Kleene modules and linear languages

A Kleene algebra (K, +, ·, *, 0, 1) is an idempotent semiring with an iteration * as axiomatised by Kozen. We consider left semiring modules (A, +, 0, :) over Kleene algebras. We call such a left semiring module a Kleene module if each linear equation x = a + r : x has a least solution, where : is the product from K × A to A. The linear context-free languages can be viewed as a Kleene module A over a Kleene algebra R of binary regular word relations. Thus, the simultaneous linear fixed-point operator μ on languages can be reduced to iteration * on R and the scalar product :.     

Pole/zero cancellations in the general ∞ problem with reference to a two block design

Necessary and sufficient conditions are given for pole/zero cancellations in the close--loop transfer function from input disturbances to error signals in the general _∞ problem. These pole/zero cancellations can place restrictions on the suitability of particular _∞ design procedures. This will be shown by reference to a typical two-block design procedure.     

On minimal order stabilization of single loop plants

It is shown by example that a single loop plant of order n, relative degree 1, with one right half plane pole and one right half plane zero may not be stabilizable by a compensator of order n−2. A further example shows that a minimum phase plant of order n, relative degree r, with one right half plane pole may not be stabilizable by a compensator of order r−2.     

On pole assignment problems in polynomial rings

A result giving conditions under which a polynomial ring over a principal ideal domain is not pole assignable is proved. It is then deduced that Z[Xa] and K[X, Y] (K a field) are not pole assignable rings. Explicit examples of reachable pairs of matrices which are not pole assignable are also given.     

The μ-basis of a planar rational curve—properties and computation

A moving line L(x,y;t)=0 is a family of lines with one parameter t in a plane. A moving line L(x,y;t)=0 is said to follow a rational curve P(t) if the point P(t₀) is on the line L(x,y;t₀)=0 for any parameter value t₀. A μ-basis of a rational curve P(t) is a pair of lowest degree moving lines that constitute a basis of the module formed by all the moving lines following P(t), which is the syzygy module of P(t). The study of moving lines, especially the μ-basis, has recently led to an efficient method, called the moving line method, for computing the implicit equation of a rational curve [3 and 6]. In this paper, we present properties and equivalent definitions of a μ-basis of a planar rational curve. Several of these properties and definitions are new, and they help to clarify an earlier definition of the μ-basis [3]. Furthermore, based on some of these newly established properties, an efficient algorithm is presented to compute a μ-basis of a planar rational curve. This algorithm applies vector elimination to the moving line module of P(t), and has O(n²) time complexity, where n is the degree of P(t). We show that the new algorithm is more efficient than the fastest previous algorithm [7].     

Language Parametric Module Management for IDEs

An integrated development environment (IDE) monitors all the changes that a user makes to source code modules and responds accordingly by flagging errors, by reparsing, by rechecking, or by recompiling modules and by adjusting visualizations or other information derived from a module. A module manager is the central component of the IDE that is responsible for this behavior. Although the overall functionality of a module manager in a given IDE is fixed, its actual behavior strongly depends on the programming languages it has to support. What is a module? How do modules depend on each other? What is the effect of a change to a module?We propose a concise design for a language parametric module manager: a module manager that is parameterized with the module behavior of a specific language. We describe the design of our module manager and discuss some of its properties. We also report on the application of the module manager in the construction of IDEs for the specification language Asf+Sdf as well as for Java.Our overall goal is the rapid development (generation) of IDEs for programming languages and domain specific languages. The module manager presented here represents a next step in the creation of such generic language workbenches.     

Robust H∞ control for uncertain discrete-time systems with circular pole constraints

This paper investigates the problem of robust H_∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H_∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H_∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H_∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H_∞ control and robust pole assignment of uncertain systems.     

Bases for projective modules in An(k)

Let A_n(k) be the Weyl algebra, with k a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let M be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of M. If M is projective and rank(M)≥2 we give a procedure to find a basis.     

