Showing papers in "International Journal of Systems Science in 2011"

On topology and dynamics of consensus among linear high-order agents

Abstract: Consensus of a group of agents in a multi-agent system with and without a leader is considered. All agents are modelled by identical linear n-th order dynamical systems while the leader, when it exists, may evolve according to a different linear model of the same order. The interconnection topology between the agents is modelled as a directed weighted graph. We provide answers to the questions of whether the group converges to consensus and what consensus value the group eventually reaches. To that end, we give a detailed analysis of relevant algebraic properties of the graph Laplacian. Furthermore, we propose an LMI-based design for group consensus in the general case.

Fuzzy H∞ filtering for nonlinear Markovian jump neutral systems

Abstract: This article is concerned with the problem of H∞ filter design for nonlinear Markovian jump neutral systems through the Takagi-Sugeno fuzzy model approach. By using a novel Markovian switched Lyapunov functional, a delay-dependent bounded real lemma (BRL) is presented in terms of linear matrix inequalities. Based on the derived BRL, both normal H∞ filters and non-fragile H∞ filters are designed, which guarantee that the corresponding filtering error systems are stochastically stable with a specified H∞ performance level. A numerical example is given to demonstrate the effectiveness of the proposed approach.

An economic order quantity model of imperfect quality items with partial backlogging

Abstract: This article deals with an economic order quantity (EOQ) model in which a certain percentage of a lotsize is of imperfect quality products. This percentage follows a uniform distribution function. During the inspection of the total lot-size, a stock-out situation may occur. In a stock-out situation, a partial fraction of the demand is adjusted by partial back ordering and the rest of the demand is considered as a case of lost sales. The associated integrated expected profit function is generalised for the general distribution function of imperfect quality products. Then the objective function is maximised. Also, three special cases of the general model are studied. A suitable numerical example is provided to illustrate the model and the solution procedure. Comparison between the general and special cases are also shown with the help of numerical examples. Sensitivity analysis of the optimal solutions with respect to all individual parameters of the general model is carried out.

Path optimisation of a mobile robot using an artificial neural network controller

Abstract: This article proposed a novel approach for design of an intelligent controller for an autonomous mobile robot using a multilayer feed forward neural network, which enables the robot to navigate in a real world dynamic environment. The inputs to the proposed neural controller consist of left, right and front obstacle distance with respect to its position and target angle. The output of the neural network is steering angle. A four layer neural network has been designed to solve the path and time optimisation problem of mobile robots, which deals with the cognitive tasks such as learning, adaptation, generalisation and optimisation. A back propagation algorithm is used to train the network. This article also analyses the kinematic design of mobile robots for dynamic movements. The simulation results are compared with experimental results, which are satisfactory and show very good agreement. The training of the neural nets and the control performance analysis has been done in a real experimental setup.

Nonlinear sliding mode high-gain observers for fault estimation

Abstract: A robust high gain observer for state and unknown inputs/faults estimations for a special class of nonlinear systems is developed in this article. Ensuring the observability of the faults/unknown inputs with respect to the outputs, the faults can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the high gain observers are designed under some regularity assumptions. In the sliding mode, the convergence of the estimation error dynamics is proven similar to the analysis of high-gain observers.

Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution

Abstract: In this article, the Legendre wavelet operational matrix of integration is used to solve boundary ordinary differential equations with non-analytic solution Although the standard Galerkin method using Legendre polynomials does not work well for solving ordinary differential equations in which at least one of the coefficient functions or solution function is not analytic, it is shown that the Legendre wavelet Galerkin method is very efficient and suitable for solving this kind of problems Several numerical examples are given to illustrate the efficiency and performance of the presented method

Consensus of multi-agent linear dynamic systems via impulsive control protocols

Abstract: In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.

Protecting complex infrastructures against multiple strategic attackers

Abstract: Infrastructures are analysed subject to defence by a strategic defender and attack by multiple strategic attackers. A framework is developed where each agent determines how much to invest in defending versus attacking each of multiple targets. A target can have economic, human and symbolic values, which generally vary across agents. Investment expenditure functions for each agent can be linear in the investment effort, concave, convex, logistic, can increase incrementally, or can be subject to budget constraints. Contest success functions (e.g., ratio and difference forms) determine the probability of a successful attack on each target, dependent on the relative investments of the defender and attackers on each target, and on characteristics of the contest. Targets can be in parallel, in series, interlinked, interdependent or independent. The defender minimises the expected damage plus the defence expenditures. Each attacker maximises the expected damage minus the attack expenditures. The number of free choice variables equals the number of agents times the number of targets, or lower if there are budget constraints. Each agent is interested in how his investments vary across the targets, and the impact on his utilities. Alternative optimisation programmes are discussed, together with repeated games, dynamic games and incomplete information. An example is provided for illustration.

