We describe a new variant of zero dynamics attack (ZDA), what we call a switched ZDA, targeting linear time-invariant (LTI) sampled-data systems with non-uniform sampling. Specifically, we consider continuous-time systems and construct attacks that exploit the unstable sampling zeros resulting from a zero-order hold (ZOH) mechanism. These attacks can be constructed by strong adversaries who have knowledge of the plant dynamics, with the additional requirement that they can determine the next sampling instant. We provide sufficient conditions when cyber-physical systems are vulnerable to switched ZDAs, and prove that these attacks can be disruptive while remaining stealthy. We also provide two possible countermeasures that make switched ZDAs ineffective. The first countermeasure revolves around creating a mismatch between the next sampling instant as predicted by the adversary and the true one, which makes the switched ZDAs no longer stealthy. The second countermeasure relies on increasing the inter-sample times such that the system no longer contains unstable sampling zeros, making the switched ZDA no longer disruptive. We demonstrate the vulnerability of sampled-data systems with non-uniform sampling to switched ZDAs in several illustrative examples, and exemplify the effectiveness of the proposed countermeasures.

We propose a novel watermarking scheme by modifying a self-triggered control (STC) policy, aimed at detecting replay attacks for linear time-invariant (LTI) systems. We show that by employing non-deterministic early triggering of the STC mechanism, replay attacks can be detected by a modified χ2 detector which takes into account the aperiodic nature of the inter-sample times. Specifically, we consider the case where a periodic reference signal is tracked, which makes these systems vulnerable to replay attacks. The proposed approach is modular and can be retrofitted to legacy systems. An approach for designing an online optimal early triggering mechanism is provided. This is validated through an illustrative numerical example in which we compare our method to scenarios employing both additive and multiplicative watermarking.

We employ the scenario optimisation theory to compute a traffic abstraction, with probability guarantees of correctness, of a PETC system with unknown dynamics from a finite number of samples. To this end, we extend the scenario optimisation approach to multiclass SVM in order to compute a map between the concrete state space and the intersample times of the PETC. This map allows the construction of a traffic abstraction, through an <inline-formula><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula>-complete relation, that provides upper and lower bounds on the sampling performance of the concrete system. We further propose an alternative path to build such abstraction, first we identify the model and then apply a model-based procedure. Numerical benchmarks show the practical applicability of our methods for noiseless and noisy samples.

We present a hierarchical architecture to improve the efficiency of event-triggered control (ETC) in reducing resource consumption. This paper considers event-triggered systems generally as an impulsive control system in which the objective is to minimize the number of impulses. Our architecture recognizes that traditional ETC is a greedy strategy towards optimizing average inter-event times and introduces the idea of a deadline policy for the optimization of long-term discounted inter-event times. A lower layer is designed employing event-triggered control to guarantee the satisfaction of control objectives, while a higher layer implements a deadline policy designed with reinforcement learning to improve the discounted inter-event time. We apply this scheme to the control of an orbiting spacecraft, showing superior performance in terms of actuation frequency reduction with respect to a standard (one-layer) ETC while maintaining safety guarantees.

Estimating the expectation of a Bernoulli random variable based on N independent trials is a classical problem in statistics, typically addressed using Binomial Proportion Confidence Intervals (BPCI). In the control systems community, many critical tasks—such as certifying the statistical safety of dynamical systems—can be formulated as BPCI problems. Conformal Prediction (CP), a distribution-free technique for uncertainty quantification, has gained significant attention in recent years and has been applied to various control systems problems, particularly to address uncertainties in learned dynamics or controllers. A variant known as training-conditional CP was recently employed to tackle the problem of safety certification. In this note, we highlight that the use of training-conditional CP in this context does not provide valid safety guarantees. We demonstrate why CP is unsuitable for BPCI problems and argue that traditional BPCI methods are better suited for statistical safety certification.

Model-based fault detection identifies anomalies by comparing a system's output with the prediction from a model. Although such a technique can be very powerful, it may suffer from the computational complexity of its underlying models, especially for large systems. An alternative approach that circumvents this cost increase uses barrier functions, which abstract the system's behaviour into a single value. In this paper, we propose a fault detection mechanism via output-based barrier functions, that does not require to estimate the full state, copes with noisy processes, and is tailored to safety-critical faults as given by a user-defined safe region. We leverage such a mechanism by introducing so-called p-fault tolerant sets, which guarantee that a faulty system requires at least p time steps before reaching any unsafe state. Our approach is validated through numerical experiments on two systems with linear and nonlinear dynamics, along with the classic three-tank model.

