arXiv subjects

Scott A. Smolka

Publications and source records attributed to Scott A. Smolka.

36 records · Page 2Linked to original sources

arXiv2018

Tight Continuous-Time Reachtubes for Lagrangian Reachability

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time $t_i$ to time $t_{i+1}$. We have developed simple explicit analytic formulas for the optimal metric for this deformation; this is superior to prior work, which used semi-definite programming. CLRT also uses infinitesimal strain theory to derive an optimal time increment $h_i$ between $t_i$ and $t_{i+1}$, nonlinear optimization to minimally bloat (i.e., using a minimal radius) the state set at time $t_i$ such that it includes all the states of the solution flow in the interval $[t_i,t_{i+1}]$. We use $δ$-satisfiability to ensure the correctness of the bloating. Our results on a series of benchmarks show that CLRT performs favorably compared to state-of-the-art tools such as CAPD in terms of the continuous reachtube volumes they compute.

math.NA↗

arXiv2018

Neural State Classification for Hybrid Systems

We introduce the State Classification Problem (SCP) for hybrid systems, and present Neural State Classification (NSC) as an efficient solution technique. SCP generalizes the model checking problem as it entails classifying each state $s$ of a hybrid automaton as either positive or negative, depending on whether or not $s$ satisfies a given time-bounded reachability specification. This is an interesting problem in its own right, which NSC solves using machine-learning techniques, Deep Neural Networks in particular. State classifiers produced by NSC tend to be very efficient (run in constant time and space), but may be subject to classification errors. To quantify and mitigate such errors, our approach comprises: i) techniques for certifying, with statistical guarantees, that an NSC classifier meets given accuracy levels; ii) tuning techniques, including a novel technique based on adversarial sampling, that can virtually eliminate false negatives (positive states classified as negative), thereby making the classifier more conservative. We have applied NSC to six nonlinear hybrid system benchmarks, achieving an accuracy of 99.25% to 99.98%, and a false-negative rate of 0.0033 to 0, which we further reduced to 0.0015 to 0 after tuning the classifier. We believe that this level of accuracy is acceptable in many practical applications, and that these results demonstrate the promise of the NSC approach.

cs.LG↗

arXiv2018

Adaptive Neighborhood Resizing for Stochastic Reachability in Multi-Agent Systems

We present DAMPC, a distributed, adaptive-horizon and adaptive-neighborhood algorithm for solving the stochastic reachability problem in multi-agent systems, in particular flocking modeled as a Markov decision process. At each time step, every agent calls a centralized, adaptive-horizon model-predictive control (AMPC) algorithm to obtain an optimal solution for its local neighborhood. Second, the agents derive the flock-wide optimal solution through a sequence of consensus rounds. Third, the neighborhood is adaptively resized using a flock-wide, cost-based Lyapunov function V. This way DAMPC improves efficiency without compromising convergence. We evaluate DAMPC's performance using statistical model checking. Our results demonstrate that, compared to AMPC, DAMPC achieves considerable speed-up (two-fold in some cases) with only a slightly lower rate of convergence. The smaller average neighborhood size and lookahead horizon demonstrate the benefits of the DAMPC approach for stochastic reachability problems involving any controllable multi-agent system that possesses a cost function.

eess.SY↗

arXiv2017

How to Learn a Model Checker

We show how machine-learning techniques, particularly neural networks, offer a very effective and highly efficient solution to the approximate model-checking problem for continuous and hybrid systems, a solution where the general-purpose model checker is replaced by a model-specific classifier trained by sampling model trajectories. To the best of our knowledge, we are the first to establish this link from machine learning to model checking. Our method comprises a pipeline of analysis techniques for estimating and obtaining statistical guarantees on the classifier's prediction performance, as well as tuning techniques to improve such performance. Our experimental evaluation considers the time-bounded reachability problem for three well-established benchmarks in the hybrid systems community. On these examples, we achieve an accuracy of 99.82% to 100% and a false-negative rate (incorrectly predicting that unsafe states are not reachable from a given state) of 0.0007 to 0. We believe that this level of accuracy is acceptable in many practical applications and we show how the approximate model checker can be made more conservative by tuning the classifier through further training and selection of the classification threshold.

