Balancing transformations for unstable nonminimal linear systems

It is shown that an unstable nonminimal continuous (discrete) realization (A, B, C) can be transformed via a similarity transformation into a balanced one if and only if the product of the controllability, observability Gramians is similar to a real diagonal matrix Λ. If, in addition, the eigenvalues of A , say λ, satisfy the relation λ_i+λ _j≠0(λ_iλ_j≠1) then the matrix Λ will always be positive semidefinite, and a balanced realization with its minimal part in the internally balanced form can always be obtained     

The design of a precompensator for multivariable adaptive control-anetwork-theoretic approach

A network-theoretic approach to the design of a dynamic precompensator C(s) for a multiinput, multioutput plant T(s) is considered. The design is based on the relative degree of each element of T(s). Specifically, an efficient algorithm is presented for determining whether a given plant T(s) has a diagonal precompensator C( s) such that, for almost all cases, T(s)C (s) has a diagonal interactor. The algorithm also finds any optimal precompensator, in the sense that the total relative degree is minimal. The algorithm can be easily modified to work even when a T(s) represented by a nonsquare matrix is given     

A parallel algorithm for 2-D DFT computation with no interprocessorcommunication

A parallel algorithm is proposed for the two-dimensional discrete Fourier transform (2-D DFT) computation which eliminates interprocessor communications and uses only O(N) processors. The mapping of the algorithm onto architectures with broadcast and report capabilities is discussed. Expressions are obtained for estimating the speed performance on these machines as a function of the size N×N of the 2-D DFT, the bandwidth of the communications channel, the time for an addition, the time T( F_N) for a single processing element to perform an N-point DFT, and the degree of parallelism. For single I/O channel machines that are capable of exploiting the full degree of parallelism of the algorithm, attainable execution times are as low as the time T(F_N) plus the I/O time for data upload and download. An implementation on a binary tree computer is discussed     

Comments on `Conditions for stable zeros of sampled systems' by M.Ishitobi

The commenter argues that the result of the above-titled work (see ibid., vol.37, no.10, p.1558-1561, Oct. 1992) is incorrect. It is pointed out that when sampling a continuous-time system G(s ) using zero-order hold, the zeros of the resulting discrete-time system H(z) become complicated functions of the sampling interval T. The system G(s) has unstable continuous-time zeros, s=0.1±i. The zeros of the corresponding sampled system start for small T from a double zero at z=1 as exp(T(0.1±i )), i.e., on the unstable side. For T>1.067 . . . the zeros become stable. The criterion function of the above-titled work, F(T)=G*(jω_s/2)= H(-1)T/2, is, however, positive for all T, indicating only stable zeros. The zero-locus crosses the unit circle at complex values     

Properties of optimal hop-by-hop allocation policies in networkswith multiple transmitters and linear equal holding costs

Flow control between one receiving node and its adjacent transmitting nodes in a computer network is modeled as a Markov decision problem. By deriving several qualitative properties of an optimal allocation policy, it is shown that finding dynamic optimal allocations for only T states suffices to completely describe an optimal allocation policy. When the number of transmitters M=2, for all but one of the T states there are only two allocations that are candidates for optimality. It is desirable to extend this property to M>2. However, it appears that the technique used for M =2 does not generalize to M>2     

Phase identification in linear time-periodic systems

An identification procedures is developed for a (T=2π)-periodic linear observed system. Cases where C (a real matrix) is diagonizable and not diagonizable are considered     

Some new properties of the structured singular value

J.C. Doyle et al. (1982) have shown that a necessary and sufficient condition for robust stability or robust performance in the H^∞-frame work may be formulated as a bound on the structured singular value (μ) of a specific matrix M which includes information on the system model, the controller, the model uncertainty, and the performance specifications. Often it is desirable to express the robust stability and performance conditions as norm bounds on transfer matrices (T) which are of direct interest to the engineer, e.g. sensitivity or complementary sensitivity. The present paper shows how to derive bounds on σ(T) from bounds on μ(M)     

Linear periodic systems: eigenvalue assignment using discreteperiodic feedback

The eigenvalue assignment problem of a T-periodic linear system using discrete periodic state feedback gains is discussed. For controllable systems, an explicit formula for the feedback law is given that can be used for the arbitrary assignment of the eigenvalues of Φ_c1(T,0), the closed-loop state transition matrix from 0 to T. For the special case of periodic systems controllable over one period, this control law can be used to obtain any desired Φ_c1(T,0)     