We propose a novel cyber-attack detection scheme for control schemes regulated via Stochastic Event-Triggered Control, to detect packets that are maliciously injected by an adversary. The diagnosis scheme relies on assessing whether the arrival time of the information packets received from the controller are compatible with the nominal probability distribution of triggering, or whether they are anomalous. To contrast the threat of an eavesdropping adversary capable of estimating the nominal triggering distribution, we propose a switching scheme, whereby the probability of triggering is drawn among a set of stochastic triggering mechanisms, which is such that the reconstruction of the communication pattern by an eavesdropper becomes computationally infeasible. We design the set of stochastic triggering mechanisms via the solution of an optimization problem, which embeds an explicit trade-off between the properties of the nominal Stochastic Event-Triggered Controller and the detection scheme. The results are illustrated through a numerical example.

We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of distributions that are ɛ−close, in the Wasserstein distance sense, to a nominal one. We propose algorithms for the efficient synthesis of distributionally robust control strategies that maximize the satisfaction probability of reach-avoid specifications with either a given or an arbitrary (not specified) time horizon, i.e., unbounded-time reachability. The framework consists of two main steps: finite abstraction and control synthesis. First, we construct a finite abstraction of the switched stochastic system as a robust Markov decision process (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution. Then, we synthesize a strategy that is robust to the distributional uncertainty on the resulting robust MDP. We employ techniques from optimal transport and stochastic programming to reduce the strategy synthesis problem to a set of linear programs, and propose a tailored and efficient algorithm to solve them. The resulting strategies are correctly refined into switching strategies for the original stochastic system. We illustrate the efficacy of our framework on various case studies comprising both linear and non-linear switched stochastic systems.

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of stochastic systems, methods based on discrete, finite Markov approximations - abstractions - thereof have surged in recent years. These are found in contexts where: either a) one only has partial, discrete observations of the underlying continuous stochastic process, or b) the original system is too complex to analyze, so one partitions the continuous state-space of the original system to construct a handleable, finite-state model thereof. In both cases, the abstraction is an approximation of the discrete stochastic process that arises precisely from the discretization of the underlying continuous process. The fact that the abstraction is Markov and the discrete process is not (even though the original one is) leads to approximation errors. Towards accounting for non-Markovianity, we introduce memory-dependent abstractions for stochastic systems, capturing dynamics with memory effects. Our contribution is twofold. First, we provide a formalism for memory-dependent abstractions based on transfer operators. Second, we quantify the approximation error by upper bounding the total variation distance between the true continuous state distribution and its discrete approximation.

We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

Analyzing event-triggered control's (ETC) sampling behavior is of paramount importance, as it enables formal assessment of its sampling performance and prediction of its sampling patterns. In this work, we formally analyze the sampling behavior of stochastic linear periodic ETC (PETC) systems by computing bounds on associated metrics. Specifically, we consider functions over sequences of state measurements and intersampling times that can be expressed as average, multiplicative or cumulative rewards, and introduce their expectations as metrics on PETC's sampling behavior. We compute bounds on these expectations, by constructing Interval Markov Chains equipped with suitable reward functions, that abstract stochastic PETC's sampling behavior. Our results are illustrated on a numerical example, for which we compute bounds on the expected average intersampling time and on the probability of triggering with the maximum possible intersampling time in a finite horizon.

The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic processes in terms of richer discrete stochastic models, whose actions lead to nondeterministic transitions over the space of probability measures. The data-driven component of the proposed methodology lies in the fact that we only assume samples from an unknown probability distribution. We also rely on the model of the underlying dynamics to build our abstraction through backward reachability computations. The nondeterminism in the probability space is captured by a collection of Markov Processes, and we identify how this model can improve upon existing abstraction techniques in terms of satisfying temporal properties, such as safety or reach-avoid. The connection between the discrete and the underlying dynamics is made formal through the use of the scenario approach theory. Numerical experiments illustrate the advantages and main limitations of the proposed techniques with respect to existing approaches.

