Non-identical Dimensions Research Articles

Cluster lag synchronization in fractional-order community networks with nondelay and delay coupling

Lag synchronization is a special synchronization manner and has wide applications. For community network, in view of the differences among communities, the synchronization lags in different communities may be nonidentical. This paper investigates the cluster lag synchronization in fractional-order community networks with nondelay and delay coupling. The node dynamics in different communities are nonidentical and even have nonidentical dimensions. Based on the Lyapunov stability theory, effective feedback controllers are designed for achieving cluster lag synchronization and several synchronization criteria are derived. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

High-order fully actuated system models for discrete-time strict-feedback systems with increasing dimensions

This work aims to propose a high-order fully actuated system (FAS) model for discrete-time strict-feedback systems with nonuniform dimensions. In most of existing works, the authors only consider strict-feedback systems with uniform dimension, i.e. all subsystems have the same dimension. In contrast, we assume that the subsystems may have different or nonidentical dimensions. In particular, the dimensions are assumed to be increasing. Both step-forward and step-backward FAS models for discrete-time strict-feedback systems with nonuniform dimensions are given, based on which the exponentially stabilised controllers can be directly obtained. We consider not only first-order strict-feedback systems but also second-order case.

Distributed Adaptive Control for a Class of Heterogeneous Nonlinear Multi-Agent Systems with Nonidentical Dimensions

Distributed Adaptive Control for a Class of Heterogeneous Nonlinear Multi-Agent Systems with Nonidentical Dimensions

Cargo securing under multi-drop and axle weight constraints

This study emerges from a real-world cargo securing application to ensure safer road transportation and falls into the category of container loading problems with practical constraints. The literature has lacked efficient methods for the secure loading of items with non-identical dimensions, weights and rotations into containers while ensuring that the securing efforts necessary are minimal when also taking into account multi-drop and axle weight constraints. This paper puts forward a new way of ensuring cargo stability that gives rise to a novel combinatorial optimization problem, which is a generalization of the two-dimensional rectangular strip packing problem with orthogonal rotations. We formally demonstrate the intractability of the problem and provide a mixed integer programming formulation. The formulation is based on a discretization of the packing polyhedron, enabling us to model a range of complicated and practical constraints. A group of practical constraints tends to be large in number and makes it difficult to solve the formulation in a reasonable amount of time. In order to overcome this difficulty, we develop an exact algorithmic framework. This framework initially solves certain relaxations of the problem to obtain strong lower bounds before subsequently embedding those lower bounds into a branch-and-cut algorithm. The experimental study serves three purposes: (i) evaluating the performance of the algorithmic framework and the mathematical formulation to assess the merits of the two methods, (ii) identifying the characteristics of hard problem instances and (iii) extracting insights regarding challenges in cargo securing to help managers and practitioners in decision making.

Distributed Adaptive Control for Nonlinear Heterogeneous Multi-agent Systems with Different Dimensions and Time Delay

A distributed neural network adaptive feedback control system is designed for a class of nonlinear multi-agent systems with time delay and nonidentical dimensions. In contrast to previous works on nonlinear heterogeneous multi-agent with the same dimension, particular features are proposed for each agent with different dimensions, and similar parameters are defined, which will be combined parameters of the controller. Second, a novel distributed control based on similarity parameters is proposed using linear matrix inequality (LMI) and Lyapunov stability theory, establishing that all signals in a closed loop system are eventually ultimately bounded. The consistency tracking error steadily decreases to a field with a small number of zeros. Finally, simulated examples with different time delays are utilized to test the effectiveness of the proposed control technique.

Cooperative fault estimation for a class of heterogeneous multi‐agents with stochastic nonlinearities based on finite impulse response filter

AbstractThis article investigates the cooperative fault estimation problem for a class of heterogeneous multi‐agent systems, in which the agent dynamics are governed by linear discrete time‐varying systems with nonidentical dimensions subject to stochastic nonlinearities. A finite impulse response (FIR) filter based fault estimation scheme is developed via relative outputs to estimate the possible faults of the local and neighboring agents simultaneously. An analytical redundancy expressed in terms of all the states in the previous time window is originally established for deriving the fault estimation signal. The prior variance information coupled with fault estimation error in nonlinear form, is fully considered to design performance index through analysis of random matrix inequality. The optimal FIR filter gain is analytically obtained with computational efficiency by searching the minimum point of the relevant matrix trace function. Illustrative examples are finally provided to demonstrate the effectiveness and advantages of the developed results.

Stabilization and Synchronization of Discrete-time Fractional Chaotic Systems with Non-identical Dimensions

Stabilization and Synchronization of Discrete-time Fractional Chaotic Systems with Non-identical Dimensions

Distributed type‐2 fuzzy adaptive control for heterogeneous nonlinear multiagent systems

AbstractA novel type‐2 fuzzy adaptive consensus control is studied for a class of heterogeneous multiagent systems with identical or nonidentical dimensions. At first, the similar composite structure for a class of heterogeneous multiagent systems with identical or nonidentical dimensions is introduced. Some similar parameters among each agent are defined that can be obtained by calculating the proposed similar properties. Second, according to the graph theory and Lyapunov stability, a novel distributed type‐2 fuzzy adaptive control with similar parameters is constructed for the consensus of nonlinear heterogeneous multiagents with different dimensions, in which all signals can converge to small zero fields. Finally, two simulation examples are addressed for the considered systems to show the effectiveness of the control scheme, and some merits of the control approach are also demonstrated by comparison of similar control.

