Integrating Data Flow Equations with UML/Realtime

Object-oriented (OO) modeling languages, tools, and methods more and more attract the interest of embedded (real-time) system developers. This is especially true if embedded (real-time) system software has to cooperate with interactive multimedia software, as it is more and more the case in automotive systems. It is still an open question whether and how the standard OO modeling language UML and its accompanying tools have to be adapted to the regarded application domain. This paper evaluates the development of a rapid prototype for an air condition controller with the popular CASE tool Rational Rose/RT^®. We point out some weaknesses of the presented solution and propose an extension to Rose/RT^®, which overcomes the weaknesses by combining Rose/RTs UML dialect with data flow equations.     

Achieving nonvanishing stability regions with high-gain cheap control using H techniques: the second-order case

This paper demonstrates how to use an asymptotically H^∞-optimal controller to stabilize a second-order system subject to unknown disturbances such that the stability region does not vanish as the feedback gains increase. The high-gain feedback arises when one attempts to achieve the lowest achievable limit of the disturbance attenuation under the H^∞ design. This type of gain increase can cause the stability region to vanish if the disturbance contains nonlinear terms. The analysis using Lyapunov techniques derives a sufficient condition on the design parameters to prevent the stability region from vanishing. In addition to describing exact solutions for six different cases, the paper provides simulations to illustrate the results.     

H robust stabilizability

In this paper, we improve on the results of robust stabilizability obtained by Kimura. We do this in a constructive way by using an H^∞-approach, and exhibit an upper bound for the order of robust controllers.     

An inequality governing nonlinear H∞ control

This note gives necessary and sufficient conditions for solving a reasonable version of the nonlinear H^∞ control problem. The most objectionable hypothesis is elegant and holds in the linear case, but every possibly may not be forced for nonlinear systems. What we discover in distinction to Isidori and Astolfi (1992) and Ball et al. (1993) is that the key formula is not a (nonlinear) Riccati partial differential inequality, but a much more complicated inequality mixing partial derivatives and an approximation theoretic construction called the best approximation operator. This Chebeshev-Riccati inequality when specialized to the linear case gives the famous solution to the H^∞ control problem found in Doyle et al. (1989). While complicated the Chebeshev-Riccati inequality is (modulo a considerable number of hypotheses behind it) a solution to the nonlinear H^∞ control problem. It should serve as a rational basis for discovering new formulas and compromises. We follow the conventions of Ball et al. (1993) and this note adds directly to that paper.     

Lattice structure of e-implications on L

In this paper, we consider the set of all e-implications on L^∗ and define two operations on the set of all representable e-implications on L^∗, thus endowing it with monoid structure which is also a distributive complete lattice.     

Designing robustly stabilising controllers for LTI spatially distributed systems using coprime factor synthesis

This paper considers the design of feedback controllers for linear, time-invariant, spatially distributed systems in an approach which generalises the H^∞-framework and in particular the H^∞ loop-shaping method. To this end, we introduce a class of spatially distributed system models called finite dimensional, distributed, linear, time-invariant systems. Sensors and actuators are considered to be part of the controller, rather than part of the plant, and thus the controller we wish to design is itself a spatially distributed system. Optimising over placements and shapes of the sensor and actuator spatial distribution functions is an integrated part of the controller design procedure. As an illustrative design example, we present the feedback stabilisation of an electrostatically destabilised, electrically conducting membrane.     

Achievable H performance in sampled-data smoothing: beyond the -barrier

The lifting technique is a powerful tool for handling the periodically time-varying nature of sampled-data systems. Yet all known solutions of sampled-data H^∞ problems are limited to the case when the feedthrough part of the lifted system, , satisfies , where γ is the required H^∞ performance level. While this condition is always necessary in feedback control, it might be restrictive in signal processing applications, where some amount of delay or latency between measurement and estimation can be tolerated. In this paper, the sampled-data H^∞ fixed-lag smoothing problem with a smoothing lag of one sampling period is studied. The problem corresponds to the a-posteriori filtering problem in the lifted domain and is probably the simplest problem for which a smaller than performance level is achievable. The necessary and sufficient solvability conditions derived in the paper are compatible with those for the sampled-data filtering problem. This result extends the scope of applicability of the lifting technique and paves the way to the application of sampled-data methods in digital signal processing.     