An H∞ approach to feedback design withtwo objective functions

The problem of tightly bounding and shaping the frequency responses of two objective functions T_i(s)( i=1,2) associated with a closed-loop system is considered. It is proposed that an effective way of doing this is to minimize (or bound) the function max {∥T₁(s)∥ _∞, ∥T₂(s)∥_∞} subject to internal stability of the closed-loop system. The problem is formulated as an H^∞ control problem, and an iterative solution is given     

A simulation-based estimator for hidden Markov random fields

An estimator for estimating the parameters of a Markov random field X from inaccurate observations is introduced. The author considers first a Markov (Gibbs) random field X={X_i,j} on a lattice L={(i ,j): i=1,2,. . .,n; j=1,2,. . .,m}. The marginal distributions of (X_i,j, X_i+u,j+v) (u,v=-1,0,1) are first estimated from an image. Then, random fields X* are simulated with the probability of X*_i+u,j+v)=b nearly equal to the estimate of P{X_i,j=X _i+u,=b}. A simulation method similar to the Gibbs sampler is used. The parameters of the Markov random field model are estimated from the X*'s with the pseudolikelihood method     

Efficient routing schemes for multiple broadcasts in hypercubes

The authors analyze the problem in which each node of the binary hypercube independently generates packets according to a Poisson process with rate λ; each of the packets is to be broadcast to all other nodes. Assuming unit packet length and no other communications taking place, it is observed that the system can be stable in steady-state only if the load factor ρ≡λ (2^d-1)/d satisfies ρ<1 where d is the dimensionality (diameter) of the hypercube. Moreover, the authors establish some lower bounds for the steady-state average delay D per packet and devise and analyze two distributed routing schemes that are efficient in the sense that stability is maintained for all ρ<ρ* where ρ* does not depend on the dimensionality d of the network, while the average delay D per packet satisfies D⩽Kd(1+ρ) for small values of ρ (with constant K). The performance evaluation is rigorous for one scheme, while for the other the authors resort to approximations and simulations     

Explicit expressions for cascade factorization of generalnonminimum phase systems

Explicit expressions for two different cascade factorizations of any detectable left invertible nonminimum phase systems are given. The first one is a well known minimum phase/all-pass factorization by which all nonminimum phase zeros of a transfer function G(s) are collected into an all-pass factor V(s), and G (s) is written G_m(s)V$ where G_ms is considered as a minimum phase image of G(s). The second one is a new cascade factorization by which G(s) is rewritten as G_M( s)U(s) where U(s) collects all `awkward' zeros including all nonminimum phase zeros of G( s). Both G_m(s) and G_M(s) retain the given infinite zero structure of G(s). Further properties of G _m(s), G_M(s), and U (s) are discussed. These factorizations are useful in several applications including loop transfer recovery     

Performance of shared memory in a parallel computer

A method for analyzing the lengths of memory queues when the network is conflict-free is described. An algorithm based on this method is shown to efficiently determine the upper and lower bounds of the queue length. Analysis indicates that the strategy of using hashing to spread data across memory modules is a good one. Results show that if the size of the system is increased while maintaining a constant ratio of numbers of processors to memories, then, asymptotically, the slowdown in performance from conflicts at the memory modules is Θ(log m /log log m). For m and n less than 100000 and λ between 0.25 and 4.0, the graphical data confirm this growth rate     

CAREL: computer aided reliability evaluator for distributedcomputing networks

An efficient method to compute the terminal reliability (the probability of communication between a pair of nodes) of a distributed computing system (DCS) is presented. It is assumed that the graph model G(V,E) for DCS is given and that the path and/or cut information for the network G(V,E) is available. Boolean algebraic concepts are used to define four operators: compare, reduce, combine, and generate. The proposed method, called CAREL, uses the four operators to generate exclusive and mutually disjoint events. CAREL has been implemented using bit vector representation on an Encore MULTIMAX 320 system. It is shown that CAREL solves large DCS networks (having a pathset on the order of 780 and a cutset on the order of 7300 or more) with a reasonable memory requirement. A comparison with other algorithms reveals the computational efficiency of the method. The proof of correctness of CAREL is included     

