Funnel control for fully actuated systems under a fragment of signal temporal logic specifications

Temporal logics have lately proven to be a valuable tool for various control applications by providing a rich specification language. Existing temporal logic-based control strategies discretize the underlying dynamical system in space and/or time. We will not use such an abstraction and consider continuous-time systems under a fragment of signal temporal logic specifications by using the associated robust semantics. In particular, this paper provides computationally-efficient funnel-based feedback control laws for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design so that some degree of robustness is obtained. We first leverage the transient properties of a funnel-based feedback control strategy to maximize the robust semantics of some atomic temporal logic formulas. We then guarantee the satisfaction for specifications consisting of conjunctions of such atomic temporal logic formulas with overlapping time intervals by a suitable switched control system. The result is a framework that satisfies temporal logic specifications with a user-defined robustness when the specification is satisfiable. When the specification is not satisfiable, a least violating solution can be found. The theoretical findings are demonstrated in simulations of the nonlinear Lotka–Volterra equations for predator–prey models.     

Time-constrained temporal logic control of multi-affine systems

In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on estimating the time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition system and an automaton that enforces the satisfaction of the specification. A random optimization algorithm is used to iteratively improve the solution.     

Adaptive testing for specification coverage and refinement in CPS models

Design of correct cyber–physical systems (CPS) is of uttermost importance for safety-critical applications. This crucial yet extremely challenging property is often addressed in practice by simulation-based methods. The simulation activity can be made more systematic and rigorous by using formal specifications to express requirements and guide the testing of the system.In this paper, we develop a procedure for generating tests from formal specifications given in Signal Temporal Logic (STL), a declarative language used to express CPS requirements. The proposed test generation method is adaptive with the aim at achieving specification coverage. We devise to this goal cooperative reachability games, which we enhance with numerical optimization to facilitate exercising various parts of specifications. The resulting approach is effective in finding specification violations, but also in increasing confidence (via coverage) that the specification is satisfied. In the latter case, we also propose a method for automatically refining the specification into its part that is actually implemented, thus gaining additional insight into the system-under-test.     

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.     

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.     

An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure

Although the concept of Batch Markovian Arrival Processes (BMAPs) has gained widespread use in stochastic modelling of communication systems and other application areas, there are few statistical methods of parameter estimation proposed yet. However, in order to practically use BMAPs for modelling, statistical model fitting from empirical time series is an essential task. The present paper contains a specification of the classical EM algorithm for MAPs and BMAPs as well as a performance comparison to the computationally simpler estimation procedure recently proposed by Breuer and Gilbert. Furthermore, it is shown how to adapt the latter to become an estimator for hidden Markov models.     

Subjective estimation of the delay time distribution in maintenance modelling

In this paper, the problems in the current method for obtaining a subjective estimate of the delay time distribution used in maintenance modelling are discussed and a brief literature survey on assessing subjective probability and expert judgment in decision making is presented. Based upon the results of the survey and experience in conducting a subjective estimating procedure for the delay time distribution, a revised procedure and method for obtaining the subjective delay time estimate is proposed, and the models for combining experts' opinions and updating the delay time distribution are also discussed. Case examples are given in the paper to demonstrate the methodology.     

SDML: A Multi-Agent Language for Organizational Modelling

A programming language which is optimized for modelling multi-agent interaction within articulated social structures such as organizations is described with several examples of its functionality. The language is SDML, a strictly declarative modelling language which has object-oriented features and corresponds to a fragment of strongly grounded autoepistemic logic. The virtues of SDML include the ease of building complex models and the facility for representing agents flexibly as models of cognition as well as modularity and code reusability. Two representations of cognitive agents within organizational structures are reported and a Soar-to-SDML compiler is described. One of the agent representations is a declarative implementation of a Soar agent taken from the Radar-Soar model of Ye and Carley (1995). The Ye-Carley results are replicated but the declarative SDML implementation is shown to be much less computationally expensive than the more procedural Soar implementation. As a result, it appears that SDML supports more elaborate representations of agent cognition together with more detailed articulation of organizational structure than we have seen in computational organization theory. Moreover, by representing Soar-cognitive agents declaratively within SDML, that implementation of the Ye-Carley specification is necessarily consistent and sound with respect to the formal logic to which SDML corresponds.     

Propositions and specifications of programs in Martin-Löf's type theory

The constructive meaning of mathematical propositions makes it possible to identify specifications for computer programs with propositions. In Martin-Löf's type theory, constructing a program satisfying a specification corresponds to proving the proposition expressing the specification. These ideas are explained and some examples of specifications are given.     

Computational complexity of hybrid interval temporal logics

Interval logics are very expressive temporal formalisms, but reasoning with them is often undecidable or has high computational complexity. As a result, a vast number of approaches limiting their expressive power—in order to obtain better computational behaviour—have been introduced. Unfortunately, due to such restrictions, interval logics often lose referentiality, that is, the capacity to refer to specific time intervals, which is crucial for temporal representation and reasoning. The computational price that needs to be paid in order to regain referentiality is not well studied and our research aims to fill this gap. In particular we study the main interval temporal logic, called the Halpern-Shoham logic, and its low complexity modifications. To regain referentiality in these modifications, we extend the language with the hybrid machinery—nominals and satisfaction operators—and classify the obtained logics according to their computational complexity. We show that such a hybridisation often makes tractable logics intractable but not undecidable. This allows us to construct hybrid interval temporal logics which are referential as well as maintain a good compromise between expressiveness and complexity; it makes them valuable formalisms for temporal knowledge representation. We also introduce a class of models which, due to a specific interplay between the interpretation of modal operators and a structure of time, makes reasoning in interval logics computationally hard even in the absence of the hybrid machinery.     

