Some advances in tools and algorithms for the construction and analysis of systems

Because of the complexity of software systems and their increasing criticality, there is a pressing need for sophisticated and highly automated tools for the analysis of software artifacts and their expected behavioral properties. A growing body of research is using formal methods to produce increasingly powerful and scalable analysis tools, although several challenges still remain. We briefly outline some recent achievements in automated analysis represented by four selected papers from the 21st International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2015). Two of the selected papers describe major achievements in the field of parallel model checking. The third paper presents an auto-active theorem prover for the verification of Eiffel programs. The fourth paper reports on a non-trivial case study with hybrid automata and interactive theorem proving techniques.     

混合动态系统有界性定理及应用

从连续系统的角度出发，提出并证明了混合动态系统的有界性定理，并以一类具体的数字反馈采样控制系统为例，详细阐述了有界性定理的具体应用，最终得到系统在其状态空间内有界的充分条件。     

Comparison theorem of one-dimensional stochastic hybrid delay systems

The comparison theorem of stochastic differential equations has been investigated by many authors. However, little research is available on the comparison theorem of stochastic hybrid systems, which is the topic of this paper. The systems discussed is stochastic delay differential equations with Markovian switching. It is an important class of hybrid systems.     

Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem

In this paper, we study hybrid fuzzy differential equation initial value problems (IVPs). We consider the problem of finding their numerical solutions by using a recent characterization theorem of Bede for fuzzy differential equations. We prove a corollary to Bede’s characterization theorem and give a characterization theorem for hybrid fuzzy differential equation IVPs. Then we prove that any suitable numerical method for ODEs can be applied piecewise to numerically solve hybrid fuzzy differential equation IVPs. Numerical examples are provided which connect the new results with previous findings.     

Hybrid logical analyses of the ambient calculus

In this paper, hybrid logic is used to formulate three control flow analyses for Mobile Ambients, a process calculus designed for modelling mobility. We show that hybrid logic is very well-suited to express the semantic structure of the ambient calculus and how features of hybrid logic can be exploited to reduce the “administrative overhead” of the analysis specification and thus simplify it. Finally, we use HyLoTab, a fully automated theorem prover for hybrid logic, both as a convenient platform for a prototype implementation as well as to formally prove the correctness of the analysis.     

A Methodological View of Constraint Solving

Constraints are an effective tool to define sets of data by means of logical formulae. Our goal here is to survey the notion of constraint system and to give examples of constraint systems operating on various domains, such as natural, rational or real numbers, finite domains, and term domains. We classify the different methods used for solving constraints, syntactic methods based on transformations, semantic methods based on adequate representations of constraints, hybrid methods combining transformations and enumerations. The concepts and methods are illustrated via examples. We also discuss applications of constraints to various fields, such as programming, operations research, and theorem proving.     

A fast PO–PO hybrid method for analysing the Doppler spectrum of a plasma-coated object above a rough sea surface: horizontal polarization

A fast hybrid method based on physical optics (PO) and the reciprocity theorem is proposed to analyse the Doppler spectrum of a two-dimensional, moving plasma-coated object above a one-dimensional time-evolving lossy dielectric rough sea surface. This hybrid method eliminates the need for numerical solution of the polarization currents on the object and the time-evolving sea surface, thereby greatly improving the computing speed. The method is verified by conventional numerical methods. The characteristics of the Doppler spectrum of a plasma-coated object above a time-evolving sea surface are analysed in detail, including the effects of several parameters such as the incident angle and the velocity of the moving object. The effects of some key parameters on the stealth performance are also examined.     

混合动态系统的稳定性

讨论混合动态系统（HDS）的稳定性问题。首先给出关于HDS的稳定性、可吸收性和渐近稳定性的几个结论,然后给出关于HDS的Lyapunov稳定性定量。     

A result on the hyperstability of a class of hybrid dynamic systems

This paper presents a hyperstability theorem for a class of hybrid dynamic systems composed of coupled differential and difference equations subject to (possibly) time-varying nonlinearities satisfying a Popov-type inequality. The nonlinear controller generates the plant input at all times from its sampled values by defining an extended discrete system. The hyperstability results are obtained from this discrete system of special type whose state consists of the sampled continuous substate and the digital substate of the given hybrid system. Some corollaries and related physical interpretations are also given     

高维复杂函数的混合模拟退火全局优化策略

对于高维复杂函数优化问题,经典的优化算法存在着初始点敏感、局部收敛等问题;而模拟退火算法等智能算法则有着计算成本高昂、算法早熟等缺陷。NFL定理犤1犦预示了混合优化策略是解决实际优化问题的最好途径。该文融合了模拟退火算法和经典算法的优点,设计了高维复杂函数混合模拟退火优化策略。混合优化策略具有模拟退火算法的全局收敛性,同时引入强局部收敛经典算法作为模拟退火算法的精英个体提高算子,提高了模拟退火算法局部开采能力,加快了收敛速度。数值仿真计算结果表明,混合模拟退火策略求解高维复杂函数的性能大大优于单一算法,具有强鲁棒性、高收敛速度和高精度等优点。该文的算法设计思想对于解决实际问题有较好的借鉴意义。     

On Input-to-State Stability of Stochastic Retarded Systems With Markovian Switching

This note develops a Razumikhin-type theorem on pth moment input-to-state stability of hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), which is an improvement of an existing result. An application to hybrid stochastic delay systems verifies the effectiveness of the improved result.     