Least-squares output estimation with multirate sampling

A least-squares output estimation algorithm is presented for applications where the output is sampled at a slower rate than the input. Given the sequence {u(kT), y(kJT )k=1,2,...}, where J is a positive integer and T is the basic sampling period, it is proven that the output estimation error converges to zero for instants at or between the output measurement instants. The assumptions required are essentially the same as for the case with equal sampling rates, i.e., for J=1. Simulation examples show excellent output estimation, based on measured y(kJT) with J=8     

Approximation of infinite-dimensional systems

A Fourier series-based method for approximation of stable infinite-dimensional linear time-invariant system models is discussed. The basic idea is to compute the Fourier series coefficients of the associated transfer function T_d(Z) and then take a high-order partial sum. Two results on H^∞ convergence and associated error bounds of the partial sum approximation are established. It is shown that the Fourier coefficients can be replaced by the discrete Fourier transform coefficients while maintaining H^∞ convergence. Thus, a fast Fourier transform algorithm can be used to compute the high-order approximation. This high-order finite-dimensional approximation can then be reduced using balanced truncation or optimal Hankel approximation leading to the final finite-dimensional approximation to the original infinite-dimensional model. This model has been tested on several transfer functions of the time-delay type with promising results     

A VLSI constant geometry architecture for the fast Hartley andFourier transforms

An application-specific architecture for the parallel calculation of the decimation in time and radix 2 fast Hartley (FHT) and Fourier (FFT) transforms is presented. A real sequence with N=2ⁿ data items is considered as input. The system calculates the FHT and the FFT in n and n+1 stages. respectively. The modular and regular parallel architecture is based on a constant geometry algorithm using butterflies of four data items and the perfect unshuffle permutation. With this permutation, the mapping of the algorithm in VLSI technology is simplified and the communications among processors are minimized. Organization of the processor memory based on first-in, first-out (FIFO) queues facilitates a systolic data flow and permits the implementation in a direct way of the complex data movements and address sequences of the transforms. This is accomplished by means of simple multiplexing operations, using hardwired control. The total calculation time is (Nlog₂N)/4Q cycles for the FHT and N(1+log₂N)/4Q cycles for the FFT, where Q is the number of processors ( Q= 2^q, Q⩽N/4)     

Distributed detection with consulting sensors and communicationcost

The problem of distributed detection with consulting sensors in the presence of communication cost associated with any exchange of information (consultation) between sensors is considered. The system considered has two sensors, S1 and S2; S1 is the primary sensor responsible for the final decision u₀ , and S2 is a consulting sensor capable of relaying its decision u₂ to S1 when requested by S 1. The final decision u₀ is either based on the raw data available to S1 only, or, under certain request conditions, also takes into account the decision u₂ of sensor S2. Random and nonrandom request schemes are analyzed and numerical results are presented and compared for Gaussian and slow-fading Rayleigh channels. For each decision-making scheme, an associated optimization problem is formulated whose solution is shown to satisfy certain set design criteria that the authors consider essential for sensor fusion     

Adaptive structuring of binary search trees using conditionalrotations

Consider a set A={A₁,A₂ ,. . ., A_n} of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S=[s₁,s₂ ,. . ., s_N] and are to be arranged lexicographically using a binary search tree (BST). If S is known a priori, it is well known that an optimal BST may be constructed using A and S. The case when S is not known a priori is considered. A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme, the restructuring is performed only if it decreases the weighted path length (WPL) of the overall resultant tree. An optimized version of the latter method, which requires only one extra integer field per record has, is presented. Initial simulation results comparing this algorithm with various other static and dynamic schemes indicates that this scheme asymptotically produces trees which are an order of magnitude closer to the optimal one than those produced by many of the other BST schemes reported in the literature     

A study of associative evidential reasoning

Associative evidential reasoning is the mechanism of combining evidence and evaluating hypotheses, which is the core of many computational systems. It is shown that under the generalized symmetry condition, that is, f(a,b)=neg (f(neg(a), neg(b))), where f is the combination operator satisfying common requirements like associativity and monotonicity, and neg maps positive elements to negative ones and vice versa, f is uniquely determined by a one-place mapping from the positive region to the set of positive reals. Furthermore, such combination formulas cannot be made robust, and quantizing the region will cause the loss of associativity or other inconsistencies. The implications on evidential reasoning system are: there exists often only one kind of formula for combining evidence; the quest for robust combination is often infeasible; and the attempt of converting numerical degrees of belief to linguistic quantifiers and vice versa is destined to be fruitless