Statistical verification and differential privacy in cyber-physical systems

This thesis studies the statistical verification and differential privacy in Cyber-Physical Systems. The first part focuses on the statistical verification of stochastic hybrid system, a class of formal models for Cyber-Physical Systems. Model reduction techniques are performed on both Discrete-Time and Continuous-Time Stochastic Hybrid Systems to reduce them to Discrete-Time Markov Chains and Continuous-Time Markov Chains, respectively; and statistical verification algorithms are proposed to verify Linear Inequality LTL and Metric Interval Temporal Logic on these discrete probabilistic models. In addition, the advantage of stratified sampling in verifying Probabilistic Computation Tree Logic on Labeled Discrete-Time Markov Chains is studied; this method can potentially be extended to other statistical verification algorithms to reduce computational costs. The second part focuses on the Differential Privacy in multi-agent systems that involve share information sharing to achieve overall control goals. A general formulation of the systems and a notion of Differential Privacy are proposed, and a trade-off between the Differential Privacy and the tracking performance of the systems is demonstrated. In addition, it is proved that there is a trade-off between Differential Privacy and the entropy of the unbiased estimator of the private data, and an optimal algorithm to achieve the best trade-off is given

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Topics in multiscale modeling: numerical analysis and applications

We explore several topics in multiscale modeling, with an emphasis on numerical analysis and applications. Throughout Chapters 2 to 4, our investigation is guided by asymptotic calculations and numerical experiments based on spectral methods. In Chapter 2, we present a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, the numerical methodology that we present is based on a spectral method. We use an expansion in Hermite functions to approximate the solution of an appropriate Poisson equation, which is used in order to calculate the coefficients in the homogenized equation. Extensions of this method are presented in Chapter 3 and 4, where they are employed for the investigation of the Desai—Zwanzig mean-field model with colored noise and the generalized Langevin dynamics in a periodic potential, respectively. In Chapter 3, we study in particular the effect of colored noise on bifurcations and phase transitions induced by variations of the temperature. In Chapter 4, we investigate the dependence of the effective diffusion coefficient associated with the generalized Langevin equation on the parameters of the equation. In Chapter 5, which is independent from the rest of this thesis, we introduce a novel numerical method for phase-field models with wetting. More specifically, we consider the Cahn—Hilliard equation with a nonlinear wetting boundary condition, and we propose a class of linear, semi-implicit time-stepping schemes for its solution.Open Acces

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

Aggregation dynamics of bulk nanoparticle haloing systems and the influence of non-ambient temperatures.

One of the methods of assembling colloids into 3D crystal structures is through the use of nanoparticle haloing. Nanoparticle haloing is a stabilization mechanism in binary particle suspensions possessing both a size and charge asymmetry, with which the nanoparticles aid in the bulk suspension’s stability. By altering the volume fractions of nanoparticles, it is possible to control the effective repulsion between the microparticles. Understanding the colloidal interactions and aggregate crystallinity as a function of nanoparticle concentration, temperature, and time are key challenges in developing future materials and designing crystalized 3D colloidal systems. In this study, we investigated the effect of temperature and nanoparticle volume fraction on the aggregation size using experimental techniques and molecular dynamics simulations. Gravity settling results showed a rapid aggregation in the absence of the nanoparticles due to the van der Waals interactions. However, by adding the nanoparticles to the system, the rate of gravity settling and aggregation significantly decreased due to the effective potential barrier that arises from the nanoparticle halo formation. The effect of temperature on the aggregation of the nanoparticle haloing systems was investigated using a confocal microscopy. By applying a temperature shock to the binary suspensions, the average colloid aggregates\u27 size increased while the systems\u27 coarseness decreased. The average aggregate size growth was more significant at the higher temperatures and the lower nanoparticle volume fractions. Overall, applying the temperature shock resulted in a more idealized structure with higher crystallinity. Molecular dynamics simulations were employed to determine the repulsive barrier between colloidal particles induced by the nanoparticles as a function of nanoparticle volume fraction. Results showed that the induced repulsive barrier between the microparticles increases with increasing the volume fractions of nanoparticles, and it reaches 6.5 kBT at the highest nanoparticle volume fraction of 10-3. This potential barrier was strong enough to prevent aggregation gelation and increase the stability of the suspension, which was in agreement with the experimental results