Stability Analysis of a Simple-Structured Fuzzy Logic Controller

The stability analysis for the fuzzy logic controller (FLC) has widely been reported. Furthermore some researches have been introduced to simplify the design process of FLCs. One of them is to decrease the number of parameters representing the antecedent part of the fuzzy control rule. So we briefly explain a simple-structured fuzzy logic controller (SFLC) which uses only a single variable at the antecedent part of a fuzzy control rule. We analyze that it is absolutely stable based on the sector bounded condition. We expand a nonlinear controlled plant into a Taylor series about a nominal operating point. The fuzzy control system is transformed into a Lure system with nonlinearities. We also show the feasibility of the proposed stability analysis through a numerical example of a mass-damper-spring system.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

Two and three-quarter dimensional meshing facilitators

This paper presents generated enhancements for robust two and three-quarter dimensional meshing, including: (1) automated interval assignment by integer programming for submapped surfaces and volumes, (2) surface submapping, and (3) volume submapping. An introduction to the simplex method, an optimization technique of integer programming, is presented. Simplification of complex geometry is required for the formulation of the integer programming problem. A method of i-j unfolding is defined which explains how irregular geometry can be realigned into a simplified form that is suitable for submap interval assignment solutions. Also presented is the processes by which submapping eliminates the decomposition of surface geometry, through a pseudodecomposition process, producing suitable mapped meshes. The process of submapping involves the creation of interpolated virtual edges, user defined vertex types and i-j-k space traversals. The creation of interpolated virtual edges is the method by which submapping automatically subdivides surface geometry. The interpolated virtual edge is formulated according to an interpolation scheme using the node discretization of curves on the surface. User defined vertex types allow direct user control of surface decomposition and interval assignment by modifying i-j-k space traversals. Volume submapping takes the geometry decomposition to a higher level by using mapped virtual surfaces to eliminate decomposition of complex volumes.     

Validating the PSL/Sugar Semantics Using Automated Reasoning

The Accellera organisation selected Sugar, IBMs formal specification language, as the basis for a standard to drive assertion-based verification in the electronics industry. Sugar combines regular expressions, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL) into a property language intended for both static verification (e.g. model checking) and dynamic verification (e.g. simulation). In 2003 Accellera decided to rename the evolving standard to Accellera Property Specification Language (or PSL for short). We motivate and describe a deep semantic embedding of PSL in the version of higher-order logic supported by the HOL 4 theorem-proving system. The main goal of this paper is to demonstrate that mechanised theorem proving can be a useful aid to the validation of the semantics of an industrial design language.     

Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of knowledge they contain (i.e., the level of support they provide) and in their ability to learn (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ Prolog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend Prolog with the necessity operator of modal logic. We develop a meta-interpreter realizing EBG for the extended language, Prolog, and provide examples of higher-order EBG.     

Control surface failure detection and accommodation using neuro-controllers

The ability of neural networks to learn from repeated exposure to system characteristics has made them a popular choice for many applications in linear and non-linear control. In this paper, the capabilities of neural networks in detecting and accommodating control surface failures for a modified F/A-18 super-manoeuverable fighter aircraft are examined. To detect and accommodate a failure in the thrust vectoring vane during a pitch manoeuvre, a hierarchical neuro-controller is designed using thrust vectoring, symmetric leading edge flap and the throttle. This neuro- controller is then used as the fault accommodating neuro- controller. A separate neural network is trained to detect failures in the thrust vectoring vane. The performance of the controller and fault-detection networks are verified using a numerical simulation of a longitudinal model of the aircraft.     

Fuzzy Logic Decision Mechanism Combined with a Neuro-Controller for Fabric Tension in Robotized Sewing Process

A new approach for flexible automated handling of fabrics in the sewing process is described, which focuses to control the cloth tension applied by a robot. The proposed hierarchical robot control system includes a Fuzzy decision mechanism combined with a Neuro-controller. The expert's actions during the sewing process are investigated and this human behavior is interpreted in order to design the controller. The Fuzzy Logic decision mechanism utilizes only qualitative knowledge concerning the properties of the fabrics, in order to determine the desired tensional force and the location of the robot hand on the fabric. A Neural Network controller regulates the fabric tension to achieve the desired value by determining the robot end effector velocity. The simulation results demonstrate the efficiency of the system as well as the robustness of the controller performance since the effects of the noise are negligible. The system capabilities are more evident when the controller uses its previously acquired experience.     

Simple adaptive stabilization of output feedback stabilizable distributed parameter systems

We show that the simple universal adaptive control lawu(t)=N(k(t))y(t)=|y(t)| ², withN(k)=(logk) cos((logk)) and 3+<1, stabilizes all detectable and stabilizable infinite dimensional systems of Pritchard-Salamon type which are externally stabilized by somescalar output feedback. The same controller is also shown to stabilize time varying systems satisfying the same type of output feedback stabilizability.     