cs.LG↗

arXiv2017

Declarative vs Rule-based Control for Flocking Dynamics

The popularity of rule-based flocking models, such as Reynolds' classic flocking model, raises the question of whether more declarative flocking models are possible. This question is motivated by the observation that declarative models are generally simpler and easier to design, understand, and analyze than operational models. We introduce a very simple control law for flocking based on a cost function capturing cohesion (agents want to stay together) and separation (agents do not want to get too close). We refer to it as {\textit declarative flocking} (DF). We use model-predictive control (MPC) to define controllers for DF in centralized and distributed settings. A thorough performance comparison of our declarative flocking with Reynolds' model, and with more recent flocking models that use MPC with a cost function based on lattice structures, demonstrate that DF-MPC yields the best cohesion and least fragmentation, and maintains a surprisingly good level of geometric regularity while still producing natural flock shapes similar to those produced by Reynolds' model. We also show that DF-MPC has high resilience to sensor noise.

cs.MA↗

arXiv2017

Data-Driven Robust Control for Type 1 Diabetes Under Meal and Exercise Uncertainties

We present a fully closed-loop design for an artificial pancreas (AP) which regulates the delivery of insulin for the control of Type I diabetes. Our AP controller operates in a fully automated fashion, without requiring any manual interaction (e.g. in the form of meal announcements) with the patient. A major obstacle to achieving closed-loop insulin control is the uncertainty in those aspects of a patient's daily behavior that significantly affect blood glucose, especially in relation to meals and physical activity. To handle such uncertainties, we develop a data-driven robust model-predictive control framework, where we capture a wide range of individual meal and exercise patterns using uncertainty sets learned from historical data. These sets are then used in the controller and state estimator to achieve automated, precise, and personalized insulin therapy. We provide an extensive in silico evaluation of our robust AP design, demonstrating the potential of this approach, without explicit meal announcements, to support high carbohydrate disturbances and to regulate glucose levels in large clusters of virtual patients learned from population-wide survey data.

eess.SY↗

arXiv2017

Quantitative Regular Expressions for Arrhythmia Detection Algorithms

Motivated by the problem of verifying the correctness of arrhythmia-detection algorithms, we present a formalization of these algorithms in the language of Quantitative Regular Expressions. QREs are a flexible formal language for specifying complex numerical queries over data streams, with provable runtime and memory consumption guarantees. The medical-device algorithms of interest include peak detection (where a peak in a cardiac signal indicates a heartbeat) and various discriminators, each of which uses a feature of the cardiac signal to distinguish fatal from non-fatal arrhythmias. Expressing these algorithms' desired output in current temporal logics, and implementing them via monitor synthesis, is cumbersome, error-prone, computationally expensive, and sometimes infeasible. In contrast, we show that a range of peak detectors (in both the time and wavelet domains) and various discriminators at the heart of today's arrhythmia-detection devices are easily expressible in QREs. The fact that one formalism (QREs) is used to describe the desired end-to-end operation of an arrhythmia detector opens the way to formal analysis and rigorous testing of these detectors' correctness and performance. Such analysis could alleviate the regulatory burden on device developers when modifying their algorithms. The performance of the peak-detection QREs is demonstrated by running them on real patient data, on which they yield results on par with those provided by a cardiologist.

cs.LO↗

arXiv2017

Automated Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems

We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for deriving a PID controller (or any other type of controller, for that matter) with safety and performance guarantees for such a general class of systems. In particular, we consider hybrid systems with nonlinear dynamics (Lipschitz-continuous ordinary differential equations) and random parameters, and we synthesize PID controllers such that the resulting closed-loop systems satisfy safety and performance constraints given as probabilistic bounded reachability properties. Our technique leverages SMT solvers over the reals and nonlinear differential equations to provide formal guarantees that the synthesized controllers satisfy such properties. These controllers are also robust by design since they minimize the probability of reaching an unsafe state in the presence of random disturbances. We apply our approach to the problem of insulin regulation for type 1 diabetes, synthesizing controllers with robust responses to large random meal disturbances, thereby enabling them to maintain blood glucose levels within healthy, safe ranges.

eess.SY↗

arXiv2017

Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.