Distributed Fuzzy Adaptive Consensus Control for a Class of Heterogeneous Multi-agent Systems with Nonidentical Dimensions

A novel distributed fuzzy adaptive control approach is studied for a class of heterogeneous uncertain nonlinear multi-agent systems with different dimensions. Similar definition and property of each agent are introduced, and similar parameters among each agent can be obtained using the proposed properties, then the feedback distributed fuzzy adaptive control based on similar matrices and vectors is designed such that all followers can asymptotically track the leader’s dynamic behaviors. It is proved that the consensus problem of heterogeneous nonlinear multi-agent systems with different dimensions can be guaranteed by applying the proposed control strategy. An efficient framework is that the computation burden can be alleviated greatly because of a few adaptive laws. Finally, two simulation examples are provided to verify the effectiveness of the designed control method.

Event-Triggered Optimal Dynamic Formation of Heterogeneous Affine Nonlinear Multiagent Systems

This article studies an optimal dynamic formation problem for heterogeneous affine nonlinear systems. The nonidenticality in agents and the requirement for dynamic spatial reconfiguration make it a challenging task to coordinate different types of agents to maintain an optimized formation shape. In an architecture of event-triggered decision and control, this article investigates how to fulfill dynamic formation by distributively optimizing a team cost function. The basic idea is to design a decision unit for each agent to generate an implicit trajectory as a servo signal, based on which a control unit is designed with a displacement-gradient-based law to achieve the desired local solution. Typical heterogeneous characteristics including different nonlinearities and nonidentical dimensions are dealt with in a unified framework. It is shown that with the proposed triggering mechanisms, the optimal dynamic formation problem can be solved by a distributed control law with only intermittent communication. In theory, the properties of convergence of trajectory tracking errors, optimality of the team solution, and Zeno-freeness of event-triggered mechanisms are proved. Two simulation examples are given to verify the proposed method.

Secure Multiple-Input Multiple-Output Communications Based on F–M Synchronization of Fractional-Order Chaotic Systems with Non-Identical Dimensions and Orders

This paper investigates the F – M synchronization between non-identical fractional-order systems characterized by different dimensions and different orders. F – M synchronization combines the inverse generalized synchronization with the matrix projective synchronization. In particular, the proposed approach enables the F – M synchronization to be achieved between an n-dimensional master system and an m-dimensional slave system. The developed approach is applied to chaotic and hyperchaotic fractional systems with the aim of illustrating its applicability and suitability. A multiple-input multiple-output (MIMO) secure communication system is also developed by using the F – M synchronization and verified through computer simulations.

Generalized and inverse generalized synchronization of fractional-order discrete-time chaotic systems with non-identical dimensions

In this paper, we introduce two approaches to the generalized synchronized synchronization and the inverse generalized synchronization of fractional discrete-time chaotic systems with non-identical dimensions. The convergence of the proposed approaches is established by means of recently developed stability theory. Numerical results are presented based on well-known maps in the literature. Two examples are considered: a 3D generalized synchronization and a 2D inverse generalized synchronization.

Adaptive Hybrid Function Projective Synchronization of General Chaotic Complex Systems With Different Orders

A lot of progress has been made in the research of hybrid function projective synchronization (HFPS) for chaotic real nonlinear systems, while the HFPS of two different chaotic complex nonlinear systems with nonidentical dimensions is seldom reported in the literatures. So this paper discusses the HFPS of general chaotic complex system described by a unified mathematical expression with different dimensions and fully unknown parameters. Based on the Lyapunov stability theory, the adaptive controller is designed to synchronize two general uncertain chaotic complex systems with different orders in the sense of HFPS and the parameter update laws for estimating unknown parameters of chaotic complex systems are also given. Moreover, the control coefficients can be automatically adapted to updated laws. Finally, the HFPS between hyperchaotic complex Lorenz system and complex Chen system and that between chaotic complex Lorenz system and hyperchaotic complex Lü are taken as two examples to demonstrate the effectiveness and feasibility of the proposed HFPS scheme.

Heuristic algorithms for scheduling a heat-treatment furnace of steel-casting foundry manufacturing

This paper addresses a new research problem of minimising makespan (Cmax) on a batch processor (BP) with single job family (SJF), non-identical job sizes (NIJS), non-identical job dimensions (NIJD) and non-agreeable release times and due dates (NARD). We were led to this problem through a real-world application involving the scheduling of heat-treatment operations of steel casting foundry. The scheduling of furnace for heat-treatment of castings is of considerable interest as a large proportion of the total production time is the processing times of these operations. Due to the computational difficulty of the research problem, a few heuristic algorithms are proposed. In order to evaluate the solution quality of the proposed heuristic algorithms, a lower bound procedure is proposed. A series of computational experiments are conducted for absolute evaluation of heuristic algorithms in comparison with lower bound for large scale problems. This understanding facilitates the selection of the best algorithm under specific conditions for the research problem.

Three-dimensional stresses in adhesively bonded lap joints with non-identical adherends

This paper is concerned with the three-dimensional stress distributions in adhesively bonded joints with non-identical adherends and different geometrical dimensions and materials. The constitutive relations for the adhesive are developed using a modified pressure-dependent von Mises yield function and elasto-plastic idealization for the experimental stress-strain curve. The adherends and adhesive layers are both modelled using 20-noded solid elements. Observations have been made in particular on peel and shear stresses in the adhesive layer. Finite element results are found to match reasonably well with analytical solutions. Peel, shear and bending stresses in the lap joint address the three-dimensional behaviour prevailing in the single lap joint structure.