基于分数阶滑模控制技术的永磁同步电机控制

针对传统整数阶滑模控制系统中存在的抖震问题,本文提出了分数阶滑模控制策略并应用到永磁同步电机的速度控制.传统滑模控制器中的开关函数由作用在切换流型或其整数阶导数面推广到其分数阶导数面,利用分数阶系统的特性,缓慢地传递系统的能量,有效地削减抖震.本文采用模糊逻辑推理算法,实现软开关切换增益的自整定.仿真和实验证明,本文提出的分数阶滑模控制系统不但能有效地削减抖震,而且能保持滑模控制器对系统参数变化和外部扰动的鲁棒性.     

Rigid model-based fuzzy control of flexible-joint manipulators

This paper considers the application of fuzzy control to achieve global trajectory tracking and active damping of flexible-joint manipulators. A reasonable approach based on the combined computed torque control using rigid robot model and fuzzy control is suggested for flexible-joint manipulators. Sets of four input variables — one output variable fuzzy control rules for each actuator respectively, are suggested for the perturbation control. The simulation results show that the transient performance and steady-state accuracy are near those of the feedback linearization approach. The simulation results with payload or joint stiffness variation for the single-link case are also shown to demonstrate the robustness of the control law.     

Intelligent Control for an Acrobot

The acrobot is an underactuated two-link planar robot that mimics the human acrobat who hangs from a bar and tries to swing up to a perfectly balanced upside-down position with his/her hands still on the bar. In this paper we develop intelligent controllers for swing-up and balancing of the acrobot. In particular, we first develop classical, fuzzy, and adaptive fuzzy controllers to balance the acrobot in its inverted unstable equilibrium region. Next, a proportional-derivative (PD) controller with inner-loop partial feedback linearization, a state-feedback, and a fuzzy controller are developed to swing up the acrobot from its stable equilibrium position to the inverted region, where we use a balancing controller to catch and balance it. At the same time, we develop two genetic algorithms for tuning the balancing and swing-up controllers, and show how these can be used to help optimize the performance of the controllers. Overall, this paper provides (i) a case study of the development of a variety of intelligent controllers for a challenging application, (ii) a comparative analysis of intelligent vs. conventional control methods (including the linear quadratic regulator and feedback linearization) for this application, and (iii) a case study of the development of genetic algorithms for off-line computer-aided-design of both conventional and intelligent control systems.     

Obvious inferences

The notion of obvious inference in predicate logic is discussed from the viewpoint of proof-checker applications in logic and mathematics education. A class of inferences in predicate logic is defined and it is proposed to identify it with the class of obvious logical inferences. The definition is compared with other approaches. The algorithm for implementing the obviousness decision procedure follows directly from the definition.     

Design and Implementation of Fuzzy Sliding-Mode Controller for a Wedge Balancing System

In this paper, we address the design and implementation of fuzzy sliding-mode controller for balancing a wedge system. At first, we examine the mathematical model of the wedge balancing system. The dynamic system is complex and ill defined; hence we propose the fuzzy sliding-mode control (FSMC) method to achieve the control objective. The proposed control method enhances the ability of fuzzy logic control so that the minimal number of fuzzy inference rules is systematically obtained even the plant parameters are unknown. Both computer simulations and real-time experiments are exploited to demonstrate the validity and feasibility of the developed control scheme.     

The conjoinability relation in Lambek calculus and linear logic

In 1958 J. Lambek introduced a calculusL of syntactic types and defined an equivalence relation on types: x y means that there exists a sequence x=x₁,...,x_n=y (n 1), such thatx _i x _i+1 or x_i+ x _i (1 i n). He pointed out thatx y if and only if there is joinz such thatx z andy z. This paper gives an effective characterization of this equivalence for the Lambeck calculiL andLP, and for the multiplicative fragments of Girard's and Yetter's linear logics. Moreover, for the non-directed Lambek calculusLP and the multiplicative fragment of Girard's linear logic, we present linear time algorithms deciding whether two types are equal, and finding a join for them if they are.The author was sponsored by project NF 102/62-356 (Structural and Semantic Parallels in Natural Languages and Programming Languages), funded by the Netherlands Organization for the Advancement of Research (N.W.O.).     

Automated knowledge acquisition for design and manufacturing: The case of micromachined atomizer

In order to remain competitive in the global market, original equipment manufacturers (OEMs) are developing a process-based, knowledge-driven product development environment with emphasis on the acquisition, storing, and utilization of manufacturing knowledge. This is usually achieved by using the symbolic artificial intelligence (AI) approach. Specifically, knowledge-based expert systems are developed to capture human expertise, mostly in terms of IF–THEN production rules. It has been recognized that the development of symbolic knowledge-based expert systems suffers from the so-called knowledge acquisition bottleneck. Knowledge acquisition is the process of collecting domain knowledge and transforming the knowledge into a computerized representation. It is a challenging and time-consuming process due to the difficulties involved in eliciting knowledge from human experts. This paper presents an automated approach for knowledge acquisition by integrating neural networks learning ability and fuzzy logics structured knowledge representation. Using this approach, knowledge is automatically acquired from data and represented using humanly intelligible fuzzy rules. The approach is applied to a case study of the design and manufacturing of micromachined atomizers for gas turbine engine. The influence of geometric features on the performance of the atomizers is investigated. The results are then compared with those obtained using traditional regression analysis approach (abstract mathematical models). It was found that the automated approach provides an efficient means for knowledge acquisition. Since the fuzzy rules extracted are easy to understand, they can be used to allow more clear specification of manufacturing processes and to shorten learning curves for novice manufacturing engineers.     