eess.SY↗

arXiv2017

A Component-Based Simplex Architecture for High-Assurance Cyber-Physical Systems

We present Component-Based Simplex Architecture (CBSA), a new framework for assuring the runtime safety of component-based cyber-physical systems (CPSs). CBSA integrates Assume-Guarantee (A-G) reasoning with the core principles of the Simplex control architecture to allow component-based CPSs to run advanced, uncertified controllers while still providing runtime assurance that A-G contracts and global properties are satisfied. In CBSA, multiple Simplex instances, which can be composed in a nested, serial or parallel manner, coordinate to assure system-wide properties. Combining A-G reasoning and the Simplex architecture is a challenging problem that yields significant benefits. By utilizing A-G contracts, we are able to compositionally determine the switching logic for CBSAs, thereby alleviating the state explosion encountered by other approaches. Another benefit is that we can use A-G proof rules to decompose the proof of system-wide safety assurance into sub-proofs corresponding to the component-based structure of the system architecture. We also introduce the notion of coordinated switching between Simplex instances, a key component of our compositional approach to reasoning about CBSA switching logic. We illustrate our framework with a component-based control system for a ground rover. We formally prove that the CBSA for this system guarantees energy safety (the rover never runs out of power), and collision freedom (the rover never collides with a stationary obstacle). We also consider a CBSA for the rover that guarantees mission completion: all target destinations visited within a prescribed amount of time.

eess.SY↗

arXiv2017

Model Checking Cyber-Physical Systems using Particle Swarm Optimization

We present a novel approach to the problem of model checking cyber-physical systems. We transform the model checking problem to an optimization one by designing an objective function that measures how close a state is to a violation of a property. We use particle swarm optimization (PSO) to effectively search for a state that minimizes the objective function. Such states, if found, are counter-examples describing safe states from which the system can reach an unsafe state in one time step. We illustrate our approach with a controller for the Quickbot ground rover. Our PSO model checker quickly found a bug in the controller that could cause the rover to collide with an obstacle.

eess.SY↗

arXiv2017

Attacking the V: On the Resiliency of Adaptive-Horizon MPC

We introduce the concept of a V-formation game between a controller and an attacker, where controller's goal is to maneuver the plant (a simple model of flocking dynamics) into a V-formation, and the goal of the attacker is to prevent the controller from doing so. Controllers in V-formation games utilize a new formulation of model-predictive control we call Adaptive-Horizon MPC (AMPC), giving them extraordinary power: we prove that under certain controllability assumptions, an AMPC controller is able to attain V-formation with probability 1. We define several classes of attackers, including those that in one move can remove R birds from the flock, or introduce random displacement into flock dynamics. We consider both naive attackers, whose strategies are purely probabilistic, and AMPC-enabled attackers, putting them on par strategically with the controllers. While an AMPC-enabled controller is expected to win every game with probability 1, in practice, it is resource-constrained: its maximum prediction horizon and the maximum number of game execution steps are fixed. Under these conditions, an attacker has a much better chance of winning a V-formation game. Our extensive performance evaluation of V-formation games uses statistical model checking to estimate the probability an attacker can thwart the controller. Our results show that for the bird-removal game with R = 1, the controller almost always wins (restores the flock to a V-formation). For R = 2, the game outcome critically depends on which two birds are removed. For the displacement game, our results again demonstrate that an intelligent attacker, i.e. one that uses AMPC in this case, significantly outperforms its naive counterpart that randomly executes its attack.

eess.SY↗

arXiv2016

ARES: Adaptive Receding-Horizon Synthesis of Optimal Plans

We introduce ARES, an efficient approximation algorithm for generating optimal plans (action sequences) that take an initial state of a Markov Decision Process (MDP) to a state whose cost is below a specified (convergence) threshold. ARES uses Particle Swarm Optimization, with adaptive sizing for both the receding horizon and the particle swarm. Inspired by Importance Splitting, the length of the horizon and the number of particles are chosen such that at least one particle reaches a next-level state, that is, a state where the cost decreases by a required delta from the previous-level state. The level relation on states and the plans constructed by ARES implicitly define a Lyapunov function and an optimal policy, respectively, both of which could be explicitly generated by applying ARES to all states of the MDP, up to some topological equivalence relation. We also assess the effectiveness of ARES by statistically evaluating its rate of success in generating optimal plans. The ARES algorithm resulted from our desire to clarify if flying in V-formation is a flocking policy that optimizes energy conservation, clear view, and velocity alignment. That is, we were interested to see if one could find optimal plans that bring a flock from an arbitrary initial state to a state exhibiting a single connected V-formation. For flocks with 7 birds, ARES is able to generate a plan that leads to a V-formation in 95% of the 8,000 random initial configurations within 63 seconds, on average. ARES can also be easily customized into a model-predictive controller (MPC) with an adaptive receding horizon and statistical guarantees of convergence. To the best of our knowledge, our adaptive-sizing approach is the first to provide convergence guarantees in receding-horizon techniques.

