A remark on the converging-input converging-state property

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This "well-known" but hard-to-cite fact is proved and slightly generalized here.     

L/sup p/ approximation of Sigma-Pi neural networks

A feedforward Sigma-Pi neural network with a single hidden layer of m neurons is given by /sup m//spl Sigma//sub j=1/c/sub j/g(n/spl Pi//sub k=1/x/sub k/-/spl theta//sub k//sup j///spl lambda//sub k//sup j/) where c/sub j/, /spl theta//sub k//sup j/, /spl lambda//sub k//spl isin/R. We investigate the approximation of arbitrary functions f: R/sup n//spl rarr/R by a Sigma-Pi neural network in the L/sup p/ norm. An L/sup p/ locally integrable function g(t) can approximate any given function, if and only if g(t) can not be written in the form /spl Sigma//sub j=1//sup n//spl Sigma//sub k=0//sup m//spl alpha//sub jk/(ln|t|)/sup j-1/t/sub k/.     

Remarks on -input bounded-state stability of linear controllable infinite-dimensional systems

It is shown that every eP-input bounded-state stable linear (infinite-dimensional) system x_k+1=A_kx_k+B_ku_k is uniformly power equistable, if it is uniformly equicontrollable.     

Remarks on strong stabilization and stable H/sup /spl infin// controller design

A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H/sup /spl infin// controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).     

On the dead-time compensation from L/sup 1/ perspectives

It is known that both H/sup 2/ and H/sup /spl infin// optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L/sup 1/ control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L/sup 1/ problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor.     

Remarks on stability of solutions of the property domination problem

A class of combinatorial problems is considered whose investigation and solution require the notions of the theory of fuzzy sets. The necessary and sufficient conditions of stability are given. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 36–40, July–August, 1999.     

Inducing NNC-trees with the R/sup 4/-rule

An NNC-Tree is a decision tree (DT) with each nonterminal node containing a nearest neighbor classifier (NNC). Compared with the conventional axis-parallel DTs (APDTs), the NNC-Trees can be more efficient, because the decision boundary made by an NNC is more complex than an axis-parallel hyperplane. Compared with single-layer NNCs, the NNC-Trees can classify given data in a hierarchical structure that is often useful for many applications. This paper proposes an algorithm for inducing NNC-Trees based on the R/sup 4/-rule, which was proposed by the author for finding the smallest nearest neighbor based multilayer perceptrons (NN-MLPs). There are mainly two contributions here. 1) A heuristic but effective method is given to define the teacher signals (group labels) for the data assigned to each nonterminal node. 2) The R/sup 4/-rule is modified so that an NNC with proper size can be designed automatically in each nonterminal node. Experiments with several public databases show that the proposed algorithm can produce NNC-Trees effectively and efficiently.     

QSNET/sup II/: defining high-performance network design

QSNET/sup II/ optimizes interprocessor communication in systems built from standard server building blocks. Its short-message processing unit permits fast injection of small messages, providing ultra-low latency and scalability to thousands of nodes. Thus, in a sense, the high-performance network in a cluster computer is the computer because it largely defines achievable performance, widening the range of the applications a cluster can efficiently execute, as well as defining its scalability, fault tolerance, system software, and overall usability.     

Remarks on commutative n-rational series

Commutative N-rational formal power series are considered. Series giving polynomial functions as their coefficients are characterized, and a monotonicity result for commutative series is proved. As an application the division problem for N-rational formal power series is solved.     

Some constructions of the join of fuzzy subgroups and certain lattices of fuzzy subgroups with sup property

In this paper, some new lattices of fuzzy substructures are constructed. For a given fuzzy set μ in a group G, a fuzzy subgroup S(μ) generated by μ is defined which helps to establish that the set L_s of all fuzzy subgroups with sup property constitutes a lattice. Consequently, many other sublattices of the lattice L of all fuzzy subgroups of G like , etc. are also obtained. The notion of infimum is used to construct a fuzzy subgroup i(μ) generated by a given fuzzy set μ, in contrast to the usual practice of using supremum. In the process a new fuzzy subgroup i(μ)^∗ is defined which we shall call a shadow fuzzy subgroup of μ. It is established that if μ has inf property, then i(μ)^∗ also has this property.     