Stabilisation of discrete 2D time switching systems by state feedback control

Abstract: This article deals with sufficient conditions of asymptotic stability for discrete two-dimensional (2D) time switching systems represented by a model of Roesser type with state feedback control. This class of systems can correspond to 2D state space or 2D time space switching systems. This work is based on common and multiple Lyapunov functions. The results are presented in LMI form. Two examples are given to illustrate the results.

Robust finite time observer design for multicellular converters

Abstract: In this article, a nonlinear finite time observer is designed for multicellular converters. The aim is to estimate the capacitor voltages by taking into account the hybrid behaviour of the converter. This article extends the validity of the strong Lyapunov function, proposed in Moreno and Osorio (Moreno, J., and Osorio, M. (2008), 'A Lyapunov Approach to Second Order Sliding Mode Controllers and Observers', in Proceedings of the IEEE Conference on Decision and Control, New Orleans, USA, pp. 2856-2861), in order to deeply study the reaching time estimation and robustness of the homogeneous finite time observer given in Perruquetti et al. (Perruquetti, W., Floquet, T., and Moulay, E. (2008), 'Finite Time Observers: Application to Secure Communication', IEEE Transactions on Automatic Control, 53, 356-360). The proposed approach enables the stabilisation of the observation errors in spite of the presence of perturbations and uncertainties. Some simulations and comparisons with the super-twisting sliding mode observer highlight the efficiency of the proposed strategy.

Guaranteed cost control with poles assignment for a flexible air-breathing hypersonic vehicle

Abstract: This article investigates the problem of guaranteed cost control for a flexible air-breathing hypersonic vehicle (FAHV). The FAHV includes intricate coupling between the engine and flight dynamics as well as complex interplay between flexible and rigid modes, which results in an intractable system for the control design. A longitudinal model is adopted for control design due to the complexity of the vehicle. First, for a highly nonlinear and coupled FAHV, a linearised model is established around the trim condition, which includes the state of altitude, velocity, angle of attack, pitch angle and pitch rate, etc. Secondly, by using the Lyapunov approach, performance analysis is carried out for the resulting closed-loop FAHV system, whose criterion with respect to guaranteed performance cost and poles assignment is expressed in the framework of linear matrix inequalities (LMIs). The established criterion exhibits a kind of decoupling between the Lyapunov positive-definite matrices to be determined and the FAHV system matrices, which is enabled by the introduction of additional slack matrix variables. Thirdly, a convex optimisation problem with LMI constraints is formulated for designing an admissible controller, which guarantees a prescribed performance cost with the simultaneous consideration of poles assignment for the resulting closed-loop system. Finally, some simulation results are provided to show that the guaranteed cost controller could assign the poles into the desired regional and achieve excellent reference altitude and velocity tracking performance.

Delay-dependent robust H∞ control for uncertain stochastic T-S fuzzy systems with time-varying state and input delays

Abstract: In this article, the problem of delay-dependent robust H∞ control for uncertain stochastic Takagi-Sugeno fuzzy systems with time-varying state and input delays is investigated. The parameter uncertainties are assumed to be time-varying and norm bounded. Through construction of a new Lyapunov-Krasovskii functional, the delay-dependent robust H∞ control scheme is presented in terms of linear matrix inequalities (LMIs). By solving these LMIs, a desired fuzzy controller can be obtained. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

Robust distributed state estimation for sensor networks with multiple stochastic communication delays

Abstract: This article is concerned with the robust distributed state estimation problem for a class of uncertain sensor networks with multiple stochastic communication delays. A sequence of mutually independent random variables obeying the Bernoulli distribution is introduced to account for the randomly occurred communication delays. Both the discrete-time target plant and the sensor model are subject to parameter uncertainties as well as stochastic disturbance. The parameter uncertainties are norm-bounded and enter both the system and the measurement matrices. The external stochastic disturbance is given in the form of a scalar Wiener process. Through available output measurements from not only each individual sensor but also its neighbouring sensors, we aim to design distributed state estimators in order to approximate the state of the target plant. By using the Kronecker product, stochastic analysis is carried out to derive a sufficient criterion ensuring the estimation error systems to be convergent in the mean square sense for all randomly occurred delays, admissible stochastic disturbance and parameter uncertainties. Then, an explicit expression of the individual estimator is given in terms of the solution to a convex optimisation problem that can be easily solved by using the semi-definite programme method. A numerical example is given at the end of this article to demonstrate the usefulness of the developed theoretical results.

