Model reduction for state-space symmetric systems

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H_∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions.     

Continuous time-varying linear systems

We discuss implicit systems of ordinary linear differential equations with (time-) variable coefficients, their solutions in the signal space of hyperfunctions according to Sato and their solution spaces, called time-varying linear systems or behaviours, from the system theoretic point of view. The basic result, inspired by an analogous one for multidimensional constant linear systems, is a duality theorem which establishes a categorical one–one correspondence between time-varying linear systems or behaviours and finitely generated modules over a suitable skew-polynomial ring of differential operators. This theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic (hyper-)functions or of distributions on . It is used to obtain various results on key notions of linear system theory. Several new algorithms for modules over rings of differential operators and, in particular, new Gröbner basis algorithms due to Insa and Pauer make the system theoretic results effective.     

Classifying and detecting anomalies in hybrid knowledge-based systems

The increasing need for hybrid Knowledge-Based Systems (KBS) that accommodate more complex applications has led to the need for new verification concerns that are more specific to the hybrid representation using objects and rule-based inference. Traditionally, verification of expert systems has focused solely on rule-based inference systems. Hybrid KBSs present additional verification problems not found in traditional rule-based systems. This paper is an investigation into the anomalies that may be present in a hybrid representation that warrant detection for the verification of the KBS. Many anomalies are due to the interaction of the component parts of the hybrid KBS. For example, subsumption anomalies arise due to an interaction between inheritance of objects and rule-based inference. In this paper, we extend the context of subsumption anomalies and introduce additional types of anomalies that may be present in the KBS. The goal of this research is to make hybrid KBSs more reliable by detecting such anomalies.     

A skew-symmetric property of rigid-body systems

The configuration space for the attitude of a vehicle can be modeled as SO(3), namely the rotation matrix group. This work investigates the globally valid dynamics of natural Lagrangian systems and gyroscopic systems with configuration space including SO(3). The dynamics is derived by using the global representations of jet bundles of SO(3). A skew-symmetric property associated with the systems can be then established. Such property can be used in many applications such as the adaptive controller design.     

Generalized sampled data feedback control of distributed parameter systems

In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems the necessary conditions are also known to be sufficient. We show that this equivalence extends to the infinite-dimensional case if the underlying semigroup is analytic. However, for general systems, the necessary conditions are not sufficient, nor are the sufficient conditions necessary. We prove this by a single example with a free parameter – one choice of parameter shows that the necessary conditions are too weak, and another choice shows that the sufficient conditions are too strong.     

Adaptive control of a class of discrete-time affine nonlinear systems

The adaptive control problem is addressed in the paper for a class of discrete-time affine nonlinear input/output stochastic models with linear unknown parameters. The controller is a certainty equivalence weighted one-step-ahead control and is constructed by using the weighted-least-squares and random regularization methods. Global stability of the closed-loop systems is established, which shows that arbitrarily large growth rate is allowed for the multiplicative nonlinear part of the systems.     

Continuity properties of balanced realizations

In this paper topological and geometrical properties of pre-balanced and balanced realizations are considered. It is shown that analytic pre-balancing coordinate transformations do exist and that the set of pre-balanced realizations forms an analytic submanifold. Explicit formulas for the tangent spaces and their dimension are derived. Continuity properties of balanced realizations are studied. For systems with more than two inputs and two outputs explicit points of discontinuity of balancing coordinate transformations are described. A certain class of balancing coordinate transformations is shown to be discontinuous, even for distinct and fixed singular values.     

Transputer-based robot control system for six-joint robot manipulators

A transputer-based robot control system was designed and built to control an industrial robot PUMA 560. The goal was to develop a research tool for the investigation of practical and theoretical aspects of various advanced control strategies in the robot system. A transputer network consisting of thirteen transputers is employed for the application, where the parallelization of the algorithms is utilized for speeding up the computation. The kinematics, path planning and a collision avoidance module associated with a vision system are implemented on the network. Six joint controller modules were designed and constructed to handle input/output signals from the joint motors of the robot manipulator. The advanced multitransputer structure is capable of integrating the extern sensor information in a simple way and implementing control algorithms in parallel processes. For Software development, the parallel programming language Occam is used. The code development is performed on an IBM-PC-based toolset system.     

Switching through singularities

Asymptotic tracking is studied for systems which are not regular, that is, the relative degree is not well defined. For these systems, the input–output linearizing control law has singularities. We propose a tracking control law which switches between an approximate tracking law (Hauser et al., IEEE Trans. Automat. Control 37 (3) (1992) 392–398) close to the singularities, and an exact tracking law away from the singularities, and we study the applicability of this law based on the behavior of the system’s zero dynamics at the switching boundary. As in Hauser et al. (IEEE Trans. Automat. Control 37 (3) (1992) 392–398), the ball and beam example is used to motivate the study.     

Coprimeness properties of nonlinear fractional system realizations

In this paper, the relationship between the Bezout and the set-theoretic approaches to left coprimeness is studied. It is shown that left coprimeness in the set-theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relations between two left coprime realizations of the same system.     

