Conditions to ensure the 2-D characteristic polynomial of uncertain matrix is very strict Hurwitz

This article derives some new conditions for the bivariate characteristic
polynomial of an uncertain matrix to be very strict Hurwitz. The uncertainties are assumed of the structured and unstructured type. Using the two-dimensional inverse Laplace transform, we derive the bounds on the uncertainties, which will ensure that the bivariate characteristic polynomial is very strict Hurwitz. Two numerical examples are given to illustrate the results.

Robust strictly positive real synthesis of polynomial segments for discrete time systems

By using the result of robust strictly positive real synthesis of polynomial segments for continuous time systems, it is proved that, for any two n-th order polynomials a(z) and b(z), the Schur stability of their convex combination is necessary and sufficient for the existence of an n-th order polynomial c(z) such that c(z)/a(z) and c(z)/b(z) are both strictly positive real. We also provide the construction method of c(z). Illustrative examples are provided to show the effectiveness of this method.

Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.

Software reliability growth models based on local polynomial modeling with kernel smoothing

Software reliability growth models (SRGMs) are extensively employed in software engineering to assess the reliability of software before their release for operational use. These models are usually parametric functions obtained by statistically fitting parametric curves, using Maximum Likelihood estimation or Least–squared method, to the plots of the cumulative number of failures observed N(t) against a period of systematic testing time t. Since the 1970s, a very large number of SRGMs have been proposed in the reliability and software engineering literature and these are often very complex, reflecting the involved testing regime that often took place during the software development process. In this paper we extend some of our previous work by adopting a nonparametric approach to SRGM modeling based on local polynomial modeling with kernel smoothing. These models require very few assumptions, thereby facilitating the estimation process and also rendering them more relevant under a wide variety of situations. Finally, we provide numerical examples where these models will be evaluated and compared.

A secure search protocol based on Quadratic Residues for EPC Class-1 Gen-2 UHF RFID tags

Radio Frequency Identification (RFID) is a technological revolution that is expected to soon replace barcode systems. One of the important features of an RFID system is its ability to search for a particular tag among a group of tags. This task is quite common where RFID systems play a vital role. To our knowledge not much work has been done in this secure search area of RFID. Also, most of the existing work do not comply with the C1G2 standards. Our work aims to fill that gap by proposing a protocol based on Quadratic Residues property that does not use the expensive hash functions or any complex encryption schemes but achieves total compliance with industry standards while meeting the security requirements.

Secure RFID tag ownership transfer based on quadratic residues

In this paper, we propose a novel approach to secure ownership transfer in RFID systems based on the quadratic residue property. We present two secure ownership transfer schemes-the closed loop and open loop schemes. An important property of our schemes is that ownership transfer is guaranteed to be atomic. Further, both our schemes are suited to the computational constraints of EPC Class-1 Gen-2 passive RFID tags as they only use operations that such passive RFID tags are capable of. We provide a detailed security analysis to show that our schemes achieve strong privacy and satisfy the required security properties of tag anonymity, tag location privacy, forward secrecy, and forward untraceability. We also show that the schemes are resistant to replay (both passive and algebraic), desynchronization, and server impersonation attacks. Performance comparisons demonstrate that our schemes are practical and can be implemented on low-cost passive RFID tags.

Polynomial based key predistribution scheme in wireless mesh networks

Wireless mesh networks (WMNs) have the ability to integrate with other networks while providing a fast and cost-saving deployment. The network security is one of important challenge problems in this kind of networks. This paper is focused on key management between mesh and sensor networks. We propose an efficient key pre-distribution scheme based on two polynomials in wireless mesh networks by employing the nature of heterogeneity. Our scheme realizes the property of bloom filters, i.e., neighbor nodes can discover their shared keys but have no knowledge on the different keys possessed by the other node, without the probability of false positive. The analysis presented in this paper shows that our scheme has the ability to establish three different security level keys and achieves the property of self adaptive security for sensor networks with acceptable computation and communication consumption.

Robust optimal motion cueing algorithm based on the linear quadratic regulator method and a genetic algorithm

The aim of this paper is to design and develop an optimal motion cueing algorithm (MCA) based on the genetic algorithm (GA) that can generate high-fidelity motions within the motion simulator's physical limitations. Both, angular velocity and linear acceleration are adopted as the inputs to the MCA for producing the higher order optimal washout filter. The linear quadratic regulator (LQR) method is used to constrain the human perception error between the real and simulated driving tasks. To develop the optimal MCA, the latest mathematical models of the vestibular system and simulator motion are taken into account. A reference frame with the center of rotation at the driver's head to eliminate false motion cues caused by rotation of the simulator to the translational motion of the driver's head as well as to reduce the workspace displacement is employed. To improve the developed LQR-based optimal MCA, a new strategy based on optimal control theory and the GA is devised. The objective is to reproduce a signal that can follow closely the reference signal and avoid false motion cues by adjusting the parameters from the obtained LQR-based optimal washout filter. This is achieved by taking a series of factors into account, which include the vestibular sensation error between the real and simulated cases, the main dynamic limitations, the human threshold limiter in tilt coordination, the cross correlation coefficient, and the human sensation error fluctuation. It is worth pointing out that other related investigations in the literature normally do not consider the effects of these factors. The proposed optimized MCA based on the GA is implemented using the MATLAB/Simulink software. The results show the effectiveness of the proposed GA-based method in enhancing human sensation, maximizing the reference shape tracking, and reducing the workspace usage.

Primary voltage control of a single-phase inverter using linear quadratic regulator with integrator

This paper proposes a linear quadratic regulator with integral action, ensuring fast dynamic response and resisting capability of voltage deviation from instantaneous reference grid voltage, to control the inverter voltage that can also be used in a microgrid. The proposed control strategy is based on a linear quadratic regulator, minimizing the cost function of the system, with integral action used to impede voltage degradation from a reference voltage for outside disturbances of the system, such as abrupt load change. The combined integral term assists to recover the voltage difference between grid and reference grid voltage. The validity of the proposed controller has been tested with linear and non-linear loads under various conditions. In both cases, the effectiveness of the controller has been proved. The result of the proposed controller is good to track the instantaneous reference grid voltage.

Switch point finding using polynomial regression for fuzzy type reduction algorithms

Karnik-Mendel (KM) algorithm is the most widely used type reduction (TR) method in literature for the design of interval type-2 fuzzy logic systems (IT2FLS). Its iterative nature for finding left and right switch points is its Achilles heel. Despite a decade of research, none of the alternative TR methods offer uncertainty measures equivalent to KM algorithm. This paper takes a data-driven approach to tackle the computational burden of this algorithm while keeping its key features. We propose a regression method to approximate left and right switch points found by KM algorithm. Approximator only uses the firing intervals, rnles centroids, and FLS strnctural features as inputs. Once training is done, it can precisely approximate the left and right switch points through basic vector multiplications. Comprehensive simulation results demonstrate that the approximation accuracy for a wide variety of FLSs is 100%. Flexibility, ease of implementation, and speed are other features of the proposed method.