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The purpose of this paper is to use α‐dense curves for solving some Diophantine equations, such as Pythagorean triples, Linear Diophantine equations, the Pell Fermat equation, the Mordell equation for positive values.

The paper's aim is to present the applications in Number Theory of a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. The α‐dense curves generalize the space filling curves (Peanocurves,…) and fractal curves. This technique can be used for solving all problems of operational research in a simple way. The main idea consists in expressing n variables by means of a single one.

Apply the method to Number Theory. One of the most important applications is related to global optimization. Multivariable optimization problems coming from operational research or from industry can be quickly and easily solved.

The paper presents a new method based on α‐dense curves for solving Diophantine equations.

The purpose of this paper is to derive the output predictor for a stationary normal process with rational spectral density and linear stochastic discrete-time state-space model, respectively, as the output predictor is very important in model predictive control. The derivations are only dependent on matrix operations. Based on the output predictor, one quadratic programming problem is constructed to achieve the goal of subspace predictive control. Then an improved ellipsoid optimization algorithm is proposed to solve the optimal control input and the complexity analysis of this improved ellipsoid optimization algorithm is also given to complete the previous work. Finally, by the example of the helicopter, the efficiency of the proposed control strategy can be easily realized.

First, a stationary normal process with rational spectral density and one stochastic discrete-time state-space model is described. Second, the output predictors for these two forms are derived, respectively, and the derivation processes are dependent on the Diophantine equation and some basic matrix operations. Third, after inserting these two output predictors into the cost function of predictive control, the control input can be solved by using the improved ellipsoid optimization algorithm and the complexity analysis corresponding to this improved ellipsoid optimization algorithm is also provided.

Subspace predictive control can not only enable automatically tune the parameters in predictive control but also avoids many steps in classical linear Gaussian control. It means that subspace predictive control is independent of any prior knowledge of the controller. An improved ellipsoid optimization algorithm is used to solve the optimal control input and the complexity analysis of this algorithm is also given.

To the best knowledge of the authors, this is the first attempt at deriving the output predictors for stationary normal processes with rational spectral density and one stochastic discrete-time state-space model. Then, the derivation processes are dependent on the Diophantine equation and some basic matrix operations. The complexity analysis corresponding to this improved ellipsoid optimization algorithm is analyzed.

The purpose of this paper is to present a neural network approach to control performance assessment.

The performance index under study is based on the minimum variance control benchmark, a radial basis function network (RBFN) is used as the pre‐whitening filter to estimate the white noise sequence, and a stable filtering and correlation analysis method is adopted to calculate the performance index by estimating innovations sequence using the RBFN pre‐whitening filter. The new approach is compared with the auto‐regressive moving average model and the Laguerre model methods, for both linear and nonlinear cases.

Simulation results show that the RBFN approach works satisfactorily for both linear and nonlinear examples. In particular, the proposed scheme shows merits in assessing controller performance for nonlinear systems and surpasses the Laguerre model method in parameter selection.

A RBFN approach is proposed for control performance assessment. This new approach, in comparison with some well‐known methods, provides satisfactory performance and potentials for both linear and nonlinear cases.

Rice’s Theorem is a notorious stumbling block in Computer Science. We review some previous work of us that shows that we can extend Rice’s result to large segments of everyday mathematics, so that similar stumbling blocks appear in many areas of mathematics, as well as applied areas such as mathematical economics; one of its applications (Koppl’s conjecture) is discussed in some detail. Note: this paper has been written in an informal style.

Some new and powerful resources for cybernetics and system theory are explored, stemming from number theory, chronotopology, and the cybernetics of history — a field previously not considered.

The purpose of this paper is to address the synthesis and experimental application of a generalized predictive control (GPC) technique on an Orthoglide robot.

The control strategy is composed of two control loops. The inner loop aims at linearizing the nonlinear robot dynamics using feedback linearization. The outer loop tracks the desired trajectory based on GPC strategy, which is robustified against measurement noise and neglected dynamics using Youla parameterization.

The experimental results show the benefits of the robustified predictive control strategy on the dynamical performance of the Orthoglide robot in terms of tracking accuracy, disturbance rejection, attenuation of noise acting on the control signal and parameter variation without increasing the computational complexity.

The paper shows the implementation of the robustified predictive control strategy in real time with low computational complexity on the Orthoglide robot.