Stabilisation of neutral systems with saturating control inputs

Abstract: This article focuses on the stabilisation problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilisation conditions are derived using Lyapunov-Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow one to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimisation problems with LMI constraints are therefore proposed to compute stabilising state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results.

High-order sliding mode control of a DC motor drive via a switched controlled multi-cellular converter

Abstract: In this article, we present a high-order sliding mode controller of a DC motor drive connected to a multi-cellular converter. More specifically, we design a second-order (super-twisting) control algorithm for the speed regulation of a DC motor. For this, a switching control for the multi-cellular converter is derived in order to supply the correct reference value for the speed regulation. A practical implementation of the controller is realised using a laboratory set-up. The performance and the validity of the controller are shown experimentally.

Constrained feedback robust model predictive control for polytopic uncertain systems with time delays

Abstract: An approach to design robust model predictive control (MPC) is proposed by considering constrained time-delayed systems with polytopic uncertainty description. The contribution consists of two aspects. First, compared with the existing techniques which apply a single state feedback law, the feedback MPC is utilised, which applies a sequence of feedback control laws. Second, for systems with input delay, an augmented polytopic uncertainty description is invoked to remove the input delay. By feedback MPC, the conservativeness of the traditional MPC is reduced. By the augmented system description, the difficulties in handling the input delay, such as inability to deal with some unstable system matrices in the previous robust MPC literature, are overcome. Two simulation results are given to illustrate the effectiveness of the proposed approach.

Two-warehouse partial backlogging inventory model for deteriorating items with linear trend in demand under inflationary conditions

Abstract: In today's business transactions, there are various reasons, namely, bulk purchase discounts, re-ordering costs, seasonality of products, inflation induced demand, etc., which force the buyer to order more than the warehouse capacity. Such situations call for additional storage space to store the excess units purchased. This additional storage space is typically a rented warehouse. Inflation plays a very interesting and significant role here: It increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organisation prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space, which is facilitated by a rented warehouse. Ignoring the effects of the time value of money and inflation might yield misleading results. In this study, a two-warehouse inventory model with linear trend in demand under inflationary conditions having different rates of deterioration has been developed. Shortages at the owned warehouse are also allowed subject to partial backlogging. The solution methodology provided in the model helps to decide on the feasibility of renting a warehouse. Finally, findings have been illustrated with the help of numerical examples. Comprehensive sensitivity analysis has also been provided.

Operator-based robust control for nonlinear systems with Prandtl-Ishlinskii hysteresis

Abstract: This article presents an operator-based robust control method for nonlinear systems with Prandtl-Ishlinskii (PI) hysteresis On the existence of the hysteresis, the system usually exhibits undesirable oscillations and even instability While addressing the hysteresis, PI model is adopted to describe it Especially, the PI model is decomposed into two terms: an invertible part and a disturbance part In this way, the invertible part could be considered as a part of the nonlinear system Based on the concept of Lipschitz's operator and the robust right coprime factorisation condition, a robust control design scheme is given to guarantee the bounded input bounded output stability of the obtained system Further, a tracking operator design method is given to ensure the control system output-tracking performance under the existence of the disturbance part Numerical simulation results are presented to validate the effectiveness of the proposed method

Robust H∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

Abstract: This article investigates the problem of robust H∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Ito-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an H∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed H∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov-Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.

Air-fuel ratio control in a gasoline engine

Abstract: The aim of this article is to design an air-fuel ratio control law for a gasoline IC engine. The air-fuel ratio is measured by a lambda sensor in the exhaust manifold. As a consequence, a variable transport delay arises in the model considered. A non-linear control approach based on a Takagi-Sugeno's model of the system is used. Then, two structures of control law are compared based on parallel distributed compensation control laws, which take into account the variable time delay. Finally, some simulations are given to show the efficiency of the developed control law.

Periodic motion planning and nonlinear H∞ tracking control of a 3-DOF underactuated helicopter

Abstract: Nonlinear H∞ synthesis is developed to solve the tracking control problem into a 3-DOF helicopter prototype. Planning of periodic motions under a virtual constraints approach is considered prior the controller design in order to achieve our goal. A local H∞ controller is derived by means of a certain perturbation of the differential Riccati equations that appear while solving the corresponding H∞ control problem for the linearised system. Stabilisability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential Riccati equations, and hence the proposed synthesis procedure obviates an extra verification work of these properties. Due to the nature of the approach, the resulting controller additionally yields the desired robustness properties against unknown but bounded external disturbances. Convergence and robustness of the proposed design are supported by simulation results.

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

Abstract: The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.

