Asymptotic characterizations of input–output-to-state stability for discrete-time systems

We establish the equivalence between global detectability and output-to-state stability for difference inclusions with outputs, and we present equivalent asymptotic characterizations of input–output-to-state stability for discrete-time nonlinear systems. These new stability characterizations for discrete-time systems parallel what have been developed for continuous-time systems in Angeli et al. [Uniform global asymptotic stability of differential inclusions, J. Dynamical Control Systems 10 (2004) 391–412] and Angeli et al. [Seperation principles for input–output and integral-input-to-state stability, SIAM J. Control Optim. 43 (2004) 256–276].     

Stability of a nonuniform Rayleigh beam with indefinite damping

This is a continuation of our earlier work [J.M. Wang, G.Q. Xu, S.P. Yung, Exponential stability for variable coefficients Rayleigh beams under boundary feedback control: a Riesz basis approach, Systems Control Lett. 51 (1) (2004) 33–50] on the study of a nonhomogeneous Rayleigh beam and this time the stabilization is achieved via an internal damping instead of the boundary feedbacks. We continue to address a conjecture of Guo [Basis property of a Rayleigh beam with boundary stabilization, J. Optim. Theory Appl. 112(3) (2002) 529–547] in this paper and demonstrate how the damping term can affect the decay rate asymptotically. By a detailed spectral analysis, we obtain a necessary condition for the stability and establish the Riesz basis property as well as the spectrum determined growth condition for the system. Furthermore, when the damping is indefinite, we provide a condition on how “negative” the damping can be without destroying the exponential stability.     

A converse Lyapunov theorem for nonlinear switched systems

In this paper we present a converse Lyapunov theorem for uniform asymptotic stability of switched nonlinear systems. Its proof is a simple consequence of some results on converse Lyapunov theorems for systems with bounded disturbances obtained by Lin et al. (SIAM J. Control Optim. 34 (1996) 124–160), once an association of the switched system with a nonlinear system with disturbances is established.     

A global stability result in network flow control

This paper concerns recently proposed algorithms for network flow control, where source transmission rates are chosen based on an individual utility function and a network price signal propagated from the links. Link prices are, in turn, dynamically updated based on overall link congestion. In particular, we consider here the second-order update law of Athuraliya et al. [IEEE Network 15 (3) (2001) 48–53], which has attractive features in equilibrium: full link utilization and no backlog. Using a non-linear, continuous-time model which enforces non-negativity constraints in prices and backlogs, we prove the global asymptotic stability of the equilibrium, by means of a Lyapunov argument.     

Solution to the “Champagne problem” on the simultaneous stabilisation of three plants

In this paper, the problem proposed in Blondel et al. (SIAM J. Optim. 32 (2) 572–590) as an illustration of the difficulty of the simultaneous stabilization problem has been solved. The same problem was also mentioned in Blondel and Gevers (Math. Control, Signals, Systems 6 (1994) 135–145), where a bottle of good French champagne was offered for its solution. A new open problem is proposed based on the solution of the problem in this paper.     

Robustness of network flow control against disturbances and time-delay

This paper studies robustness of Kelly's source and link control laws in (J. Oper. Res. Soc. 49 (1998) 237) with respect to disturbances and time-delays. This problem is of practical importance because of unmodelled flows, and propagation and queueing delays, which are ubiquitous in networks. We first show L_p-stability, for p[1,∞], with respect to additive disturbances. We pursue L_∞-stability within the input-to-state stability (ISS) framework of Sontag (IEEE Trans. Automat. Control 34 (1989) 435), which makes explicit the vanishing effect of initial conditions. Next, using this ISS property and a loop transformation, we prove that global asymptotic stability is preserved for sufficiently small time-delays in forward and return channels. For larger delays, we achieve global asymptotic stability by scaling down the control gains as in Paganini et al. (Proceedings of 2001 Conference on Decision and Control, Orlando, FL, December 2001, pp. 185–190)     

Comments on: “Efficient robust constrained model predictive control with a time varying terminal constraint set” by Wan and Kothare

We present an algorithm that modifies the original formulation proposed in Wan and Kothare [Efficient robust constrained model predictive control with a time-varying terminal constraint set, Systems Control Lett. 48 (2003) 375–383]. The modified algorithm can be proved to be robustly stabilizing and preserves all the advantages of the original algorithm, thereby overcoming the limitation pointed out recently by Pluymers et al. [Min–max feedback MPC using a time-varying terminal constraint set and comments on “Efficient robust constrained model predictive control with a time-varying terminal constraint set”, Systems Control Lett. 54 (2005) 1143–1148].     