配置弹簧阻尼空间机器人基于灰狼优化算法的双臂捕获卫星操作缓冲柔顺控制

空间机器人在捕获卫星操作过程中会发生剧烈碰撞,若不对其脆弱的关节进行保护,则可能造成空间机器人的损坏.为此在空间机器人关节电机与机械臂之间加入一种弹簧阻尼机构,该机构不仅可以在碰撞过程中缓冲、吸收冲击能量,而且可以通过设计与之配合的柔顺策略实现混合体系统的镇定控制.首先,针对捕获前的双臂空间机器人开环系统与目标卫星系统,分别利用Lagrange法与Newton-Euler法建立分体系统动力学模型; 结合动量定理、速度约束、闭链几何约束及牛顿第三定律,导出捕获后的闭链混合体系统动力学模型,并计算冲击效应与碰撞力;然后,针对混合体系统的控制问题,提出一种配合弹簧阻尼机构的积分终端滑模控制方案,通过灰狼优化算法对滑模控制器的参数进行优化,实现混合体系统快速、稳定的镇定控制;最后,利用Lyapunov定理证明系统的稳定性,并通过数值仿真验证缓冲机构的抗冲击性能与柔顺策略的有效性.     

Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots

Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation.     

A complete-order hybrid identifier for multiprogrammed stabilization

Stabilization of a family of programmed motions of a linear control system with a first-order nonlinear hybrid state identifier is studied. Such an identifier and a multiprogrammed hybrid control are designed in the form of nonlinear feedback. A theorem on sufficient conditions for the existence of a solution to the formulated problem is proved.     

Exploring structural symmetry automatically in symbolic trajectory evaluation

This paper presents a formal theory to characterize symmetry in netlists and symmetry in properties. The inherent correlation between the two types of symmetry is formalized as a theorem, which provides the soundness of our symmetry reduction method. A practical tactic is introduced to effectively integrate the symmetry reduction approach in a hybrid verification environment which combines theorem proving and symbolic trajectory evaluation. Finally, the effecitveness of the symmetry reduction method is demonstrated by case studies.     

Eliminating duplication with the hyper-linking strategy

The efficiency of almost all theorem proving methods suffers from a phenomenon called duplication of instances of clauses. In this paper, we present a novel technique, called the hyper-linking strategy, to eliminate such duplication. This strategy is complete for the full first-order predicate calculus. We show the effectiveness of this strategy by comparing it with other proving methods. We give empirical evidence that both the Davis-Putnam procedure and the hyper-linking strategy are comparable to each other and better than other common theorem proving strategies on propositional calculus problems. The fact that the Davis-Putnam procedure is faster than resolution and other common methods on propositional problems seems not to be appreciated by a large segment of the theorem proving community. Also, we give empirical evidence that the hyper-linking strategy is better than other common theorem proving methods on near-propositional problems like logic puzzles. We attempt to explain the superior behavior of the hyper-linking strategy and the Davis-Putnam procedure by examining the kinds of duplication that can occur during the search with the different methods. In addition, we show the completeness of the hyper-linking strategy combined with several support strategies.This research was partially supported by NSF under grant CCR-8802282.     

A formally verified hybrid system for safe advisories in the next-generation airborne collision avoidance system

The Next-Generation Airborne Collision Avoidance System (ACAS X) is intended to be installed on all large aircraft to give advice to pilots and prevent mid-air collisions with other aircraft. It is currently being developed by the Federal Aviation Administration (FAA). In this paper, we determine the geometric configurations under which the advice given by ACAS X is safe under a precise set of assumptions and formally verify these configurations using hybrid systems theorem proving techniques. We consider subsequent advisories and show how to adapt our formal verification to take them into account. We examine the current version of the real ACAS X system and discuss some cases where our safety theorem conflicts with the actual advisory given by that version, demonstrating how formal hybrid systems proving approaches are helping to ensure the safety of ACAS X. Our approach is general and could also be used to identify unsafe advice issued by other collision avoidance systems or confirm their safety.     

Dynamical properties of hybrid automata

Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results on existence, uniqueness, and continuity serve as a starting point for stability analysis. Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata.     

Approximation capabilities of hierarchical hybrid systems

This paper investigates the approximation capabilities of hierarchical hybrid systems, which are motivated by research in hierarchical fuzzy systems, hybrid intelligent systems, and modeling of model partly known systems. For a function (system) with known hierarchical structure (i.e., one that can be represented as a composition of some simpler and lower dimensional subsystems), it is shown that hierarchical hybrid systems have the structure approximation capability in the sense that such a hybrid approximation scheme can approximate both the overall system and all the subsystems to any desired degree of accuracy. For a function (system) with unknown hierarchical structure, Kolmogorov's theorem is used to construct the hierarchical structure of the given function (system). It is then shown that hierarchical hybrid systems are universal approximators.     

Approximation of a Metric on a Dominating Cone

A theorem on the representation of a pseudoball of a dominating cone is proven. This theorem is an analog of the Caratheodory theorem on the representation of convex sets. The theorem allows to develop numerical methods for quantitative evaluation of systems in many indicators.