Set invariance under output feedback: a set-dynamics approach

Abstract: The article offers a framework to define and analyse the notion of invariance with respect to output feedback under non-parametric disturbances. The motivation is that the straightforward generalisation of the definition of invariance under state feedback to the output feedback framework, namely relying only on feedback from the output, does not yield a useful notion. Our model follows standard feedback invariance considerations with, however, a crucial modification that is needed when only an observation of the state, rather than the state itself, is available. The model incorporates information gathered by the controller during the process; this is in similarity with the observer-based dynamics model; however our framework represents the information within a set dynamics. The evolution of the resulting information sets determines invariant sets and attractors of the state dynamics. The framework in this article is discrete-time control systems. We offer an analysis of the notion with results on existence of, and convergence to, output feedback invariant sets; illustrative examples related to potentially practical feedback rules are exhibited.

State exact reconstruction for switched linear systems via a super-twisting algorithm

Abstract: This article discusses the problem of state reconstruction synthesis for switched linear systems. Based only on the continuous output information, an observer is proposed ensuring the reconstruction of the entire state (continuous and discrete) in finite time. For the observer design an exact sliding mode differentiator is used, which allows the finite time convergence of the observer trajectories to the actual trajectories. The design scheme includes both cases: zero control input and nonzero control input. Simulations illustrate the effectiveness of the proposed observer.

On pinning synchronisability of complex networks with arbitrary topological structure

Abstract: This article aims to investigate the pinning synchronisability of complex networks under arbitrary topological structures with a focus on the case with directed graph topology. More specifically, we explore the necessary and sufficient conditions on choosing the pinned nodes to guarantee the pinning synchronisability of complex networks. It is found that the pinning synchronisability of complex networks relies totally on the way to pin the nodes as long as the coupling strength is large enough. Furthermore, it is proven that the entire network can synchronise exponentially fast. The least synchronisation speed can be specified as well. Finally, based on the theoretical findings proposed in this article, we provide the specific procedures for finding a least number of pinned nodes to realise the pinning synchronisability of complex networks.

On average consensus in directed networks of agents with switching topology and time delay

Abstract: In this article, the average consensus problem in directed networks of agents with both switching topology and coupling delay is investigated. First, based on a specific orthogonal transformation of the Laplacian matrix, an important proposition for verifying the positive definiteness of a class of quadratic forms is provided, which is of independent interest in matrix theory. And the relation between weakly connected and strongly connected digraphs is also investigated. Then, it is proved that all the agents reach the average consensus asymptotically for appropriate time delay if the communication topology keeps weakly connected and balanced. Finally, a numerical example is given to demonstrate the effectiveness and advantage of the new result.

Robust reliable control for a near space vehicle with parametric uncertainties and actuator faults

Abstract: Based on fuzzy control techniques, this article is concerned with the problem of robust reliable control for a near space vehicle (NSV) with parametric uncertainties and actuator faults. The nonlinear dynamics of a NSV is represented by the Takagi-Sugeno fuzzy models, and then the actuator fault model and fuzzy state-space observer are developed. Next, the fuzzy observer-based robust reliable control strategy is proposed. It is proved that the fuzzy control systems for the NSV is reliable in the sense that the closed-loop system is asymptotically stable and the actuator components can operate well in the presence of some actuator faults. The developed theoretical results are in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Finally, simulation results are given to illustrate the applicability of the proposed approach.

H∞ filtering for a class of switched linear parameter varying systems

Abstract: This article addresses the filtering problem for a class of discrete-time switched linear parameter varying systems under average dwell time switching. The stability result for general discrete-time switched systems with average dwell time is first presented. A mode-dependent full-order parameterised filter is then designed and the corresponding existence conditions of such filters are derived via LMI formulation. The desired filter gains and the admissible switching signals are obtained for a given system decay degree such that the resulting filter error system is exponentially stable and has a guaranteed H∞ performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results.

Delay-dependent stabilisation of systems with time-delayed state and control: application to a quadruple-tank process

Abstract: This work presents a study on the stabilisation of linear systems with delays in the control and states, motivated by a benchmark problem from the literature (a quadruple-tank system). A methodology for the stabilisation of this kind of systems is presented, expressing the conditions as LMIs. Using several examples from the literature, it is shown that the proposed stabilisation theorem is less conservative than previous results. Finally, the technique is applied to the benchmark problem, showing how it is possible to derive efficient controllers for realistic problems, using the proposed technique.

Dynamic output feedback robust model predictive control

Abstract: The synthesis approach for dynamic output feedback robust model predictive control is considered. The notion of quadratic boundedness is utilised to characterise the stability properties of the augmented closed-loop system. A finite horizon performance cost, which corresponds to the worst case of both the polytopic uncertainty and the bounded disturbance/noise, is utilised. It is not required to specify the horizon length. A numerical example is given to illustrate the effectiveness of the proposed controller.