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Event-triggered systems sample and transmit data when a state dependent criterion is violated. Many event-triggered systems are efficiently attentive, i.e., longer inter-sampling intervals are achieved as the system gets closer to its equilibrium. This property allows event-triggered systems to use fewer communication resources since control systems are usually operated around their equilibria. Efficient attentiveness, however, is not a necessary property of all event-triggered systems. To ensure efficient attentiveness, this technical note proposes an approach to design event triggers and quantization maps for nonlinear systems with transmission delays. We present sufficient conditions to guarantee input-to-state stability (ISS) of the resulting systems without exhibiting Zeno behavior. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to provide a complete and chronological view of the evolution of the main acceptance and use of technology models, from the 1970s to the present day. Design/methodology/approach – A comparison of partial least squares (linear model) and WarpPLS (non-linear model) has been run for each acceptation of technology model: TRA, TAM0, TAM1, TAM2, TAM3, UTAUT, UTAUT2. The data set collects the information of mobile internet users. Findings – The authors have concluded that UTAUT2 model obtains a better explanation power than the rest of technology acceptance models (TAMs) in the sample of mobile internet users. Furthermore, all models have a better explanation power using non-linear relationships than the traditional linear approach. Originality/value – The vast majority of research published to date with regard to the Theory of Reasoned Action (TRA), the Technology Acceptance Model (TAM), and the Unified Theory of Acceptance and Use of Technology (UTAUT) are based on structural equation models assuming linear relationships between variables. The originality of this study is that it incorporates non-linear relationships and compares the same models using both approaches. [ABSTRACT FROM AUTHOR]

Abstract: A control system that uses type-2 fuzzy logic controllers (FLC) is proposed for the control of a non-isothermal continuous stirred tank reactor (CSTR), where a first order irreversible reaction occurs and that is characterized by the presence of bifurcations. Bifurcations due to parameter variations can bring the reactor to instability or create new working conditions which although stable are unacceptable. An extensive analysis of the uncontrolled CSTR dynamics was carried out and used for the choice of the control configuration and the development of controllers. In addition to a feedback controller, the introduction of a feedforward control loop was required to maintain effective control in the presence of disturbances. Simulation results confirmed the effectiveness and the robustness of the type-2 FLC which outperforms its type-1 counterpart particularly when system uncertainties are present. [Copyright &y& Elsevier]

Dilated homogeneous systems are local canonical forms of nonlinear control systems. For input affine homogeneous systems, existence of continuous homogeneous stabilizing controllers is equivalent to existence of differentiable homogeneous control Lyapunov functions. In this technical note, we propose an homogeneous stabilizing controller and an homogeneous inverse optimal controller for multi-input affine homogeneous systems with given homogeneous control Lyapunov functions. [ABSTRACT FROM AUTHOR]

Real systems are often driven by switching reference signals which affect dynamics and/or equilibrium points. This technical note addresses the computation of upper bounds of the minimum commutation time ensuring stability for switching nonlinear systems. Specifically, we consider the cases of constant and variable equilibrium point of interest, for polynomial systems and for a class of non-polynomial systems. We hence propose upper bounds of the sought minimum commutation time by adopting homogeneous polynomial Lyapunov functions for the former case and polynomial Lyapunov functions for the latter one, which can be computed via linear matrix inequaltiy optimizations for given Lyapunov functions. [ABSTRACT FROM AUTHOR]

Existing algorithms for computing the nth-order frequency response functions of the Duffing oscillator have helped promote frequency domain analysis of nonlinear systems but still have a number of practical difficulties. A very efficient algorithm to enable the nth-order symmetric generalized frequency response functions (GFRFs) to be written down directly in terms of the coefficients of the generalized higher order Duffing oscillator model is developed in this paper. The analytical expression derived in this paper shows that the key procedure in the determination of the higher order GFRFs is the computation of the Stirling set of the second kind. This enables the structure of the higher order GFRFs to be seen more clearly. [ABSTRACT FROM AUTHOR]

Abstract: A neuro-fuzzy system specially suited for efficient implementations is presented. The system is of the same type as the well-known “adaptive network-based fuzzy inference system” (ANFIS) method. However, different restrictions are applied to the system that considerably reduce the complexity of the inference mechanism. Hence, efficient implementations can be developed. Some experiments are presented which demonstrate the good performance of the proposed system despite its restrictions. Finally, an efficient digital hardware implementation is presented for a two-input single-output neuro-fuzzy system. [Copyright &y& Elsevier]

Abstract: In this paper, it is shown that the SIR epidemic model, with the force of infection subject to seasonal variation, and a proportion of either the prevalence or the incidence measured, is unidentifiable unless certain key system parameters are known, or measurable. This means that an uncountable number of different parameter vectors can, theoretically, give rise to the same idealised output data. Any subsequent parameter estimation from real data must be viewed with little confidence as a result. The approach adopted for the structural identifiability analysis utilises the existence of an infinitely differentiable transformation that connects the state trajectories corresponding to parameter vectors that give rise to identical output data. When this approach proves computationally intractable, it is possible to use the converse idea that the existence of a coordinate transformation between states for particular parameter vectors implies indistinguishability between these vectors from the corresponding model outputs. [Copyright &y& Elsevier]

