Mathematical Structures in Computer Science bridges the gap between theoretical computer science and software design. By publishing original perspectives from all areas of computing, the journal stresses applications from logic, algebra, geometry, category theory and other areas of logic and mathematics. Through issues such as this special issue, the journal also plans to play an occasional, but important role in the fields of intelligent computation and automation.

The flow shop scheduling problem based on ideal and precise conditions has been a focus of considerable research since the first easy scheduling problem was formulated. In reality, some uncertain factors always restrict the scheduling optimisation problem. In this paper, taking uncertain processing time as an example, we use generalised rough sets theory to transform the rough flow shop scheduling model into the precise scheduling model. We adopt a cooperative co-evolutionary particle swarm optimisation algorithm based on a niche sharing scheme (NCPSO) to minimise the makespan in comparison with the particle swarm optimiser (PSO) and co-evolution particle swarm optimiser (CPSO) algorithms. The new algorithm is characterised by a strengthening of the ability to reserve excellent particles and searching the optimal solution. Experimental results show that the new algorithm is more effective and efficient than the others.

Wind power projects face an uncertain external environment, they are complex projects in themselves and the capabilities of the designers, erectors and operators are limited. All this makes the identification of investment risks for wind power projects extremely complicated. In this paper, we propose a method for identifying the investment risk scientifically and accurately using a back propagation (BP) neural network. Specifically, we propose a hybrid wavelet transform fuzzy BP neural network (WT-FBPNN) optimisation model based on the construction of a risk evaluating index system. This improved model can not only exploit the time frequency localisation characteristic of wavelet transforms (WT), but also enhance the fit precision and algorithm convergence speed. The simulation results show that this model is reliable, and that this method of identifying the investment risk of wind power projects is feasible.

We consider a class of uncertain non-linear systems preceded by unknown backlash-like hysteresis, which is modelled by a differential equation. We propose a new state feedback robust adaptive control scheme using a backstepping technique and properties of the differential equation. In this control scheme, we construct a new continuous function to design an estimator to estimate the unknown constant parameters and the unknown bound of a ‘disturbance-like’ term. The transient performance of the output tracking error can be guaranteed by the introduction of pre-estimates of the unknown parameters in our controller together with update laws. We do not require bounds on the ‘disturbance-like’ term or unknown system parameters in this scheme. The global stability of the closed-loop system can be proved.

In this paper we make an empirical comparison of sales time series for online and offline channels. In particular, we analyse the sales dynamic and fluctuation level underlying the sales time series in different channels. The accumulative daily sales distributions of commodities are analysed statistically and the daily sales series are also studied from the perspective of complex networks. We find that most of the commodities' accumulative sales distributions can be fitted by power-law distributions. Visibility graphs are constructed for the daily sales series, and the accumulative degree distributions are also investigated – it is found that they also almost follow power-law distribution. The constant parameter α indicates that different specifications of the same goods have different sales characteristics, and different forms of packaging of commodities, either special offer or ordinary, also show distinctive sales fluctuation levels. The differences show that the direction of these relationships is opposite for online and offline channels.

Item recognition has become a hotspot in the field of computer vision research. SIFT has the advantage of requiring a low amount of information, a fast running speed and high precision, but it requires large data calculations and thus takes a long time to perform the item recognition. In this paper we propose a method of item recognition based on SIFT and SURF that provides a new way to solve the problem of item recognition, and has both feasibility and availability. This technique currently ignores colour information when dealing with colour images, but the evaluation method is capable of taking colour quality characteristics into account so it should be possible to improve the algorithm in the future. Experimental results show that this system of item recognition based on the SURF algorithm gives better matching recognition, is faster and has greater robustness.

Active-Passive-Jamming (APJ) is formed by a chaff decoy reflecting jamming signals from an aircraft's active-ECM jammer. The effectiveness of APJ depends on many factors, one of which is the jamming signal's frequency feature. In this paper, we discuss and analyse APJ's frequency feature in a typical given offense-defense scenario for the case where the ECM jammer adopted is velocity gate pull off (VGPO), which is a kind of deception jamming technique. Our results show that the APJ's frequency feature depends not only on the jamming techniques of the jammer, but also on the Native Doppler Frequency (NDF), which is related to the relative positions, distances, angles and velocities of the jammer, radar and chaff decoy. We also carried out simulations, and the results show that the APJ mode can be useful for jamming an enemy radar.

