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The problem of approximating rational curves by polynomial curves is studied in this paper. A simple method of approximation, which uses the control points of the degree-elevated curve to approximate the original rational curve, is introduced at first. Meanwhile as to achieve better efficiency, the idea of re-parameterization of rational Bezier curves is presented. The re-parameterization makes uniform...
Reversible circuits are quite attractive because of the possibility of nearly energy-free computation. During designing and constructing a reversible circuit, it is important to test the circuit and detect faults in the circuit. However, very few algorithms are known to generate a complete test set for a given reversible circuit. In this paper, first of all, it is NP-hard to generate a minimum complete...
QoS routing and multipath routing have been receiving much attention respectively in network communication. However, the research combining those two kinds of routing is rare. This paper integrated the ideas of QoS and multipath, and presented the problem of shortest pair of disjoint paths with bandwidth guaranteed. we proved it to be NP-complete, and then proposed a heuristic algorithm. The analysis...
Multipath Routing plays an important role in communication networks. Multiple disjoint paths can increase the effective bandwidth between pairs of vertices, avoid congestion in a network and reduce the probability of dropped packets. In this paper, we built mathematical models for arc-disjoint paths problem and vertex-disjoint paths problem respectively, and then proposed polynomial algorithms for...
Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing...
Families of differential operators, like those defining affine, generally nonlinear, control systems are known to have natural Hopf algebra structures. These provide deeper insight into relationships and properties of such objects as the Chen-Fliess series and state space realizations of systems defined by input-output operators. A starting point for this work are representations of control objects...
The present work deals with a dynamical system of the form A?? = [[N, AT+A], A]+??[[AT, A], A], where A?? is an n??n real matrix, N is constant n??n real matrix, [A, B] = AB-BA, and ?? is a positive constant. In particular, the purpose of this work is to establish structure preserving properties of this dynamical system for tridiagonal, Hessenberg, and Hamiltonian matrices in combination with potential...
This paper studies the global regulation problem for a class of nonlinear polynomial systems subject to both dynamic uncertainty and static uncertainty. The dynamic uncertainty does not vanish at the origin of the state space and thus is not input-to-state stable (ISS). As a result, the small gain theory based robust control technique alone cannot handle this problem. We manage to integrate both robust...
This paper considers the max-min quantum error recovery problem; the recovery channel to be designed maximizes the fidelity between input and output states of a given noisy channel, while the minimum is taken over all possible pure input states. In general, this kind of max-min problem is cast as a non-convex optimization problem and is thus very hard to solve even with the aid of high-quality computational...
In this paper we review algorithms for checking diagnosability of discrete-event systems and timed automata. We point out that the diagnosability problems in both cases reduce to the emptiness problem for (timed) Bu??chi automata. Moreover, it is known that, checking whether a discrete-event system is diagnosable, can also be reduced to checking bounded diagnosability. We establish a similar result...
In this note, firstly a modified numerical differentiation scheme is presented. The obtained scheme is rooted, and uses the same algebraic approach based on operational calculus. Secondly an analysis of the error due to a corrupting noise in this estimation is conducted and some upper-bounds are given on this error. Lastly a convincing simulation example gives an estimation of the state variable of...
To observe occurrences of an event in a discrete event system, a sensor must be placed and activated. Both placement and activation incur costs. Assuming sensors have been placed, to minimize costs, one would like to minimize the activation of the sensors. In this paper, an online algorithm is developed to minimize sensor activation. The discrete event system under consideration is modeled by a finite...
This article presents an instrumental variable method dedicated to non-linear Hammerstein systems operating in closed loop. The linear process is a Box-Jenkins model and the non-linear part is a sum of known basis functions. The performance of the proposed algorithm is illustrated by a numerical example.
Let the observed sequence {yk} be generated by the multivariate ARMAX system A(z)yk = B(z)uk-1 + C(z)wk, where {wk} is the system noise with unknown covariance matrix Rw > 0, and {uk} is a sequence of mutually independent and identically distributed (iid) random vectors. Based on {yk} and {uk}, identification algorithms are proposed to simultaneously estimate the orders (p,q,r), the covariance...
The nonlinear filtering problem is considered for the time homogeneous diffusion model with correlated noise. A numerical approach is proposed for computing approximations of the unnormalized filtering density (UFD) and the nonlinear filtering. This approach is based on the Wiener chaos expansion (WCE) of the solution of Zakai equation. A Sparse truncation method of WCE is introduced to simplify calculation,...
This paper deals with autoregressive models of singular spectra. The starting point is the assumption that there is available a transfer function matrix W(q) expressible in the form D-1(q)B for some tall constant matrix B of full column rank and with the determinantal zeros of D(q) all stable. It is shown that, even if this matrix fraction representation of W(q) is not coprime, W(q) has a coprime...
While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are...
In this work we focus on iterative learning control (ILC) design for tracking iteration-varying reference trajectories that are generated by high-order internal models (HOIM). An HOIM can be formulated as a polynomial operator between consecutive iterations to describe the changes of desired trajectories in the iteration domain. The classical ILC for tracking iteration-invariant reference trajectories,...
A novel method is proposed for the digital redesign of analogue controllers with account for the closed-loop system performance in continuous time. The method, which is based on a two-level optimization algorithm, makes it possible to place the closed-loop poles inside a specified region of the complex plane and provides for reduced-order controllers. The effectiveness of the proposed technique is...
This paper is concerned with explicit descriptions of the optimal closed-loop system for H2 control problems in the case of single-input and single-output linear systems. We focus on two typical H2 optimal control problems, the minimal energy problem and optimal tracking control problem, and show that the transfer functions of the optimal closed-loop systems can be described in specific terms of the...
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