Neural Lyapunov Control

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.Comment: NeurIPS 201

Remedies for building reliable cyber-physical systems

Cyber-physical systems (CPS) are systems that are tight integration of computer programs as controllers or cyber parts, and physical environments. The interaction is carried out by obtaining information about the physical environment through reading sensors and responding to the current knowledge through actuators. Examples of such systems are autonomous automobile systems, avionic systems, robotic systems, and medical devices. Perhaps the most common feature of all these systems is that they are all safety critical systems and failure most likely causes catastrophic consequences. This means that while testing continues to increase confidence in cyber-physical systems, formal or mathematical proofs are needed at the very least for the safety requirements of these systems. Hybrid automata is the main modeling language for cyber-physical systems. However, verifying safety properties is undecidable for all but very restricted known classes of these automata. Our first result introduces a new subclass of hybrid automata for which bounded time safety model checking problem is decidable. We also prove that unbounded time model checking for this subclass is undecidable which suggests this is the best one can hope for the new class. Our second result in this thesis is a counter-example guided abstraction refinement algorithm for unbounded time model checking of non- linear hybrid automata. Clearly, this is an undecidable problem and that is the main reason for using abstraction refinement techniques. Our CEGAR framework for this class is sound but not complete, meaning the algorithm never incorrectly says a system is safe, but may output unsafe incorrectly. We have also implemented our algorithm and compared it with seven other tools. There are multiple inherent problems with traditional model checking approaches. First, it is well-known that most models do not depict physical environments precisely. Second, the model checking problem is undecidable for most classes of hybrid automata. And third, even when model checking is decidable, controller part in most models cannot be implemented. These problems suggest that current methods of modeling cyber-physical systems and problems might not be the right ones. Our last result focuses on robust model checking of cyber-physical systems. In this part of the thesis, we focus on the implementability issue and show how to solve four different robust model checking problem for timed automata. We also introduce an optimal algorithm for robust time bounded safety model checking of monotonic rectangular automata

Hybridization based CEGAR for Hybrid Automata with Affine Dynamics

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Relating Syntactic and Semantic Perturbations of Hybrid Automata

We investigate how the semantics of a hybrid automaton deviates with respect to syntactic perturbations on the hybrid automaton. We consider syntactic perturbations of a hybrid automaton, wherein the syntactic representations of its elements, namely, initial sets, invariants, guards, and flows, in some logic are perturbed. Our main result establishes a continuity like property that states that small perturbations in the syntax lead to small perturbations in the semantics. More precisely, we show that for every real number epsilon>0 and natural number k, there is a real number delta>0 such that H^delta, the delta syntactic perturbation of a hybrid automaton H, is epsilon-simulation equivalent to H up to k transition steps. As a byproduct, we obtain a proof that a bounded safety verification tool such as dReach will eventually prove the safety of a safe hybrid automaton design (when only non-strict inequalities are used in all constraints) if dReach iteratively reduces the syntactic parameter delta that is used in checking approximate satisfiability. This has an immediate application in counter-example validation in a CEGAR framework, namely, when a counter-example is spurious, then we have a complete procedure for deducing the same

Parameter Invariant Monitoring for Signal Temporal Logic

Signal Temporal Logic (STL) is a prominent specification formalism for real-time systems, and monitoring these specifications, specially when (for different reasons such as learning) behavior of systems can change over time, is quite important. There are three main challenges in this area: (1) full observation of system state is not possible due to noise or nuisance parameters, (2) the whole execution is not available during the monitoring, and (3) computational complexity of monitoring continuous time signals is very high. Although, each of these challenges has been addressed by different works, to the best of our knowledge, no one has addressed them all together. In this paper, we show how to extend any parameter invariant test procedure for single points in time to a parameter invariant test procedure for efficiently monitoring continuous time executions of a system against STL properties. We also show, how to extend probabilistic error guarantee of the input test procedure to a probabilistic error guarantee for the constructed test procedure

DEFINING EFFECTIVE AGGREGATE SKELETON IN ASPHALT MIXTURE USING DIGITAL IMAGING

Characterization of the asphalt mixture microstructure using two dimensional (i.e., 2-D) imaging techniques is an economically efficient approach. However, the features that have been captured and quantified using 2-D imaging techniques in most published research have been limited to simplistic analyses of aggregate structure. This dissertation focuses on introducing a more elaborate method for characterization of the internal structure of aggregates. New microstructural indices are introduced and related to the performance of asphalt mixtures. The aggregate internal structure provides the skeleton of the asphalt mixture, which plays an important role in rutting resistance. In this research, it is shown that this structure can be characterized using a combination of newly developed image analysis indices namely: number of aggregate-to-aggregate contact zones, ratio of contact length to area, and contact plane orientation. These parameters are defined for both the total aggregates and for the effective load bearing aggregate structure, referred to as the ?skeleton? in this study. A software developed in a previous study and significantly modified for this dissertation, is used to process digital images of a set of asphalt mixtures with different gradations, binder contents, types of modification, compaction efforts, compaction temperatures, and methods. The results demonstrate a correlation between the internal structure indices and the mixture rutting performance. Additionally, the indices were successfully used to show the effects of compaction effort, compaction method and temperature, gradation of aggregates, and binder modification on the mixture internal structure. The results indicate potential for using this method for quality control of mixtures during production

Realizability and Dynamic Reconfiguration of Chor Specifications

To appear.International audienceChoreography description languages aim at specifying from a global point of view interactions among a set of services involved in a new system. From this specication, local implementations or peers can be automatically generated. Generation of peers that precisely implement the choreography specication is not always possible: this problem is known as realizability. When peers corresponding to this specication are being executed we may want to modify the choreography specication and recongure dynamically the system. This is the case for instance if we add or remove interactions due to the addition of functionalities to the system at hand or the loss of a service. In this article, we present our solutions to check if a choreography is realizable and if a specic reconguration can be applied or not

Realizability and Dynamic Reconfiguration of Chor Specifications

To appear.International audienceChoreography description languages aim at specifying from a global point of view interactions among a set of services involved in a new system. From this specication, local implementations or peers can be automatically generated. Generation of peers that precisely implement the choreography specication is not always possible: this problem is known as realizability. When peers corresponding to this specication are being executed we may want to modify the choreography specication and recongure dynamically the system. This is the case for instance if we add or remove interactions due to the addition of functionalities to the system at hand or the loss of a service. In this article, we present our solutions to check if a choreography is realizable and if a specic reconguration can be applied or not