The original software reliability demonstration test (SRDT) does not take adequate account of prior knowledge or the prior distribution, which can lead to an expensive use of many resources. In the current paper, we propose a new improved Bayesian based SRDT method. We begin by constructing a framework for the SRDT scheme, then we use decreasing functions to construct the prior distribution density functions for both discrete and continuous safety-critical software, and then present schemes for both discrete and continuous Bayesian software demonstration functions (which we call DBSDF and CBSDF, respectively). We have carried out a set of experiments comparing our new schemes with the classic demonstration testing scheme on several published data sets. The results reveal that the DBSDF and CBSDF schemes are both more efficient and more applicable, and this is especially the case for safety-critical software with high reliability requirements.

We derive a delay-dependent H∞ performance criterion with a decoupled structure for systems with neutral time delay. We then extend it to an H∞ controller synthesis for systems with polytopic uncertainty. All conditions are given in terms of linear matrix inequalities (LMIs). In some previous descriptor system methods, the products of the controller and Lyapunov matrices are completely separated for the performance analysis, but not for controller synthesis - the method developed in the current paper eliminates this weakness. We present a numerical example to illustrate the effectiveness of the solution.

In this paper, we investigate the problem of robust stability for a class of delayed neural networks of neutral-type with linear fractional uncertainties. The activation functions are assumed to be unbounded, non-monotonic and non-differentiable, and the delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of the interval time-varying delay are available. By constructing a general form of the Lyapunov–Krasovskii functional, and using the linear matrix inequality (LMI) approach, we derive several delay-dependent stability criteria in terms of LMI. Finally, we give a number of examples to illustrate the effectiveness of the proposed method.

It is difficult to design a controller directly for non-square multi-variable systems with time delay. In the current paper, we propose a new design method for an Internal Model Control PID controller based on a modified effective open-loop transfer function (MEOTF) for non-square processes with time delay. The MEOTF method is used to decompose the complex non-square process into several equivalent independent single-input/single-output processes. Using the Taylor Particle Swarm Optimisation (Taylor-PSO) model reduction method, the MEOTF of the non-square process is approximated by a reduced order form. The reduced form of the MEOTF is then used to design the Internal Model Control PID controller, which is then used for the original non-square process. To improve the robust stability, a first-order filter is added in the feedback loop. Finally, we present simulation results showing the validity and reliability of this method. In particular, our method has a strong anti-interference characteristic and retains its good control performance in the presence of model perturbation and interference.

In recent years, under the dual pressure of environmental requirements and a series of conventional energy shortages, including power cuts, coal shortages and rising oil prices, there have been unprecedented opportunities for clean energy, and especially for the development and utilisation of solar energy. Hence, solar products have become increasingly popular because of the energy saving and environmental protection they offer. China's solar energy industry should be in the self-development mechanism, which is market-oriented and should act as a mainstay for enterprises. Scientifically forecasting the potential of the solar energy industry and rationally evaluating its status as a result of a market economy-oriented development is an effective means of building a low-carbon and harmonious society. In the work reported in this paper, we:

• – established a comprehensive evaluation index system, covering natural resources, economic conditions, policy support, technology and the market environment;

• – constructed a GA-SA model based on analysing the principles of GA (genetic algorithms) and SA (simulated annealing); and

• – applied these tools to predicting the potential of the solar power industry.

This paper addresses the H∞ state feedback stabilisation problem for networked control systems (NCSs) in the presence of time delays and packet losses. By introducing the concept of an effective sensor packet, the NCS is transformed into a new discrete-time switched model, where the parameters have a clear physical meaning and can be easily determined. In this framework, we derive the stability conditions of the closed-loop system in the H∞ sense, and also provide the corresponding H∞ stabilising controller design method. Finally, we give simulation and experimental results to demonstrate the effectiveness of the proposed approaches.