Reduced-order solutions for the singular H/sup /spl infin// filtering problem

We consider the filtering H/sup /spl infin// problem for linear time-varying systems. This problem has been already solved in the case when the direct feedthrough matrix F between the disturbance and the output vectors is full-row rank. Here, we consider the case when the problem is singular, that is when this feedthrough matrix is not full-row rank. We show that in this case a reduced-order observer can be designed to meet the desired performance. Moreover, we apply the obtained results to solve a particular H/sup /spl infin// singular output feedback problem.     

C/sup */-algebra of strong limit power functions

Motivated by problems in robust control of power signal set H/sub 2/ (e.g,, H/sub 2/ is not a vector space, Fourier analysis cannot be carried out on H/sub 2/ in general), we study those functions in H/sub 2/ which we call strong limit power. We show that the set of all such functions is a sufficiently large C/sup */-algebra. Fourier Analysis is carried out on the functions. In particular, the uniqueness of the Fourier expansion of a strong limit power function is established. Finally we point out how to analyze and reconstruct such functions.     

Remarks on the Dyer-Saaty controversy

Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 97–102, January–February, 1994.     

Design of stable controllers attaining low H/sup infinity / weighted sensitivity

Strong stabilization and sensitivity reduction for a linear time-invariant single-input single-output system are considered. Stable controllers are practically desirable in the presence of possible actuator or sensor failures. It is verified precisely that the optimal controller of H/sup infinity / weighted sensitivity minimization is almost always unstable when the plant has more than two zeros in the right-half plane. An algorithm for attaining the low sensitivity property for stable controllers is presented. It is based on Nevanlinna-Pick interpolation.<>     

E-service design using i* and e/sup 3/ value modeling

Two requirements engineering techniques, i* and e/sup 3/ value, work together to explore commercial e-services from a strategic-goal and profitability perspective. We demonstrate our approach using a case study on Internet radio.     

Global stabilization of cascade systems by C/sup 0/ partial-state feedback

This paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization, and the notion and properties of the input-to-state stability Lyapunov function can be effectively coupled, resulting in globally stabilizing C/sup 0/ partial-state feedback controllers for a class of cascade systems which may not be smoothly stabilizable, even locally.     

Remarks on the time-varying H∞ Riccati equations

In this paper we establish some useful properties of three Riccati equations appearing in the standard H_∞-control problems for continuous and discrete-time time-varying systems. We then give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent Riccati equations with a coupling inequality.     

A characterization of convex problems in decentralized Control/sup */

We consider the problem of constructing optimal decentralized controllers. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. We define the notion of quadratic invariance of a constraint set with respect to a system, and show that if the constraint set has this property, then the constrained minimum-norm problem may be solved via convex programming. We also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. These results are developed in a very general framework, and are shown to hold in both continuous and discrete time, for both stable and unstable systems, and for any norm. This notion unifies many previous results identifying specific tractable decentralized control problems, and delineates the largest known class of convex problems in decentralized control. As an example, we show that optimal stabilizing controllers may be efficiently computed in the case where distributed controllers can communicate faster than their dynamics propagate. We also show that symmetric synthesis is included in this classification, and provide a test for sparsity constraints to be quadratically invariant, and thus amenable to convex synthesis.     

Remarks on the makespan minimization problem

In this brief article we consider the worst-case performance of a heuristic proposed for the problem of minimizing the overall completion time in scheduling a collection of independent tasks to a system of identical processors. It has been suggested that this heuristic, based on the familiar LPTrule, possesses a vastly improved worst-case behavior. We demonstrate that it instead shares LPT's asymptotic worst-case performance bound of 4/3.