Towards integrated design and analysis

A systems analysis technique is used to investigate and better understand the processes involved in finite element modelling. Two different starting points are considered: engineering drawings and solid models. The breakdown of activities involved in finite element analysis from a solid model is used as a requirements definition and functional specification for software tools to facilitate automation of finite modelling and eventual integration of design and analysis.     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅱ):向后一步的Euler全离散化格式

1．引言本文的工作主要是讨论非定常的热传导一对流问题的向后一步的Euler全离散化的非线性Galerkin混合元解的存在性及其误差估计．该工作是对山中的同一问题研究的第二部分．在第一部分［1］，我们已经讨论了此问题的半离散化的情形．由于所研究的目标都是非定常的热传导一对流问题，其背景是相同的，在此将不重复了，请参考［1］．本文的安排如下，52先回顾非定常的热传导一对流问题的混合元解的经典性质．53回顾半离散化的非线性Galerkin混合元解的性质，并导出后续讨论需要的一些关于时间导数的估计．54讨论向后一步的Euler全离散化…     

Optimal blending of out-of-specifications substances

A chemical company produces powdery substances by a process that is difficult to control tightly. As a result, a significant proportion of production lots fail to meet the specifications of one or more of the key measurable characteristics. These lots are stored in bins that can be later blended in fixed amounts so as to produce a larger batch that is within specifications on all measurements. The blending of these bins is formulated here as an integer programming problem. This paper describes the sequential solution procedure used to find an optimal solution. The sequential procedure includes a penalty function at each step that is designed to force ‘bad’ lots, the most out-of-specifications, to blend first. The introduction of a variable step size eliminated the need for a branch-and-bound procedure.     

Effects of heterogeneity on bank efficiency scores

Bank efficiency estimates often serve as a proxy of managerial skill since they quantify sub-optimal production choices. But such deviations can also be due to omitted systematic differences among banks. In this study, we examine the effects of heterogeneity on bank efficiency scores. We compare different specifications of a stochastic cost and alternative profit frontier model with a baseline specification. After conducting a specification test, we discuss heterogeneity effects on efficiency levels, ranks and the tails of the efficiency distribution. We find that heterogeneity controls influence both banks’ optimal costs and profits and their ability to be efficient. Differences in efficiency scores are important for more than only methodological reasons. First, different ways of accounting for heterogeneity result in estimates of foregone profits and additional costs that are significantly different from what we infer from our general specification. Second, banks are significantly re-ranked when their efficiency is estimated with a specification other than the preferred, general specification. Third, the general specification gives the most reliable estimates of the probability of distress, although differences to the other specifications are low.     

A multiplicative model for volume and volatility

We first present prima facie evidence for the predictions generated by the mixture of distributions hypothesis, using daily German stock returns and their corresponding daily trading volumes and number of trades. These last two variables are used as proxies for the stochastic rate of information arrival when one wishes to explain GARCH effects by adhering to the mixture of distributions hypothesis. We show that there is no need for these proxies when the stochastic rate of information arrival follows an inverted gamma distribution. Daily trading volume and the daily number of trades, however, empirically provide an explanation for the occurrence of conditional heteroskedasticity of the GARCH form. We estimate several specifications where daily trading volume is included in the conditional variance equation additively and multiplicatively. The new multiplicative specification clearly outperforms the additive specification.     

An axiomatization of events

Most approaches to information modelling are so-called snapshot approaches. This means that they focus on static properties of a universe of discourse only. Some approaches consider the temporal dimension of a universe of discourse. In these approaches the concept of event is central. It is used to denote, e.g., a decision or an action which takes place at a certain time point.In this paper the concept of event is analyzed within the framework of first-order predicate logic. An axiom system for discrete time points and axiom schemes for events is presented. It is shown that the axiom schemes obtained apply to a number of cases with wide applicability. Further, several remaining problems are pointed out.This work is supported by the National Swedish Board for Technical Development (STU).     

Modelling the probability assessment of system state prognosis using available condition monitoring information

^** Email: w.wang{at}salford.ac.uk This paper reports on a model to assess the current and futurestates of a monitored system based on measured condition monitoringinformation to date. The true state of the system is unobservable,but is assumed to be related to the measured condition monitoringinformation in a stochastic way. We further assume that thetransition of the system state follows a time-dependent Markovchain which has only three states, namely good, defective andfailed. This assumption effectively defines a two-stage failureprocess which is widely used in delay time modelling of maintainedsystems. Three modelling techniques are used to establish themodel. First, we use a hidden Markov model to describe the transitionsbetween system states. Second, the transition matrix is establishedbased on the well-known delay time concept. The last one isthe use of the filtering technique to construct the relationshipbetween measured condition information and the underlying truestate of the system. We also discuss the procedure for modelparameter estimation. A numerical example is presented to demonstratethe modelling ideas.     

A Note on “Trial by Computer”—A Case Study of the Use of Simple Statistical Techniques in the Detection of a Fraud

We look at a statistical aspect of a recent case study. Although our discussion does not invalidate the general conclusions obtained there, it does suggest that the time series modelling may have been sub-optimal, and indicates how an alternative model specification could more probably have generated the sample statistics that were actually observed. The implication of our remarks is that discrimination between deterministic and stochastic non-stationarity, even if overlooked on preliminary inspection of the original data, will also be apparent from the raw sample autocorrelation plots.