Abstract: In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent ‘input–output’ representation of the system to be derived. The procedure is illustrated with a few examples. [Copyright &y& Elsevier]

Abstract: In this paper we propose a methodology to determine the structure of the pseudo-stoichiometric coefficient matrix κ in a macroscopic mass balance based model. The first step consists in estimating the minimal number of reactions that must be taken into account to represent the main mass transfer within the bioreactor. This provides the dimension of κ. Then we discuss the identifiability of the components of κ and we propose a method to estimate their values. Finally we present a method to select among a set of possible macroscopic reaction networks those which are in agreement with the available measurements. These methods are illustrated with three examples: real data of the growth and biotransformation of the filamentous fungi Pycnoporus cinnabarinus, real data of an anaerobic digester involving a bacterial consortium degrading a mixture of organic substrates and a process of lipase production from olive oil by Candida rugosa. [Copyright &y& Elsevier]

Recursive state and parameter reconstruction is a well-established field in control theory. In the current paper we derive a continuous-discrete version of recursive prediction error algorithm and apply the filter in an environmental and biological setting as a possible alternative to the well-known extended Kalman filter. The framework from which the derivation is started is the so-called ‘innovations-format’ of the (continuous time) system model, including (discrete time) measurements. After the algorithm has been motivated and derived, it is subsequently applied to hypothetical and ‘real-life’ case studies including reconstruction of biokinetic parameters and parameters characterizing the dynamics of a river in the United Kingdom. Advantages and characteristics of the method are discussed. [Copyright &y& Elsevier]

FastDer++ is a C++ class library for automatic differentiation designed for use in situations where a set of dependent variables and their gradients are to be evaluated in a large number of points. Typical settings constitute non-linear systems of partial differential equations (PDEs) and ODEs. Although automatic differentiation is traditionally considered to slow for implementation in non-linear PDE and ODE solvers, it has recently been demonstrated [E. Tijskens, H. Ramon, J. De Baerdemaeker, Efficient operator overloading AD for solving non-linear PDEs, in: G. Corliss, C. Faure, A. Griewank, L. Hascoe¨t, U. Nauman (Eds.), Automatic Differentiation of Algorithms—From Simulation to Optimisation, Springer, Verlag, 2002; Num. Algorithms 30 (2002) 259] that thanks to an extension called vectorised AD and careful design handcoded derivatives, finite differencing and state of the art AD tools can be outperformed in common situations. In addition, the user gains the advantage of directly dealing with the non-linear equations rather than with its linearised counterpart. This paper describes the FastDer++ library and its underlying principles in detail, both from the point of implementation and of user programming. [Copyright &y& Elsevier]

We present a methodology for the determination of sufficient conditions for the existence of a Lyapunov function in a general class of non-linear dynamical systems. The algorithm can be applied in the cases where the system parameters are numerically specified or not. The numerical algorithm involves the resolution of a linear programming problem. The algebraic version is implemented using the MAPLE programming system in the package Lyapunov. [Copyright &y& Elsevier]

Under certain controllability and observability restrictions, two different parameterisations for a non-linear compartmental model can only have the same input–output behaviour if they differ by a locally diffeomorphic change of basis for the state space. With further restrictions, it is possible to gain valuable information with respect to identifiability via a linear analysis. Examples are presented where non-linear identifiability analyses are substantially simplified by means of an initial linear analysis. For complex models, with four or more compartments, this linear analysis can prove lengthy to perform by hand and so symbolic computation has been employed to aid this procedure. [Copyright &y& Elsevier]

• GPU accelerated integration of ODE systems. • Minimisation of PCI-E and global memory transactions (including the dense output). • Efficient treatment of non-smooth, impacting dynamics. • Exploitation of shared memory in the semi-discretisation of PDEs. Challenges and efficient solution techniques during the integration of a large number of independent ordinary differential equations (ODEs) using the massively parallel architecture of graphics processing units (GPUs) are presented. One of the main difficulties is the minimisation of the memory transactions through the PCI-E bus between the host (CPU) and the device (GPU) required frequently, for instance, during the calculation of the Lyapunov exponent, winding number or maximum response diagram. The second difficulty is the minimisation of the slow global memory transactions and memory usage by exploiting the memory hierarchy of the GPU architecture. Finally, a good GPU solver has to treat the possible asynchronous features of the ODE systems efficiently; for instance, event detection occurring at distinct time instances or handling the orders of magnitude difference in the required number of time steps of the different ODE systems. The program package MPGOS (written in C++ and CUDA C software environments) can address the aforementioned issues easily via the addition of user-defined functions that must be implemented similarly to the right-hand side of the system; via the possibility of the definition of shared parameters common to all instances of the independent ODE systems; via user-programmable parameters to store only the desired properties of the trajectories; and via an easy was to overlap GPU and CPU computations. This paper focuses on the detailed description of the implementation strategies of the program package. [ABSTRACT FROM AUTHOR]