Strong convergence theorems for a new iterative method of -strictly pseudo-contractive mappings in Hilbert spaces

In this paper, we introduce a new iterative method of a k-strictly pseudo-contractive mapping for some 0≤k<1 and prove that the sequence {x_n} converges strongly to a fixed point of T, which solves a variational inequality related to the linear operator A. Our results have extended and improved the corresponding results of Y.J. Cho, S.M. Kang and X. Qin [Some results on k-strictly pseudo-contractive mappings in Hilbert spaces, Nonlinear Anal. 70 (2008) 1956–1964], and many others.     

Network flow control under capacity constraints: A case study

In this paper, we demonstrate how tools from nonlinear system theory can play an important role in tackling “hard nonlinearities” and “unknown disturbances” in network flow control problems. Specifically, a nonlinear control law is presented for a communication network buffer management model under physical constraints. Explicit conditions are identified under which the problem of asymptotic regulation of a class of networks against unknown inter-node traffic is solvable, in the presence of control input and state saturation. The conditions include a Lipschitz-type condition and a “PE” condition. Under these conditions, we achieve either asymptotic or practical regulation for a single-node system. We also propose a decentralized, discontinuous control law to achieve (global) asymptotic regulation of large-scale networks. Our main result on controlling large-scale networks is based on an interesting extension of the well-known Young's inequality for the case with saturation nonlinearities. We present computer simulations to illustrate the effectiveness of the proposed flow control schemes.     

Lifting Infinite Normal Form Definitions From Term Rewriting to Term Graph Rewriting

nfinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Böhm tree in the lambda calculus. It was first introduced in [Ariola, Z. M. and S. Blom, Cyclic lambda calculi, in: Abadi and Ito [Abadi, M. and T. Ito, editors, “Theoretical Aspects of Computer Software,” Lecture Notes in Computer Science 1281, Springer Verlag, 1997], pp. 77–106] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrite system. In [Blom, S., “Term Graph Rewriting - syntax and semantics,” Ph.D. thesis, Vrije Universiteit Amsterdam (2001)] the framework was improved by defining the infinite normal form of a term graph using the infinite normal form on terms. This approach of lifting the definition makes the non-confluence problems introduced into term graph rewriting by substitution rules much easier to deal with. In this paper, we give a simplified presentation of the latter approach.     

On the stabilization of feedforward systems with bounded control

For the global asymptotic stabilization of nonlinear—controllable in the first approximation—cascades consisting of a globally asymptotically—locally exponentially stable system driving a stable system, a Lyapunov-like design is proposed. This yields (bounded) control laws, where the control magnitude can be chosen arbitrarily large. This result provides an alternative to classical forwarding.     

Comparative study of analytical and numerical algorithms for designing reinforced concrete sections under biaxial bending

This paper presents a comparative study of different integration methods of stresses (both analytical and numerical) for concrete sections subjected to axial loads and biaxial bending. Such methods are applied to circular and rectangular sections. The constitutive equation used is a parabola-rectangle from the Eurocode-2. The comparison was performed with regard to the accuracy and the computational speed of each method. The objective of the paper is to determine which of the integration methods compared is more efficient in computing the interaction surfaces for rectangular and circular sections. The analytical method proposed by Barros et al. [Barros MHFM, Barros A, Ferreira C. Closed form solution of optimal design of rectangular reinforced concrete sections. Eng Comput 2004;21(7):761–76] for rectangular sections is compared with the numerical method termed “modified thick layer integration” proposed by Bonet et al. [Bonet JL, Romero ML, Miguel PF, Fernandez MA. A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending. Comput Struct 2004;82(2–3):213–25] and with the well-known fiber method. Furthermore, two new methods are proposed for circular sections: one analytical and one numerical based on the Gauss–Legendre quadrature. The results of both methods are compared with the classical layer decomposition method.     

Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

Consideration was given to asymptotic stabilization of the equilibria of nonlinear dynamic systems using the dynamic output feedbacks, that is, the feedbacks in the estimate of system state made by the asymptotic observer. Presented were the basic methods of constructing the asymptotic observers for the nonlinear dynamic systems with control and the approaches to system stabilization using the system state estimate made by the observer.__________Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 3–42.Original Russian Text Copyright © 2005 by Golubev, Krishchenko, Tkachev.This work was supported by the Russian Foundation for Basic Research, project no. 05-01-00840, Grant for State Support of the Leading Scientific Schools, project no. NSh-2094.2003.1, and project no. UR.03.01.141 of Section 1.2 “Russian Universities” of the Subprogram “Basic Research” of the Departmental Scientific Program “Development of the Scientific Potentialities of the Higher School” of the Federal Education Agency of the Russian Federation.     