Event-triggered control (ETC) is a major recent development in cyber–physical systems due to its capability of reducing resource utilization in networked devices. However, while most of the ETC literature reports simulations indicating massive reductions in the sampling required for control, no method so far has been capable of quantifying these results. In this work, we propose an approach through finite-state abstractions to do formal quantification of the traffic generated by ETC of linear systems, in particular aiming at computing its smallest average inter-sample time (SAIST). The method involves abstracting the traffic model through l-complete abstractions, finding the cycle of minimum average length in the graph associated to it, and verifying whether this cycle is an infinitely recurring traffic pattern. The method is proven to be robust to sufficiently small model uncertainties, which allows its application to compute the SAIST of ETC of nonlinear systems.

We present a novel framework for formal control of uncertain discrete-time switched stochastic systems against probabilistic reach-avoid specifications. In particular, we consider stochastic systems with additive noise, whose distribution lies in an ambiguity set of distributions that are ε−close to a nominal one according to the Wasserstein distance. For this class of systems we derive control synthesis algorithms that are robust against all these distributions and maximize the probability of satisfying a reach-avoid specification, defined as the probability of reaching a goal region while being safe. The framework we present first learns an abstraction of a switched stochastic system as a robust Markov decision process (robust MDP) by accounting for both the stochasticity of the system and the uncertainty in the noise distribution. Then, it synthesizes a strategy on the resulting robust MDP that maximizes the probability of satisfying the property and is robust to all uncertainty in the system. This strategy is then refined into a switching strategy for the original stochastic system. By exploiting tools from optimal transport and stochastic programming, we show that synthesizing such a strategy reduces to solving a set of linear programs, thus guaranteeing efficiency. We experimentally validate the efficacy of our framework on various case studies, including both linear and non-linear switched stochastic systems. Our results represent the first formal approach for control synthesis of stochastic systems with uncertain noise distribution.

We introduce a novel approach for the construction of symbolic abstractions - simpler, finite-state models - which mimic the behaviour of a system of interest, and are commonly utilized to verify complex logic specifications. Such abstractions require an exhaustive knowledge of the concrete model, which can be difficult to obtain in real-world applications. To overcome this, we propose to sample finite length trajectories of an unknown system and build an abstraction based on the concept of ℓ -completeness. To this end, we introduce the notion of probabilistic behavioural inclusion. We provide probably approximately correct (PAC) guarantees that such an abstraction, constructed from experimental symbolic trajectories of finite length, includes all behaviours of the concrete system, for both finite and infinite time horizon. Finally, our method is displayed with numerical examples.

Interval Markov Decision Processes (IMDPs) are finite-state uncertain Markov models, where the transition probabilities belong to intervals. Recently, there has been a surge of research on employing IMDPs as abstractions of stochastic systems for control synthesis. However, due to the absence of algorithms for synthesis over IMDPs with continuous action-spaces, the action-space is assumed discrete a-priori, which is a restrictive assumption for many applications. Motivated by this, we introduce continuous-action IMDPs (caIMDPs), where the bounds on transition probabilities are functions of the action variables, and study value iteration for maximizing expected cumulative rewards. Specifically, we decompose the max-min problem associated to value iteration to |Q| max problems, where |Q| is the number of states of the caIMDP. Then, exploiting the simple form of these max problems, we identify cases where value iteration over caIMDPs can be solved efficiently (e.g., with linear or convex programming). We also gain other interesting insights: e.g., in certain cases where the action set A is a polytope, synthesis over a discrete-action IMDP, where the actions are the vertices of A, is sufficient for optimality. We demonstrate our results on a numerical example. Finally, we include a short discussion on employing caIMDPs as abstractions for control synthesis.

We present a biologically inspired design for swarm foraging based on ant’s pheromone deployment, where the swarm is assumed to have very restricted capabilities. The robots do not require global or relative position measurements and the swarm is fully decentralized and needs no infrastructure in place. Additionally, the system only requires one-hop communication over the robot network, we do not make any assumptions about the connectivity of the communication graph and the transmission of information and computation is scalable versus the number of agents. This is done by letting the agents in the swarm act as foragers or as guiding agents (beacons). We present experimental results computed for a swarm of Elisa-3 robots on a simulator, and show how the swarm self-organizes to solve a foraging problem over an unknown environment, converging to trajectories around the shortest path, and test the approach on a real swarm of Elisa-3 robots. At last, we discuss the limitations of such a system and propose how the foraging efficiency can be increased.