Design of robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-controller for energetic boiler plant

A problem of robust controller design for control of a boiler plant is solved using an H _∞ loop-shaping method with constraints imposed on regional pole placement of transfer functions of the closed-loop system, and linear matrix inequalities tools. Requirements to the closed-loop system are formulated both in the form of frequency constraints on singular values of transfer function of the open-loop system, and in the form of pole placement constraints for the transfer function of the closed-loop system as a given region on the complex plane. A reduction of the full-order H _∞-controller obtained in the design procedure is performed.     

Transfer functions for infinite-dimensional systems

In this paper, we study three definitions of the transfer function for an infinite-dimensional system. The first one defines the transfer function as the expression C(sI−A)⁻¹B+D. In the second definition, the transfer function is defined as the quotient of the Laplace transform of the output and input, with initial condition zero. In the third definition, we introduce the transfer function as the quotient of the input and output, when the input and output are exponentials. We show that these definitions always agree on the right-half plane bounded to the left by the growth bound of the underlying semigroup, but that they may differ elsewhere.     

A covering Ka‐band two‐way switch filter module using a three‐line and an E‐plane waveguide band‐pass filters

A millimeter‐wave ultrawideband two‐way switch filter module is presented in this article. The switch filter module covers whole Ka‐band (26–40 GHz), and is composed of two wideband band‐pass filters and two monolithic microwave integrated circuit (MMIC) single pole two throw (SP2T) switches. One filter is realized using E‐plane iris waveguide band‐pass filter, and another is realized by a novel 11‐pole three‐line microstrip structure band‐pass filter. Compared with the traditional three‐line filter, the proposed three‐line filter not only retains virtues of the traditional three‐line filter, but also resolves drawbacks of it, which include discontinuities between adjacent sections, many parameters of design, and no effective matching circuits at input/output ports. The developed switch filter module is fabricated using hybrid integrated technology, which has a size of 51 × 26 × 9.8 mm³, and interconnections between MMICs and microstrip are established by bond wires. The fabricated switch filter module exhibits excellent performances: for two different states, the measured insertion loss and return loss are all better than 7 and 10 dB in each pass‐band, respectively. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:305–310, 2015.     

Local Module Checking for CTL Specifications

Model checking is a well known technique for the verification of finite state models using temporal logic specification. While model checking is suitable for transformational systems (also called closed systems), it is unsuitable for open systems (also known as reactive systems) where the nondeterminism in the environment must be considered during verification. Module checking is an approach for the verification of open systems which have both closed (internal) and open (environment or external) states. It has been demonstrated in [Orna Kupferman, Moshe Y. Vardi, and Pierre Wolper. Module checking. Information and Computation, 164:322–344, 2001] that the complexity of module checking branching time logic CTL is EXPTIME-complete. The approach to module checking is global and the method tries to establish that the property in question holds over all possible environments.This papers develops a local approach to CTL module checking using tableau rules. The proposed approach tries to determine a single environment under which the negation of the property is satisfied over the given module. Such a strategy, thus, leads to a local approach to module checking where we only explore states that are relevant to proving that the negation of the property can be satisfied over the given module using an appropriate witness (environment) that the algorithm also generates. While the worst case complexity of our algorithm is identical to the earlier complexity, we demonstrate that practical implementation of the proposed approach is feasible and yields much better results than the global approach.     

A single dynamic observer-based module for design of simultaneous fault detection,isolation and tracking control scheme

The problem of simultaneous fault detection, isolation and tracking (SFDIT) control design for linear systems subject to both bounded energy and bounded peak disturbances is considered in this work. A dynamic observer is proposed and implemented by using the H_∞/H_?/L₁ formulation of the SFDIT problem. A single dynamic observer module is designed that generates the residuals as well as the control signals. The objective of the SFDIT module is to ensure that simultaneously the effects of disturbances and control signals on the residual signals are minimised (in order to accomplish the fault detection goal) subject to the constraint that the transfer matrix from the faults to the residuals is equal to a pre-assigned diagonal transfer matrix (in order to accomplish the fault isolation goal), while the effects of disturbances, reference inputs and faults on the specified control outputs are minimised (in order to accomplish the fault-tolerant and tracking control goals). A set of linear matrix inequality (LMI) feasibility conditions are derived to ensure solvability of the problem. In order to illustrate and demonstrate the effectiveness of our proposed design methodology, the developed and proposed schemes are applied to an autonomous unmanned underwater vehicle (AUV).     

