Ensuring safety in autonomous systems with vision-based control remains a critical challenge due to the high dimensionality of image inputs and the fact that the relationship between true system state and its visual manifestation is unknown. Existing methods for learning-based control in such settings typically lack formal safety guarantees. To address this challenge, we introduce a novel semi-probabilistic verification framework that integrates reachability analysis with conditional generative networks and distribution-free tail bounds to enable efficient and scalable verification of vision-based neural network controllers. Next, we develop a gradient-based training approach that employs a novel safety loss function, safety-aware data-sampling strategy to efficiently select and store critical training examples, and curriculum learning, to efficiently synthesize safe controllers in the semi-probabilistic framework. Empirical evaluations in X-Plane 11 airplane landing simulation, CARLA-simulated autonomous lane following, F1Tenth vehicle lane following in a physical visually-rich miniature environment, and Airsim-simulated drone navigation and obstacle avoidance demonstrate the effectiveness of our method in achieving formal safety guarantees while maintaining strong nominal performance.

We address the challenge of safe control in decentralized multi-agent robotic settings, where agents use uncertain black-box models to predict other agents' trajectories. We use the recently proposed conformal decision theory to adapt the restrictiveness of control barrier functions-based safety constraints based on observed prediction errors. We use these constraints to synthesize controllers that balance between the objectives of safety and task accomplishment, despite the prediction errors. We provide an upper bound on the average over time of the value of a monotonic function of the difference between the safety constraint based on the predicted trajectories and the constraint based on the ground truth ones. We validate our theory through experimental results showing the performance of our controllers when navigating a robot in the multi-agent scenes in the Stanford Drone Dataset.

In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be (τ -)recurrent if every trajectory that starts in the set returns to it (within at most τ units of time). Recurrence entropy of a control system quantifies the complexity of making a set τ -recurrent measured by the average rate of growth, as time increases, of the number of control signals required to achieve this goal. Our analysis reveals that, compared to invariance, recurrence is quantitatively less complex, meaning that the recurrence entropy of a set is no larger than, and often strictly smaller than, the invariance entropy. We provide upper and lower bounds on recurrence entropy and show that they converge to the bounds on invariance entropy as τ decreases to zero. Further, our results show that recurrence entropy lower bounds the minimum data rate between the sensor and controller required for achieving recurrence. Finally, we present an algorithm according to which the sensor can send state estimates to the controller over a limited-bandwidth channel for achieving recurrence asymptotically at an exponential rate. We relate the data rate of the algorithm with the upper bound on entropy that we derive.

Abstract Tor has millions of daily users seeking privacy while browsing the Internet. It has thousands of relays to route users’ packets while anonymizing their sources and destinations. Users choose relays to forward their traffic according to probability distributions published by the Tor authorities. The authorities generate these probability distributions based on estimates of the capacities of the relays. They compute these estimates based on the bandwidths of probes sent to the relays. These estimates are necessary for better load balancing. Unfortunately, current methods fall short of providing accurate estimates leaving the network underutilized and its capacities unfairly distributed between the users’ paths. We present MLEFlow, a maximum likelihood approach for estimating relay capacities for optimal load balancing in Tor. We show that MLEFlow generalizes a version of Tor capacity estimation, TorFlow-P, by making better use of measurement history. We prove that the mean of our estimate converges to a small interval around the actual capacities, while the variance converges to zero. We present two versions of MLEFlow: MLEFlow-CF, a closed-form approximation of the MLE and MLEFlow-Q, a discretization and iterative approximation of the MLE which can account for noisy observations. We demonstrate the practical benefits of MLEFlow by simulating it using a flow-based Python simulator of a full Tor network and packet-based Shadow simulation of a scaled down version. In our simulations MLEFlow provides significantly more accurate estimates, which result in improved user performance, with median download speeds increasing by 30%.

Abstract We present $$\mathsf {SceneChecker}$$ SceneChecker , a tool for verifying scenarios involving vehicles executing complex plans in large cluttered workspaces. $$\mathsf {SceneChecker}$$ SceneChecker converts the scenario verification problem to a standard hybrid system verification problem, and solves it effectively by exploiting structural properties in the plan and the vehicle dynamics. $$\mathsf {SceneChecker}$$ SceneChecker uses symmetry abstractions, a novel refinement algorithm, and importantly, is built to boost the performance of any existing reachability analysis tool as a plug-in subroutine. We evaluated $$\mathsf {SceneChecker}$$ SceneChecker on several scenarios involving ground and aerial vehicles with nonlinear dynamics and neural network controllers, employing different kinds of symmetries, using different reachability subroutines, and following plans with hundreds of waypoints in complex workspaces. Compared to two leading tools, DryVR and Flow*, $$\mathsf {SceneChecker}$$ SceneChecker shows 14 $$\times $$ × average speedup in verification time, even while using those very tools as reachability subroutines.

We show that symmetry transformations and caching can enable scalable, and possibly unbounded, verification of multi-agent systems. Symmetry transformations map any solution of the system to another solution. We show that this property can be used to transform cached reachsets to compute new reachsets, for hybrid and multi-agent models. We develop a notion of a virtual system which defines symmetry transformations for a broad class of agent models that visit waypoint sequences. Using this notion of a virtual system, we present a prototype tool CacheReach that builds a cache of reachsets, in a way that is agnostic of the representation of the reachsets and the reachability analysis method used. Our experimental evaluation of CacheReach shows up to 64% savings in safety verification computation time on multi-agent systems with 3-dimensional linear and 4-dimensional nonlinear fixed-wing aircraft models following sequences of waypoints. These savings and our theoretical results illustrate the potential benefits of using symmetry-based caching in the safety verification of multi-agent systems.

Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. In this paper, we present a notion of topological entropy, to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. Since the actual value of this entropy is hard to compute in general, we compute an upper bound. We show that as the bound on the input decreases, we recover a previously known bound on estimation entropy - a similar notion of entropy - for nonlinear systems without inputs [10]. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound T > 0, constructs a function that approximates the trajectory up to an ε error up to time T. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed in addition to the state. Finally, we present an improved bound on entropy for systems with linear inputs.

Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. We present two notions of topological entropy, one to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. The other is to do the same but to estimate the state of a switched system with unknown switching signal up to an error that is bounded by ε for τ seconds after each switch and then decays exponentially at a rate of α till the next switch. Since computation of entropy is hard in general, we present upper bounds on both notions of entropy. Finally, we present preliminary results on the relation between the two notions. Note that most of the ideas presented in this abstract are from our papers [4] and [5].

State estimation is a fundamental problem for monitoring and controlling systems. Engineering systems interconnect sensing and computing devices over a shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. We present a notion of entropy for state estimation of switched nonlinear dynamical systems, an upper bound for it and a state estimation algorithm for the case when the switching signal is unobservable. Our approach relies on the notion of topological entropy and uses techniques from the theory for control under limited information. We show that the average bit rate used is optimal in the sense that, the efficiency gap of the algorithm is within an additive constant of the gap between estimation entropy of the system and its known upper-bound. We apply the algorithm to two system models and discuss the performance implications of the number of tracked modes.