Efficient migration access control for mobile agents

The speed and convenience of the Internet has facilitated dynamic development in electronic commerce in recent years. E-commerce technologies and applications are widely studied by expert researchers. Mobile agent is considered to have high potential in e-commerce; it has been attracting wide attention in recent years. Mobile agent has high autonomy and mobility; it can move unbridled in different runtime environments carrying out assigned tasks while automatically detecting its current environment and responding accordingly. The above qualities make mobile agent very suitable for use in e-commerce. The Internet is an open environment, but transfer of confidential data should be conducted only over a secure environment. So, to transfer information over the Internet, a secure Internet environment is absolutely essential. Therefore, the security of present Internet environment must be improved. During its execution, a mobile agent needs to roam around on the Internet between different servers, and it may come in contact with other mobile agents or hosts; it may also need to interact with them. So, a mobile agent might come to harm when it meets a malicious host, and the confidentiality of data could also be compromised. To tackle the above problems, this paper proposes a security scheme for mobile agents. It is designed to ensure the safety of mobile agents on the Internet, and it also has access control and key management to ensure security and data confidentiality. Volker and Mehrdad [R. Volker, J.S. Mehrdad, Access Control and Key Management for Mobile Agents, “Computer Graphics”, Vol. 22, No. 4, August 1998, pp. 457–461] have already proposed an access control and key management scheme for mobile agents, but it needs large amount of space. So, this paper proposes a new scheme that uses the concepts of Chinese Remainder Theorem [F.H. Kuo, V.R.L. Shen, T.S. Chen, F. Lai, A Cryptographic Key Assignment Scheme for Dynamic Access Control in a User Hierarchy, “IEE Proceeding on Computers & Digital Techniques”, Vol. 146, No. 5, Sept. 1999, pp. 235–240., T.S. Chen, Y.F. Chung, Hierarchical Access Control Based on Chinese Remainder Theorem and Symmetric Algorithm, ”Computers & Security”, Vol. 21, No. 6, 2002, pp. 565–570., U.P. Lei, S.C. Wang, A Study of the Security of Mambo et al.'s Proxy Signature Scheme Based on the Discrete Logarithm Problem, June 2004], hierarchical structure and Superkey [S.G. Akl, P.D. Taylor, Cryptographic Solution to a Problem of Access Control in a Hierarchy, “ACM Transactions on Computer Systems”, Vol. 1, No. 3, August 1983, pp. 239–248]. A security and performance analysis of the proposed scheme shows that the scheme effectively protects mobile agents.     

Modeling of high-affinity binding of the novel atrial anti-arrhythmic agent, vernakalant, to Kv1.5 channels

Vernakalant (RSD1235) is an investigational drug that converts atrial fibrillation rapidly and safely in patients intravenously [Roy et al., J. Am. Coll. Cardiol. 44 (2004) 2355–2361; Roy et al., Circulation 117 (2008) 1518–1525] and maintains sinus rhythm when given orally [Savelieva et al., Europace 10 (2008) 647–665]. Here, modeling using AutoDock4 allowed exploration of potential binding modes of vernakalant to the open-state of the Kv1.5 channel structure. Point mutations were made in the channel model based on earlier patch-clamp studies [Eldstrom et al., Mol. Pharmacol. 72 (2007) 1522–1534] and the docking simulations re-run to evaluate the ability of the docking software to predict changes in drug–channel interactions. Each AutoDock run predicted a binding conformation with an associated value for free energy of binding (FEB) in kcal/mol and an estimated inhibitory concentration (K_i). The most favored conformation had a FEB of −7.12 kcal/mol and a predicted K_i of 6.08 μM (the IC50 for vernakalant is 13.8 μM; [Eldstrom et al., Mol. Pharmacol. 72 (2007) 1522–1534]). This conformation makes contact with all four T480 residues and appears to be clearly positioned to block the channel pore.     