Explanation-based interpretation of open-textured concepts in logical models of legislation

In this paper we discuss a view of the Machine Learning technique called Explanation-Based Learning (EBL) or Explanation-Based Generalization (EBG) as a process for the interpretation of vague concepts in logic-based models of law.The open-textured nature of legal terms is a well-known open problem in the building of knowledge-based legal systems. EBG is a technique which creates generalizations of given examples on the basis of background domain knowledge. We relate these two topics by considering EBG's domain knowledge as corresponding to statute law rules, and EBG's training example as corresponding to a precedent case.By making the interpretation of vague predicates as guided by precedent cases, we use EBG as an effective process capable of creating a link between predicates appearing as open-textured concepts in law rules, and predicates appearing as ordinary language wording for stating the facts of a case.Standard EBG algorithms do not change the deductive closure of the domain theory. In the legal context, this is only adequate when concepts vaguely defined in some law rules can be reformulated in terms of other concepts more precisely defined in other rules. We call theory reformulation the process adopted in this situation of complete knowledge.In many cases, however, statutory law leaves some concepts completely undefined. We then propose extensions to the EBG standard that deal with this situation of incomplete knowledge, and call theory revision the extended process. In order to fill in knowledge gaps we consider precedent cases supplemented by additional heuristic information. The extensions proposed treat heuristics represented by abstraction hierarchies with constraints and exceptions.In the paper we also precisely characterize the distinction between theory reformulation and theory revision by stating formal definitions and results, in the context of the Logic Programming theory.We offer this proposal as a possible contribution to cross fertilization between machine learning and legal reasoning methods.     

Dynamic interpretation and hoare deduction

In this paper we present a dynamic assignment language which extends the dynamic predicate logic of Groenendijk and Stokhof [1991: 39–100] with assignment and with generalized quantifiers. The use of this dynamic assignment language for natural language analysis, along the lines of o.c. and [Barwise, 1987: 1–29], is demonstrated by examples. We show that our representation language permits us to treat a wide variety of donkey sentences: conditionals with a donkey pronoun in their consequent and quantified sentences with donkey pronouns anywhere in the scope of the quantifier. It is also demonstrated that our account does not suffer from the so-called proportion problem.Discussions about the correctness or incorrectness of proposals for dynamic interpretation of language have been hampered in the past by the difficulty of seeing through the ramifications of the dynamic semantic clauses (phrased in terms of input-output behaviour) in non-trivial cases. To remedy this, we supplement the dynamic semantics of our representation language with an axiom system in the style of Hoare. While the representation languages of barwise and Groenendijk and Stokhof were not axiomatized, the rules we propose form a deduction system for the dynamic assignment language which is proved correct and complete with respect to the semantics.Finally, we define the static meaning of a program of the dynamic assignment language as the weakest condition such that terminates successfully on all states satisfying , and we show that our calculus gives a straightforward method for finding static meanings of the programs of the representation language.     

Implementing the ‘Fool's model’ of combinatory logic

This paper studies Fool's models of combinatory logic, and relates them to Hindley's D-completeness problem. A fool's model is a family of sets of formulas, closed under condensed detachment. Alternatively, it is a model ofCL in naive set theory. We examine Resolution; and the P-W problem. A sequel shows T is D-complete; also, its extensions. We close with an implementation FMO of these ideas.     

TMPR: A tree-structured modified problem reduction proof procedure and its extension to three-valued logic

This paper deals with automated deduction for classical and partial logics, especially for the three-valued logic L3, which has been introduced, for example, in the study of natural language semantics. Based on ideas from a Plaisted's Gentzen style system for classical two-valued logic, we present a new tree-structured proof procedure (TMPR) together with a new completeness proof using proof transformation techniques and some improvements including the generation and use of lemmata. TMPR extends SLD-resolution with a Prolog-style backward chaining to full first-order logic by a controlled use of case analysis. This is done without having to extend negative goals needed, for example, for model elimination. A classification of TMPR, model elimination and related calculi in a common tableau framework is given. Thereafter, we present our extension of the TMPR proof procedure to L3 and show its soundness and completeness. As a side result, a TMPR proof system for the four-valued logic L4 is given. Finally, the restriction of TMPR to L3-Horn clauses is considered, and, additionally, an idea for similarly extending model elimination and related systems to L3 (and L4) is illustrated.This work is supported by the KI-Verbund NRW, founded by the Ministry for Science and Research of North Rhine Westphalia and by the Deutsche Forschungs Gemeinschaft in the scope of the research topic Deduktion, and is an extended version of a talk held at the German-Japanese Workshop on Logic and Natural Language (23–25 October 1990, in Kyoto, Japan).