e. states that belong to the maximal controlled invariant subset of the safe set) and safety-uncontrollable states. In this paper, we present a quantitative approach to safety controller synthesis. Our approach makes it possible to compute a measure of safety, which quantifies how far from the unsafe set (respectively, how close to the safe set) one can stay when starting from a given controllable (respectively, uncontrollable) state. For finite transition systems, such a measure can be computed in finite-time using a functional fixed-point iteration. In addition, we show that the level sets of the functional fixed-point coincide with the maximal controlled invariant subsets of a parameterized family of sets and that one can synthesize a common safety controller for all the sets of the family. In the second part of the paper, we show how the approach can be used in the framework of abstraction-based synthesis to lift these results to infinite transition systems with finite abstractions. To illustrate the effectiveness of the approach, we show an application of the approach to a simple boost DC-DC converter.

Run-Time Risk Mitigation in Automated Vehicles: A Model for Studying Preparatory Steps

We assume that autonomous or highly automated driving (AD) will be accompanied by tough assurance obligations exceeding the requirements of even recent revisions of ISO 26262 or SOTIF. Hence, automotive control and safety engineers have to (i) comprehensively analyze the driving process and its control loop, (ii) identify relevant hazards stemming from this loop, (iii) establish feasible automated measures for the effective mitigation of these hazards or the alleviation of their consequences. By studying an example, this article investigates some achievements in the modeling for the steps (i), (ii), and (iii), amenable to formal verification of desired properties derived from potential assurance obligations such as the global existence of an effective mitigation strategy. In addition, the proposed approach is meant for step-wise refinement towards the automated synthesis of AD safety controllers implementing such properties.

Safety Controller Synthesis for Incrementally Stable Switched Systems Using Multiscale Symbolic Models

We propose an approach to the synthesis of safety controllers for a class of switched systems, based on the use of multiscale symbolic models that describe transitions of various durations and whose sets of states are given by a sequence of embedded lattices approximating the state-space, the finer lattices being accessible only by transitions of shorter duration. We prove that these multiscale symbolic models are approximately bisimilar to the original switched system provided it enjoys an incremental stability property attested by the existence of a common Lyapunov function or of multiple Lyapunov functions with a minimal dwell-time. Then, for specifications given by a safety automaton, we present a controller synthesis algorithm that exploits the specificities of multiscale symbolic models. We formalize the notion of maximal lazy safety controller which gives priority to transitions of longer durations; the shorter transitions and thus the finer scales of the symbolic model are effectively explored only when safety cannot be ensured at the coarser level and fast switching is needed. We propose a synthesis algorithm where symbolic models can be computed on the fly, this allows us to keep the number of symbolic states as low as possible. We provide computational evidence that shows drastic improvements of the complexity of controller synthesis using multiscale symbolic models instead of uniform ones.

Safety Controller Synthesis Using Human Generated Trajectories

This paper focuses on the task of safety controller synthesis, that is, designing a controller that will take a system from any point within a compact set of initial states to a point inside a set of acceptable goal states, while never entering any state that is deemed unsafe. To do this we use a human generated trajectory-based approach. We introduce the control autobisimulation function, which is the analog of the control Lyapunov function for approximate bisimulation. We consider a class of hybrid systems and use this function to determine a set of admissible feedback control laws that guarantee trajectory robustness for underlying dynamics that are linear affine, feedback linearizable, and differentially flat. This property ensures that any trajectory of the closed-loop system that is initialized within some neighborhood of a nominal trajectory will stay within some tube of the nominal trajectory when given the same input. This feedback control and input can be used as the controller for some subset of the initial states. We demonstrate how to combine multiple trajectories into a synthesized controller that satisfies the safety problem.

Synthesis of memory-efficient, clock-memory free, and non-Zeno safety controllers for timed systems

We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a Zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a logarithmic (in the number of clocks) number of memory bits (i.e. a linear number of memory states). Precisely, we show that for safety objectives, a memory of size (3+lg(|C|+1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential memory states bound. We also settle the open question of whether winning region-based strategies require memory for safety objectives by showing with an example the necessity of memory for such strategies to win for safety objectives. Finally, we show that the decision problem of determining if there exists a receptive player-1 winning strategy for safety objectives is EXPTIME-complete over timed automaton games.