cs.AI↗

arXiv2015

Abstract Model Repair

Given a Kripke structure M and CTL formula $φ$, where M does not satisfy $φ$, the problem of Model Repair is to obtain a new model M' such that M' satisfies $φ$. Moreover, the changes made to M to derive M' should be minimum with respect to all such M'. As in model checking, state explosion can make it virtually impossible to carry out model repair on models with infinite or even large state spaces. In this paper, we present a framework for model repair that uses abstraction refinement to tackle state explosion. Our framework aims to repair Kripke Structure models based on a Kripke Modal Transition System abstraction and a 3-valued semantics for CTL. We introduce an abstract-model-repair algorithm for which we prove soundness and semi-completeness, and we study its complexity class. Moreover, a prototype implementation is presented to illustrate the practical utility of abstract-model-repair on an Automatic Door Opener system model and a model of the Andrew File System 1 protocol.

cs.LO↗

arXiv2015

A survey on unmanned aerial vehicle collision avoidance systems

Collision avoidance is a key factor in enabling the integration of unmanned aerial vehicle into real life use, whether it is in military or civil application. For a long time there have been a large number of works to address this problem; therefore a comparative summary of them would be desirable. This paper presents a survey on the major collision avoidance systems developed in up to date publications. Each collision avoidance system contains two main parts: sensing and detection, and collision avoidance. Based on their characteristics each part is divided into different categories; and those categories are explained, compared and discussed about advantages and disadvantages in this paper.

eess.SY↗

arXiv2015

Model Checking as Control: Feedback Control for Statistical Model Checking of Cyber-Physical Systems

We introduce feedback-control statistical system checking (FC-SSC), a new approach to statistical model checking that exploits principles of feedback-control for the analysis of cyber-physical systems (CPS). FC-SSC uses stochastic system identification to learn a CPS model, importance sampling to estimate the CPS state, and importance splitting to control the CPS so that the probability that the CPS satisfies a given property can be efficiently inferred. We illustrate the utility of FC-SSC on two example applications, each of which is simple enough to be easily understood, yet complex enough to exhibit all of FC-SCC's features. To the best of our knowledge, FC-SSC is the first statistical system checker to efficiently estimate the probability of rare events in realistic CPS applications or in any complex probabilistic program whose model is either not available, or is infeasible to derive through static-analysis techniques.

eess.SY↗

arXiv2015

Model Checking Tap Withdrawal in C. Elegans

We present what we believe to be the first formal verification of a biologically realistic (nonlinear ODE) model of a neural circuit in a multicellular organism: Tap Withdrawal (TW) in \emph{C. Elegans}, the common roundworm. TW is a reflexive behavior exhibited by \emph{C. Elegans} in response to vibrating the surface on which it is moving; the neural circuit underlying this response is the subject of this investigation. Specifically, we perform reachability analysis on the TW circuit model of Wicks et al. (1996), which enables us to estimate key circuit parameters. Underlying our approach is the use of Fan and Mitra's recently developed technique for automatically computing local discrepancy (convergence and divergence rates) of general nonlinear systems. We show that the results we obtain are in agreement with the experimental results of Wicks et al. (1995). As opposed to the fixed parameters found in most biological models, which can only produce the predominant behavior, our techniques characterize ranges of parameters that produce (and do not produce) all three observed behaviors: reversal of movement, acceleration, and lack of response.

cs.LO↗

arXiv2012

Model Checking with Probabilistic Tabled Logic Programming

We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logic-programming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked. To overcome this restriction, we propose a more general inference algorithm that uses finite generative structures (similar to automata) to represent families of explanations. The inference algorithm computes the probability of a possibly infinite set of explanations directly from the finite generative structure. We have implemented our inference algorithm in XSB Prolog, and use this implementation to encode probabilistic model checkers for a variety of temporal logics, including PCTL and GPL (which subsumes PCTL*). Our experiment results show that, despite the highly declarative nature of their encodings, the model checkers constructed in this manner are competitive with their native implementations.

cs.LO↗