A learning result for continuous-time recurrent neural networks

The following learning problem is considered, for continuous-time recurrent neural networks having sigmoidal activation functions. Given a “black box” representing an unknown system, measurements of output derivatives are collected, for a set of randomly generated inputs, and a network is used to approximate the observed behavior. It is shown that the number of inputs needed for reliable generalization (the sample complexity of the learning problem) is upper bounded by an expression that grows polynomially with the dimension of the network and logarithmically with the number of output derivatives being matched.     

Measuring texture classification algorithms

The texture analysis literature lacks a widely accepted method for comparing algorithms. This paper proposes a framework for comparing texture classification algorithms. The framework consists of several suites of texture classification problems, a standard functionality for algorithms, and a method for computing a score for each algorithm. We use the framework to demonstrate the peaking phenomenon in texture classification algorithms. The framework is publicly available on the Internet.     

A note on observability tests for general polynomial and simple Wiener–Hammerstein systems

We propose an algorithm, based on symbolic computation packages, for testing observability conditions of general polynomial systems, which were formulated in Sontag, SIAM J. Control Optim. 17 (1979) 139–151. Computational complexity of the observability test can be reduced and the test simplified for classes of polynomial systems. We illustrate this by considering the class of simple Wiener–Hammerstein systems, which consist of a series of two linear dynamic blocks between which a static nonlinearity is “sandwiched”. We consider the case when the nonlinearity is a monomial . Simple necessary and sufficient conditions for observability are given and they resemble, but are subtly different from, the well known result on observability for the series connection of two linear systems.     

Global L2-gain design for a class of nonlinear systems

It is known that the so-called H_∞ control problem of a nonlinear system is locally solvable if the corresponding problem for the linearized system can be solved by linear feedback. In this paper we prove that this condition suffices to solve also a globalH_∞ control problem, for a fairly large class of nonlinear systems, if one is free to choose a state-dependent weight of the control input. Using a two-way (backward and forward) recursive induction argument, we simultaneously construct, starting from a solution of the Riccati algebraic equation, a global solution of the Hamilton–Jacobi–Isaacs partial differential equation arising in the nonlinear H_∞ control, as well as a state feedback control law that achieves global disturbance attenuation with internal stability for the nonlinear systems.     

Inheritance rules for flexible model retrieval

Convenient model management requires flexible model retrieval. This paper presents a new flexible retrieval approach for mathematical model bases. The approach defines a multi-valued model inheritance relationship among models at a signature level. The inheritance provides a rich semantic information for the retrieval mechanism to refine inexact retrieval requirements. An inheritance rules reasoning system is proposed to enhance the ability and the efficiency of the model retrieval. The interface of the approach includes an SQL-like command, which enables users to retrieve their required models with inexact requirement expressions. The approach has been implemented in a rule-based mathematical model base system RMMBS. Application examples demonstrate the retrieval approach.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

Exponentially convergent control laws for nonholonomic systems in power form

This paper introduces a method for constructing exponentially convergent control laws for n-dimensional nonholonomic systems in power form. The methodology is based on the construction of a series of nested invariant manifolds for the closed-loop system under a linear control law. A recursive algorithm is presented which uses these manifolds to construct a three-dimensional system in power form. It is shown that the feedback controller for the original system is the one for this three-dimensional system with a proper choice of the gains.     

Order statistics and probabilistic robust control

Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related probability distribution. Also, the concept of distribution-free tolerance intervals is applied to estimate the range of an uncertain quantity and extract the information about its distribution. To overcome the limitations imposed by the continuity assumption in the existing order statistics theory, we have derived a cumulative distribution function of the order statistics without the continuity assumption and developed an inequality showing that this distribution has an upper bound which equals to the corresponding distribution when the continuity assumption is satisfied. By applying this inequality, we investigate the minimum computational effort needed to come up with an reliable estimate for the upper bound (or the lower bound) and the range of a quantity. We also give conditions, which are much weaker than the absolute continuity assumption, for the existence of such minimum sample size. Furthermore, the issue of making tradeoff between performance level and risk is addressed and a guideline for making this kind of tradeoff is established. This guideline can be applied in general without continuity assumption.     

Constrained stabilization via smooth Lyapunov functions

We consider the problem of stabilizing a dynamic system by means of bounded controls. We show that the largest domain of attraction can be arbitrarily closely approximated by a “smooth” domain of attraction for which we provide an analytic expression. Such an expression allows for the determination of a (non-linear) control law in explicit form.     

Exploring cache performance in multithreaded processors

Multithreading is a well known technique to hide latency in a non-blocking cache architecture. By switching execution from one thread to another, the CPU can perform useful work, while waiting for pending requests to be processed by the main memory. In this paper we examine the effects of varying the associativity and block size on cache performance in a reduced locality of reference environment, due to multithreading. We find that for associativity equal to the number of threads, the cache produces very low miss rate even for small sizes. Also by taking into account the increase in cycle time due to larger cache size or associativity we find that the optimum cache configuration for best processor performance is 16Kbytes direct mapped. Finally, with a constant main memory bandwidth, increasing the block size to more than 32 bytes, reduces the miss rate, but degrades processor performance.