Model-predictive control and closed-loop stability considerations for nonlinear plants described by local ARX-type models

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

Overview of complex systems in sport

The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena. The emphasis on the environment-system relationship, the applications of complexity principles, and the use of nonlinear dynamics mathematical tools propose a deep change in sport science. Coordination dynamics, ecological dynamics, and network approaches have been successfully applied to the study of different sport-related behaviors, from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics. Sport benefit from the use of such approaches in the understanding of technical, tactical, or physical conditioning aspects which change their meaning and dilute their frontiers. The creation of new learning and training strategies for teams and individual athletes is a main practical consequence. Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports. Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Functional encryption for threshold functions (or fuzzy IBE) from lattices

Cryptosystems based on the hardness of lattice problems have recently acquired much importance due to their average-case to worst-case equivalence, their conjectured resistance to quantum cryptanalysis, their ease of implementation and increasing practicality, and, lately, their promising potential as a platform for constructing advanced functionalities. In this work, we construct “Fuzzy” Identity Based Encryption from the hardness of the Learning With Errors (LWE) problem. We note that for our parameters, the underlying lattice problems (such as gapSVP or SIVP) are assumed to be hard to approximate within supexponential factors for adversaries running in subexponential time. We give CPA and CCA secure variants of our construction, for small and large universes of attributes. All our constructions are secure against selective-identity attacks in the standard model. Our construction is made possible by observing certain special properties that secret sharing schemes need to satisfy in order to be useful for Fuzzy IBE. We also discuss some obstacles towards realizing lattice-based attribute-based encryption (ABE).

A Lagrangian approach to nonlinear modeling of anti-roll tanks

This paper presents two novel nonlinear models of u-shaped anti-roll tanks for ships, and their linearizations. In addition, a third simplified nonlinear model is presented. The models are derived using Lagrangian mechanics. This formulation not only simplifies the modeling process, but also allows one to obtain models that satisfy energy-related physical properties. The proposed nonlinear models and their linearizations are validated using model-scale experimental data. Unlike other models in the literature, the nonlinear models in this paper are valid for large roll amplitudes. Even at moderate roll angles, the nonlinear models have three orders of magnitude lower mean square error relative to experimental data than the linear models.

Nonlinear container ship model for the study of parametric roll resonance

Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to +-40 degrees, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head seas. A Matlab/Simulink parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007). The benchmark implements a 3rd-order nonlinear model where the dynamics of roll is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic results which are in good agreement with the model tank experiments.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Energy-based nonlinear control of ship roll gyro-stabiliser with precession angle constraints

In this paper, we consider a passivity-based approach for the design of a control law of multiple ship-roll gyro-stabiliser units. We extend previous work on control of ship roll gyro-stabilisation by considering the problem within a nonlinear framework. In particular, we derive an energy-based model using the port-Hamiltonian theory and then design an active precession controller using passivity-based control interconnection and damping assignment. The design considers the possibility of having multiple gyro-stabiliser units, and the desired potential energy of the system (in closed loop) is chosen to behave like a barrier function, which allows us to enforce constraints on the precession angle of the gyros.

A nonlinear observer for estimating transverse stability parameters of marine surface vessels

This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel's centre of gravity due to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves -- propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion leading to dangerous resonance. Therefore, it is of interest to estimate and detect such changes.

Parameter estimation of thrust models of uninhabited airborne systems

This paper presents a method for the estimation of thrust model parameters of uninhabited airborne systems using specific flight tests. Particular tests are proposed to simplify the estimation. The proposed estimation method is based on three steps. The first step uses a regression model in which the thrust is assumed constant. This allows us to obtain biased initial estimates of the aerodynamic coeficients of the surge model. In the second step, a robust nonlinear state estimator is implemented using the initial parameter estimates, and the model is augmented by considering the thrust as random walk. In the third step, the estimate of the thrust obtained by the observer is used to fit a polynomial model in terms of the propeller advanced ratio. We consider a numerical example based on Monte-Carlo simulations to quantify the sampling properties of the proposed estimator given realistic flight conditions.

Damping structure selection in nonlinear ship manoeuvring models

This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data.

Assessing the threshold temperatures among different age and cause-of-deaths

The relationship between temperature and mortality is non-linear and the effect estimates depend on the threshold temperatures selected. However, little is known about whether threshold temperatures differ with age or cause of deaths in the Southern Hemisphere. We conducted polynomial distributed lag non-linear models to assess the threshold temperatures for mortality from all ages (Dall), aged from 15 to 64 (D15-64), 65- 84(D65-84), ≥85 years (D85+), respiratory (RD) and cardiovascular diseases (CVD) in Brisbane, Australia, 1996–2004. We examined both hot and cold thresholds, and the lags of up to 15 days for cold effects and 3 days for hot effects. Results show that for the current day, the cold threshold was 20°C and the hot threshold was 28°C for the groups of Dall, D15-64 and D85+. The cold threshold was higher (23°C) for the group of D65-84 and lower (21°C) for the group of CVD. The hot threshold was higher (29°C) for the group of D65-84 and lower (27°C) for the group of RD. Compared to the current day, for the cold effects of up to 15-day lags, the threshold was lower for the group of D15-64, and the thresholds were higher for the groups of D65-84, D85+, RD and CVD; while for the hot effects of 3-day lags, the threshold was higher for the group of D15-64 and the thresholds were lower for the groups of D65-84 and RD. Temperature thresholds appeared to differ with age and death categories. The elderly and deaths from RD and CVD were more sensitive to temperature stress than the adult group. These findings may have implications in the assessment of temperature-related mortality and development of weather/health warning systems.

Democratic systems

Digital signature is a breakthrough of modern cryptographic systems. A (t, n) threshold digital signature allows every set of cardinality t or more (out-of n) co-signers to authenticate a message. In almost all existing threshold digital signatures the threshold parameter t is fixed. There are applications, however, in which the threshold parameter needs to be changed from time to time. This paper considers such a scenario, in order to discuss relevant problems, and proposes a model that solves the related problems.

Ideal threshold schemes from orthogonal arrays

The work investigates the design of ideal threshold secret sharing in the context of cheating prevention. We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme. To prevent cheating, defining matrices should be nonlinear so both the cheaters and honest participants have the same chance of guessing of the valid secret. The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.

An ideal and robust threshold RSA

We present a novel implementation of the threshold RSA. Our solution is conceptually simple, and leads to an easy design of the system. The signing key is shared in additive form, which is desirable for collaboratively performing cryptographic transformations, and its size, at all times, is logn, where n is the RSA modulus. That is, the system is ideal.