灰色GM(1,1,t α)模型与自忆性原理的耦合及应用

针对实际工程应用中传统GM(1,1)模型预测的局限性,以含时间幂次项的灰色GM(1,1,tα)模型为基础,构建了灰色GM(1,1,tα)与自忆性原理的耦合预测模型;用动力系统自忆性原理来克服传统灰色模型对初值比较敏感的弱点;将灰色GM(1,1,t2)自忆性模型应用于某沿海高速软土地基沉降的模拟和预测,获得了满意的模拟和预测精度.实验算例表明,所提出的新模型显著地改善了传统灰色预测模型的模拟预测精度.     

H performance of preview control systems

Performance of the preview control is investigated in terms of H^∞-criterion. In the infinite-horizon time setting, the limitation of H^∞ performance in preview control action is characterized with the Hamiltonian matrix. By employing the property of Hamiltonian matrix, the solvability and analytic solution for the preview full-information control problem are clarified based on an auxiliary introduced matrix Riccati equation. The property of resulting control law is illustrated with a numerical example.     

Sample complexity of worst-case H-identification

We show that the sample complexity of qorst-case H^∞-identification is of order n², by proving that the minimal length of a fractional H^∞-cover for C_n, regarded as the linear space of complex-valued sequences of length n, is of order n². A unit vector u in ^∞ is a fractional H^∞-cover for C_n if for some

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for all rh ε C_n, where is the z-transform of h. We also give similar results for real-valued sequences.     

The use of representations of H in placing classical control problems in a modern control framework

Motivated by Zames' work on optimal sensitivity, it is shown that there exists in functional analysis a foundation, based upon the theory of representations of H^∞, upon which results may be developed to enable a range of classical control problems to be placed in a modern control framework.     

(J, J′)-lossless factorization based on conjugation

This paper is concerned with a derivation of the state-space form of the (J, J′)-lossless factorization which contains both the inner-outer factorization and the spectral factorization of positive matrices as special cases. Also, the (J, J′)-lossless factorization gives a unified framework of H^∞ control theory. We use the method of conjugation which makes the derivation much simpler than the previous literature, most of which used the technique of (J, J′)-spectral factorization. A necessary and sufficient condition is represented in terms of two Riccati equations one of which is degenerated.     

On the H fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^∞ filtering occur is clarified. It is shown that the H^∞ smoother exploits the information preview in an “H² manner”.     

An H-minimax approach to the design of robust control systems

A realistic feedback design problem is posed based on the minimization of a weighted combination of the sensitivity and complementary sensitivity matrices. A solution is obtained which makes use of the recently proposed methods for minimizing the sensitivity function alone.     

A novel secret image sharing scheme in color images using small shadow images

Over the past several years, secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on, in addition to traditional cryptography. Because smaller shadows can speed up the transmission of a secret color image, in this paper we combine Chang and Wu’s gradual search algorithm for a single bitmap BTC (GSBTC) and Shamir’s (k, n) threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows. Experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random-like image that prevents leakage of information about the secret color image. Furthermore, the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image, and the presented scheme also achieves, on average, an NPCR = 0.414% and AUCI = 32.78%. Thus, with our scheme one-pixel difference could cause a significant difference in the corresponding shadows. Therefore, the security of the presented scheme is also confirmed.     

On the state space and frequency domain characterization of H-norm of sampled-data systems

This paper studies the problem of characterization and computation of the H^∞-norm of sampled-data systems using the time-invariant function space model via lifting. With the advantage of time-invariance, the treatment gives an eigenvalue-type characterization, first in the operator form in the frequency domain and then in the Hamiltonian-type finite-dimensional form. The form obtained can be adopted for use with the bisection algorithm for actual computation.