On the pole location of a system designed by robust stability-degree assignment

In this paper, we examine the pole location of the feedback system composed of the nominal plant and the H_∞ central controller designed by the robust stability-degree assignment. Namely, the exact pole location at γ=∞ and the behavior near the infimum of γ are clarified where γ is the upper bound of the H_∞ norm constraint. The original design goal is to stabilize the plant against additive perturbations with the regional pole placement condition Re s<−α, and the design problem is reduced to the one-block H_∞ control problem.     

On the causal factorization problem

In this note the formalism of the infinite zero module and of the infinite pole module is used to analyze the causal factorization problem. This allows us to express its solutions in terms of zeros and poles at infinity and to have a better understanding of both the problem and the techniques previously proposed by various authors to solve it. Moreover, we obtain a characterization, in terms of the existence of certain causal factorizations, of the transfer functions having no infinite zeros.     

Multipurpose controller synthesis in discrete LQG optimal systems

This paper presents a design algorithm to synthesize a discrete-time linear-quadratic-gaussian (LQG) optimal controller that simultaneously ensures (i) input–output decoupling; (ii) pole and zero placement; and (iii) robust stability in the presence of plant perturbation. Two weighting matrices Q(Z) and R(Z) of the quadratic cost functional are shaped to synthesize an optimal controller to achieve the stated design goals.     

Improved Speech Synthesis Using Fuzzy Methods

The paper presents theoretical support for and describes the use of a fuzzy paradigm in implementing a TTS system for the Romanian language, employing a rule-based formant synthesizer. In the framework of classic TTS systems, we propose a new approach in order to improve formant trace computation, aiming at increasing synthetic speech perceptual quality. A fuzzy system is proposed for solving the problem of the phonemes that are prone to multi-definitions in rule-based speech synthesis. In the introductory section, we briefly present the background of the problem and our previous results in speech synthesis. In the second section, we deal with the problem of the context-dependent phonemes at the letter-to-sound module level of our TTS system. Then, we discuss the case of the phoneme /l/ and the solution adopted to define it for different contexts. A fuzzy system is associated with each parameter (denoted F1 and F2) to implement the results of the complete analysis of the phoneme /l/ behavior. The knowledge used in implementing the fuzzy module is acquired by natural speech analysis. In the third section, we exemplify the computation of the synthesis parameters F1 and F2 of the phoneme /l/ in the context of the two syllable sequences. The parameter values are contrasted with those obtained from the spectrogram analysis of the natural speech sequences. The last section presents the main conclusions and further research objectives.     

Exact computation of infimum for a class of continuous-time H∞ optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output

A noniterative method for the computation of infimum for a class of continuous-time H_∞ optimal control problem is considered in this paper. The problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems. The method is applicable to systems where (i) the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible, and (ii) the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible. The result presented in this paper is a continuation of the previous work of the author and his co-workers (Chen et al., 1992), in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero.     

sensitivity minimization for delay systems

This paper announces results on the problem of feedback compensator design for ^∞ norm weighted sensitivity minimization when the plant contains a delay in the input. A complete solution is presented for the case of one pole/zero weighting function and a single-input/single-output plant for stable minimum-phase rational part. Generalizations and proofs will be published elsewhere.     

An Improved Anti‐Windup Bumpless Transfer Structures Design for Controllers Switching

In this paper, an anti‐windup bumpless transfer (AWBT) control structure combined with linear interpolation method is proposed for smooth switching control. By choosing an appropriate scheduling signal, different controllers can be switched smoothly under a unified framework. Meanwhile, some robust specifications including H₂/H_∞ performance, pole placement constraint, and passivity of the closed‐loop system can be preserved through controller switching. Furthermore, for the linear system subject to input saturation, the stability and L₂ gain of the closed‐loop system can be guaranteed. Finally, a cart‐spring pendulum system is simulated to demonstrate the effectiveness of the proposed scheme.