Mixed Discontinuous Galerkin Methods for Darcy Flow

We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for discontinuos Galerkin (DG) methods (see e.g. D.N. Arnold et al. SIAM J. Numer. Anal.39, 1749–1779 (2002) and B. Cockburn, G.E. Karniadakis and C.-W. Shu, DG methods: Theory, computation and applications, (Springer, Berlin, 2000) and the references therein) we use the stabilization introduced in A. Masud and T.J.R. Hughes, Meth. Appl. Mech. Eng.191, 4341–4370 (2002) and T.J.R. Hughes, A. Masud, and J. Wan, (in preparation). We show that such stabilization works for discontinuous elements as well, provided both the pressure and the flux are approximated by local polynomials of degree ≥ 1, without any need for additional jump terms. Surprisingly enough, after the elimination of the flux variable, the stabilization of A. Masud and T.J.R. Hughes, Meth. Appl. Mech. Eng.191, 4341–4370 (2002) and T.J.R. Hughes, A. Masud, and J. Wan, (in preparation) turns out to be in some cases a sort of jump stabilization itself, and in other cases a stable combination of two originally unstable DG methods (namely, Bassi-Rebay F. Bassi and S. Rebay, Proceedings of the Conference ‘‘Numerical methods for fluid dynamics V’‘, Clarendon Press, Oxford (1995) and Baumann–Oden Comput. Meth. Appl. Mech. Eng.175, 311–341 (1999).This revised version was published online in July 2005 with corrected volume and issue numbers.     

Sturm–Liouville problems with discontinuities at two points

In this paper we extend some spectral properties of regular Sturm–Liouville problems to those which consist of a Sturm–Liouville equation with piecewise continuous potentials together with eigenparameter-dependent boundary conditions and four supplementary transmission conditions. By modifying some techniques of [C.T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977) 293–308; E. Tunç, O.Sh. Muhtarov, Fundamental solutions and eigenvalues of one boundary-value problem with transmission conditions, Appl. Math. Comput. 157 (2004) 347–355; O.Sh. Mukhtarov, E. Tunç, Eigenvalue problems for Sturm–Liouville equations with transmission conditions, Israel J. Math. 144 (2004) 367–380] and [O.Sh. Mukhtarov, M. Kadakal, F.Ş. Muhtarov, Eigenvalues and normalized eigenfunctions of discontinuous Sturm–Liouville problem with transmission conditions, Rep. Math. Phys. 54 (2004) 41–56], we give an operator-theoretic formulation for the considered problem and obtain asymptotic formulae for the eigenvalues and eigenfunctions.     

Overcoming Heterogeneity and Autonomy in Multidatabase Systems

A multidatabase system (MDBS) is a software system for integration of preexisting and independent local database management systems (DBMSs). The transaction management problem in MDBSs consists of designing appropriate software, on top of local DBMSs, such that users can execute transactions that span multiple local DBMSs without jeopardizing database consistency. The difficulty in transaction management in MDBSs arises due to the heterogeneity of the transaction management algorithms used by the local DBMSs, and the desire to preserve their local autonomy. In this paper, we develop a framework for designing fault-tolerant transaction management algorithms for MDBS environments that effectively overcomes the heterogeneity- and autonomy-induced problems. The developed framework builds on our previous work. It uses the approach described in S. Mehrotra et al. (1992, in “Proceedings of ACM–SIGMOD 1992 International Conference on Management of Data, San Diego, CA”) to overcome the problems in ensuring serializability that arise due to heterogeneity of the local concurrency control protocols. Furthermore, it uses a redo approach to recovery for ensuring transaction atomicity (Y. Breitbart et al., 1990, in “Proceedings of ACM–SIGMOD 1990 International Conference on Management of Data, Atlantic City, NJ;” Mehrotra et al., 1992, in “Proceedings of the Eleventh ACM SIGACT–SIGMOD–SIGART Symposium on Principles of Database Systems, San Diego, CA;” and A. Wolski and J. Veijalainen, 1990, in “Proceedings of the International Conference on Databases, Parallel Architectures and Their Applications”, pp. 321–330), that strives to ensure atomicity of transactions without the usage of the 2PC protocol. We reduce the task of ensuring serializability in MDBSs in the presence of failures to solving three independent subproblems, solutions to which together constitute a complete strategy for failure-resilient transaction management in MDBS environments. We develop mechanisms with which each of the three subproblems can be solved without requiring any changes be made to the preexisting software of the local DBMSs and without compromising their autonomy.     

Adaptive Stabilization of a Class of Reaction–Diffusion Systems

This paper is concerned with adaptive stabilization of a class of reaction–diffusion systems governed by a nonlinear partial differential equation of the first order in time but the fourth order in space. In the presence of bounded deterministic disturbances, the adaptive stabilizer is constructed by the concept of high-gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the control system the global asymptotic stability and the convergence of the system state to zero will be guaranteed.