The purpose of this paper is to focus on the reference model of a grid-like supply network that enables formulation of delivery routing and scheduling problems in the context of the periodic vehicle routing problem.

The conditions for seamless (collision-free) synchronization of periodically executed local transport processes presented in this paper guarantee cyclic execution of supply processes, thereby preventing traffic flow congestion.

Systems that satisfy this characteristic, cyclic deliveries executed along supply chains are given and what is sought is the number of vehicles needed to operate the local transport processes in order to ensure delivery from and to specific loading/unloading points on given dates. Determination of sufficient conditions guaranteeing the existence of feasible solutions that satisfy these constraints makes it possible to solve the considered class of problems online.

The computer experiments reported in this paper show the possibilities of practical application of the proposed approach in the construction of decision support systems for food supply chain management.

The aim of the present work is to develop a methodology for the synthesis of regularly structured supply networks that would ensure fixed cyclic execution of local transport processes. The proposed methodology, which implements sufficient conditions for the synchronization of local cyclic processes, allows one to develop a method for rapid prototyping of supply processes that satisfies the time windows constraints given.

To use a new method based on α‐dense curved for solving problems of operational research.

The method of global optimization (called Alienor) is used for solving problems involving integer or mixed variables. A reducing transformation using α‐dense curves allows to transforms a n‐variables problem into a problem of a single variable.

Extends the basic method valid for continuous variables to problems involving integer, Boolean or mixed variables. All problems of operational research, linear or nonlinear, may be easily solved by or technique based on α‐dense curves (filling a n‐dimensional space). Industrial problems can be quickly solved by this technique obtaining the best solutions.

This method is deduced from the original works of Y. Cherruault and colleagues about global optimization and α‐dense curves. It proposes new techniques for solving operational research problems.

The purpose of this paper is to design a steering control for vehicles to protect the vehicle from spin and to realize improved cornering performance.

The improved cornering performance is realized based on Takagi‐Sugeno fuzzy model and generalized predictive control (GPC). A new approach to establish model of the vehicle is presented on the basis of fuzzy neural network. The network which inputs and outputs are composed of five layers of forward structure is utilized to build the structure and parameters of T‐S fuzzy model through learning from training data. In this way, the vehicle dynamic system is divided into many linear sub‐systems, and the system output is the weighted‐sum of these sub‐systems' outputs. A CARIMA model can be derived from the presented fuzzy model, and GPC is applied to deal with the control problem of vehicle stability.

Vehicle model can be divided into local linear models, corresponding controller can be developed. Simulation results show that fuzzy model based on GPC can be applied to improve stability of the vehicle effectively.

As an exploration of a new approach, the training data are from simulation, and the result of the paper will be applied in actual vehicle trials.

The paper presents useful advice for developing a vehicle stability controller.

The paper presents a new approach to establish a model of the vehicle on the basis of fuzzy neural network, which is valuable for establishing a new controller for vehicle stability.

The purpose of this paper is to improve the transient response and the inter‐sample behavior of a model reference adaptive control system by an appropriate selection of the fractional order hold (FROH) gain β and the multirate gains used in the control reconstruction signal through a fully freely chosen reference model even when the continuous plant possesses unstable zeros.

A multiestimation adaptive control scheme for linear time‐invariant continuous‐time plant with unknown parameters is presented. The set of discrete adaptive models is calculated from a different combination of the correcting gain β in a FROH and the set of gains to reconstruct the plant input under multirate sampling with fast input sampling. Then the scheme selects online the model with the best continuous‐time tracking performance which includes a measure of the inter‐sample ripple, which is improved. The estimated discrete unstable zeros are avoided through an appropriate design of the multirate gains so that the reference model might be freely chosen with no constraints on potential unstable zeros.

The scheme is able to select online the discretization model with the best continuous‐time tracking performance without an appropriate initialization.

The switching mechanism among the different models should maintain in operation the active discretization model at least for a minimum residence time in order to guarantee closed‐loop stability. The inter‐sample behavior is improved, but it is not always completely removed.

The transient response and the inter‐sample behavior are improved by using this multiestimation‐based discrete controller compared with a single estimation‐based one. The implementation of discrete controllers makes it easier and cheaper to implement and also more reliable than continuous‐time controllers.

The main innovation of the paper compared with previous background work is that the reference output is supplied by a stable continuous transfer function. Then the scheme is able to partly regulate the continuous‐time tracking error while the controller is essentially discrete‐time and operated by a FROH in general.