Nonlinear control of the Reaction Wheel Pendulum

In this paper we introduce the Reaction Wheel Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating bob. This system has several attractive features both from a pedagogical standpoint and from a research standpoint. From a pedagogical standpoint, the dynamics are the simplest among the various pendulum experiments available so that the system can be introduced to students earlier in their education. At the same time, the system is nonlinear and underactuated so that it can be used as a benchmark experiment to study recent advanced methodologies in nonlinear control, such as feedback linearization, passivity methods, backstepping and hybrid control. In this paper we discuss two control approaches for the problems of swingup and balance, namely, feedback linearization and passivity based control. We first show that the system is locally feedback linearizable by a local diffeomorphism in state space and nonlinear feedback. We compare the feedback linearization control with a linear pole-placement control for the problem of balancing the pendulum about the inverted position. For the swingup problem we discuss an energy approach based on collocated partial feedback linearization, and passivity of the resulting zero dynamics. A hybrid/switching control strategy is used to switch between the swingup and the balance control. Experimental results are presented.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Encyclopedia contributions: entries A-B

Sections contributed by Jean Sim Agricultural Colleges; p.12 Anzac Park, Townsvile; p.22 Anzac Square, Brisbane; pp.22-23 Benson, Albert Herbert; p.86 Bick, Edward Walter; p.88 Bougainvillea Gardens; p.101 Bowen Park; pp.101-102 Boyd, A.J.; p.103 Brisbane Botanic Gardens; pp.104-105 Bush-house; pp.119-121

Encyclopedia contributions: entries C-G in Oxford Companion to Australian Gardens

Caulfield, Harold William; p.131 Cowan, Alexander; p.164 Cowley, Ebenezer; p.164 East Talgai Station; p.193 Eaves, S.H.; p.193-194 Edgar, J.S.; p.196 Everist, Selwyn; p.206 Experimental Farms and Gardens; pp.207-208 Government Houses - Queensland; pp.267-268

Encyclopedia contributions: Entries H-M in Oxford Companion to Australian Gardens

The Oxford Companion to Australian Gardens is the first comprehensive reference book to cover all aspects of Australian gardens, and the history of gardening and garden design in Australia. The book is comprised of over 400 thematic, bibliographic and place based entries, and is extensively illustrated and cross referenced to ensure ease of use and thorough coverage of the field. The Companion contributes to the understanding of gardens and gardening by including entries on designed landscapes, agriculture, architecture, art, botany, ecology, forestry, horticulture, landscape architecture, town planning and viticulture and will become the standard reference on the subject. Herbert,

Intrinsically photosensitive melanopsin retinal ganglion cell contributions to the pupillary light reflex and circadian rhythm

Recently discovered intrinsically photosensitive melanopsin retinal ganglion cells contribute to the maintenance of pupil diameter, recovery and post-illumination components of the pupillary light reflex and provide the primary environmental light input to the suprachiasmatic nucleus for photoentrainment of the circadian rhythm. This review summarises recent progress in understanding intrinsically photosensitive ganglion cell histology and physiological properties in the context of their contribution to the pupillary and circadian functions and introduces a clinical framework for using the pupillary light reflex to evaluate inner retinal (intrinsically photosensitive melanopsin ganglion cell) and outer retinal (rod and cone photoreceptor) function in the detection of retinal eye disease.

Encyclopedia contributions: entries N-R in Oxford Companion to Australian

New Farm Park; p.436 Oakman, H.O. (with Jan Seto); p.449 Paranella, Jose; p.463 Perrott family; p.469 Pink, James; p.475 Queensland; pp.495-497 The Queenslander; pp.497-498 The Queensland Horticulturist; p.498 Rawson, Mina; p.502 Rockhampton Botanic Gardens; p.572