We provide motivation for and then study the synthesis of Petri nets. Synthesis can avoid the state exploration problem by guaranteeing correctness for the Petri net. We propose conditions to be imposed on a synthesis shared pb-type subnet for systems specified in Petri nets that ensure the preservation of the liveness and boundedness structural properties. Specifically, we propose a group of sufficient conditions, or both sufficient and necessary conditions, for liveness preservation and boundedness preservation. Possible applications of this synthesis method are illustrated through an example in the form of a flexible manufacturing system. These results are useful for studying the static and dynamic properties of Petri nets for analysing the properties of large complex systems.

The process of river health evaluation is subject to uncertainty and complexity. To address this, we establish a river health evaluation system based on entropy and multi-objective space theory. We apply an analytic hierarchy process (AHP) to calculate the weight of the first grade indexes, and then apply the entropy to calculate the weight of the second indexes. In this way, the health measure can be considered in terms of objective data and a subjective classification. The results of the computation show that the whole system provides a good measure of the health. The results express the measurement of the health of the river on different levels and for different aspects, which indicates that the evaluation method is feasible.

We propose an adaptive genetic algorithm (AGA) for the multi-objective optimisation design of a fuzzy PID controller and apply it to the control of an active magnetic bearing (AMB) system. Unlike PID controllers with fixed gains, a fuzzy PID controller is expressed in terms of fuzzy rules whose consequences employ analytical PID expressions. The PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than conventional ones. Moreover, it can be easily used to develop a precise and fast control algorithm in an optimal design. An adaptive genetic algorithm is proposed to design the fuzzy PID controller. The centres of the triangular membership functions and the PID gains for all fuzzy control rules are selected as parameters to be determined. We also present a dynamic model of an AMB system for axial motion. The simulation results of this AMB system show that a fuzzy PID controller designed using the proposed AGA has good performance.

The function of airport gate assignment is to assign appropriate gates for arrival and departure flights and to ensure the flights are on schedule. A key task of airport ground operations is assigning the airport gate with high efficiency and a reasonable arrangement. In this paper we establish an optimised model based on the characteristics of both the flights (the flight type, flight down time and the number of passengers) and the airport gates (the ease of access of the airport gate). We give a representation of the solution space and a direct graph model of the airport gate configuration based on dynamic scheduling parallel machines. We design a method for solving the airport gate configuration based on an immune genetic algorithm. The simulation results show the effectiveness of this model and algorithm.

In wireless broadband communication systems, the inherent non-linearity of power amplifiers creates spectral growth beyond the signal bandwidth, which interferes with adjacent channels. It also causes distortions within the signal bandwidth. In this paper, we study five digital predistortion algorithms for linearising two different non-linear memory power amplifier models. The simulation results show that the proposed digital predistorter using different algorithms can improve the in-band distortion and out of band spreading in different ways. In particular, the DLMS algorithm with fast convergence can significantly suppress spectral regrowth (by 60dB), effectively compensating for the non-linearity of the power amplifier.

We present a novel robust control scheme that deals with multi-body spacecraft attitude tracking problems. The control scheme consists of a radial basis function network (RBFN) and a robust controller. By using the finite time convergence property of the terminal sliding mode (TSM), we derive a new online learning algorithm for updating all the parameters of the RBFN that ensures the RBFN has fast approximation for the parameter uncertainties and external disturbances. We design a robust controller to compensate RBFN approximation errors and realise the anticipative stability and performance properties. We can also achieve closed-loop system stability using Lyapunov stability theory.

No detailed knowledge of the non-linear dynamics of the spacecraft is required at any point in the entire design process, and the proposed robust scheme is simple and effective and can be applied to more complex systems. Simulation results demonstrate the good tracking characteristics of the proposed control scheme in the presence of inertial uncertainties and external disturbances.

We present a concept of robust optimisation design for the spring actuator in a 10 kV/12.5 kA vacuum circuit breaker. We assume the breaking and closing velocity characteristics, which are derived form the technical data of the interrupter, as the specifications for the problem, and take the lengths of the connecting rods of the actuator and the stiffness coefficients of the breaking and closing springs as the optimisation variables. The variance between the specifications and the velocities calculated at each breaking and closing point and the maximal variation allowed by the design variables within acceptable tolerances make up the multiple objective function. The optimal parameters for the spring actuator are given by solving a non-linear programming problem with multiple targets and two-level optimisation.