Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2009"

A new design method based on artificial bee colony algorithm for digital IIR filters

Abstract: Digital filters can be broadly classified into two groups: recursive (infinite impulse response (IIR)) and non-recursive (finite impulse response (FIR)). An IIR filter can provide a much better performance than the FIR filter having the same number of coefficients. However, IIR filters might have a multi-modal error surface. Therefore, a reliable design method proposed for IIR filters must be based on a global search procedure. Artificial bee colony (ABC) algorithm has been recently introduced for global optimization. The ABC algorithm simulating the intelligent foraging behaviour of honey bee swarm is a simple, robust, and very flexible algorithm. In this work, a new method based on ABC algorithm for designing digital IIR filters is described and its performance is compared with that of a conventional optimization algorithm (LSQ-nonlin) and particle swarm optimization (PSO) algorithm.

Direct synthesis-based controller design for integrating processes with time delay

Abstract: Using the direct synthesis method, a PID controller in series with a lead/lag compensator is designed for control of open loop integrating processes with time delay. Set-point weighting is considered for reducing the undesirable overshoot. Guidelines are provided for selection of the desired closed loop tuning parameter in the direct synthesis method and set point weighting parameter. The method gives significant load disturbance rejection performances. Illustrative examples are considered to show the performances of the proposed method. Significant improvement is obtained when compared to recently reported methods.

A delay distribution based stability analysis and synthesis approach for networked control systems

Abstract: Communication delays in networked control systems (NCSs) has been shown to have non-uniform distribution and multifractal nature. This paper proposes a delay distribution based stability analysis and synthesis approach for NCSs with non-uniform distribution characteristics of network communication delays. A stochastic control model related with the characteristics of communication networks is established to describe the NCSs. Then, delay distribution-dependent NCS stability criteria are derived in the form of linear matrix inequalities (LMIs). Also, the maximum allowable upper delay bound and controller feedback gain can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples showed that the results derived from the proposed method are less conservativeness than those derived from the existing methods.

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

Abstract: A general system of the time-dependent partial differential equations containing several arbitrary initial and boundary conditions is considered. A hybrid method based on artificial neural networks, minimization techniques and collocation methods is proposed to determine a related approximate solution in a closed analytical form. The optimal values for the corresponding adjustable parameters are calculated. An accurate approximate solution is obtained, that works well for interior and exterior points of the original domain. Numerical efficiency and accuracy of the hybrid method are investigated by two-test problems including an initial value and a boundary value problem for the two-dimensional biharmonic equation.

Constacyclic codes over F2+uF2

Abstract: We study the structure of ( 1 + u ) -constacyclic codes of an arbitrary length n over the ring F 2 + uF 2 . We find a set of generators for each ( 1 + u ) -constacyclic code and its dual. We study the rank of cyclic codes and find their minimal spanning sets. We prove that the Gray image of a ( 1 + u ) -constacyclic code is a binary cyclic code of length 2 n . We conclude by giving examples of constacyclic codes and their Gray image binary codes. We give a direct construction of a [12,7,4] linear binary cyclic code that match the Hamming distance of the best binary code with length 12 and dimension 7.

State and unknown input estimation for discrete time multiple model

Abstract: This paper deals with the state estimation of nonlinear discrete systems described by a multiple model with unknown inputs. The main goal concerns the simultaneous estimation of the system's state and the unknown inputs. This goal is achieved through the design of a multiple observer based on the elimination of the unknown inputs. It is shown that the observer gains are solutions of a set of linear matrix inequalities. After that, an unknown input estimation method is proposed. An academic example and an application dealing with message decoding illustrate the effectiveness of the proposed multiple observer.

On the stability of nonlinear systems with leakage delay

Abstract: This paper studies uniqueness and stability of the equilibrium points of nonlinear time-delay systems with leakage delay by using the appropriate model transformation that shifts the considered systems into the neutral-type time-delay systems. Delay-independent sufficient conditions for uniqueness and delay-dependent sufficient conditions for stability are derived, respectively, by using contraction mapping theorem and suitable degenerate Lyapuniv–Krasvovskii functional together with some differential inequalities and LMI technique.

Generic two-degree-of-freedom linear and fuzzy controllers for integral processes

Abstract: This paper presents a new framework for the design of generic two-degree-of-freedom (2-DOF), linear and fuzzy, controllers dedicated to a class of integral processes specific to servo systems. The first part of the paper presents four 2-DOF linear PI controller structures that are designed using the Extended Symmetrical Optimum method to ensure the desired overshoot and settling time. The second part of the paper presents an original design method for 2-DOF Takagi–Sugeno PI-fuzzy controllers based on the stability analysis theorem. Experimental results for the speed control of a servo system with variable load illustrate the performance of the new generic control structures.

H∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays

Abstract: This paper investigates the H∞ guaranteed cost control problem for mode-dependent time-delay jump systems with norm-bounded uncertain parameters. Both distributed delays and input delays appear in the system model. Based on a matrix inequality, a sufficient condition for the existence of robust H∞ guaranteed cost controller is derived, which stabilizes the considered system and guarantees that both the H∞ performance level and a cost function have upper bounds for all admissible uncertainties. By the cone complementary linearization approach, the desired state-feedback controller can be constructed. A numerical example is provided to show the effectiveness of the proposed theoretical results.

Robust exponential stability for uncertain time-varying delay systems with delay dependence

Abstract: This paper investigates the exponential stability problem for uncertain time-varying delay systems. Based on the Lyapunov–Krasovskii functional method, delay-dependent stability criteria have been derived in terms of a matrix inequality (LMI) which can be easily solved using efficient convex optimization algorithms. These results are shown to be less conservative than those reported in the literature. Four numerical examples are proposed to illustrate the effectiveness of our results.

Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems

Abstract: This paper deals with the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Then, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. Numerical example is given to illustrate the effectiveness of the developed techniques.

A new method to estimate a first-order plus time delay model from step response

Abstract: In this paper an identification method to estimate the parameters of a first-order plus time delay model is proposed. Such a method directly obtains these parameters using a new linear regression equation. No iterations in calculation are needed. Moreover, a simple true/false criterion to establish if the hypothesis on the process type is correct can be easily derived. The proposed method shows an acceptable robustness to disturbances and measurement noise as it is confirmed by several simulated experiments.

Model reference control of LPV systems

Abstract: This paper deals with the problem of model reference control for linear parameter varying (LPV) systems. The LPV systems under consideration depend on a set of parameters that are bounded and available online. The main contribution of this paper is to design an LPV model reference control scheme for LPV systems whose state-space matrices depend affinely on a set of time-varying parameters that are bounded and available online. The design problem is divided into two subproblems: the design of the coefficient matrices of the controller and the design of the gain of the state feedback controller for LPV systems. The singular value decomposition is used to obtain the coefficient matrices, while the linear matrix inequality methodology is used to obtain the parameter-dependent state feedback gain of the control scheme. A simple numerical example is used to illustrate the proposed design and a coupled-tank process example is used to demonstrate the usefulness and practicality of the proposed design. Simulation and experimental results indicate that the proposed scheme works well.

Exponential stability and stabilization of a class of uncertain linear time-delay systems

Abstract: This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov–Krasovskii functional combined with Leibniz–Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.

MEMSWear-biomonitoring system for remote vital signs monitoring

Abstract: This paper proposes a remote vital signs monitoring system, which integrates wireless body area network (WBAN) and personal digital assistant (PDA) phone technology. Four different physiological signs, e.g., ECG, SpO 2 , temperature and blood pressure, can be continuously acquired or derived from two wireless sensor nodes—ECG sensor and integrated SpO 2 /temperature sensor. Once sentinel events happened or the request to real-time display vital signs is confirmed, all physiological signs and critical indices will be immediately transmitted to patient's PDA phone through Bluetooth and further relayed to doctor's PDA phone through global system for mobile communication (GSM) technology. A prototype of such system has been successfully developed and implemented, which will offer high standard of healthcare with a major reduction in cost for our society.

Modeling and control of a piezoelectric actuator driven system with asymmetric hysteresis

Abstract: This study describes the high-precision positioning control of a system with asymmetric hysteresis. A switching system concept is adopted to describe the Preisach-type hysteresis, and a systematic modeling procedure is established to obtain the parameters of the system. A piezoelectric actuator system driven by a voltage amplifier is used to verify the modeling accuracy. A control structure, comprising a feedforward controller and a PD-type feedback controller, is used to realize the high-precision positioning control of the piezoelectric actuator driven stage. To enhance tracking control, a high-frequency modified term is incorporated into the hysteresis model. The experimental results confirm that the addition of this modified term reduces the tracking error and prevents the controlling energy from being saturated.

Global dissipativity of stochastic neural networks with time delay

Abstract: Liao and Wang [Global dissipativity of continuous-time recurrent neural networks with time delay, Phys. Rev. E 68 (2003) 016118] firstly studied the dissipativity of neural networks. In this paper, the neural network model is generalized to a stochastic case, and the global dissipativity in mean of such stochastic system is investigated. By constructing several proper Lyapunov functionals combining with Jensen's inequality, Ito's formula and some analytic techniques, several sufficient conditions for the global dissipativity in mean of such stochastic neural networks are derived in LMIs forms, which can be easily verified in practice. Three numerical examples are provided to demonstrate the effectiveness of our criteria.

Non-fragile controller design for discrete descriptor systems

Abstract: This paper is concerned with the design problem of non-fragile controller for discrete descriptor systems. The controller gain variations are assumed to be time-invariant and norm-bounded appearing in the controller coefficients. Sufficient conditions for the existence of a static state feedback controller with additive uncertainty and multiplicative uncertainty are obtained in terms of a set of matrix inequalities, respectively. With these conditions, the problems of non-fragile control for discrete descriptor systems are solved. Explicit expressions of desired non-fragile state feedback controllers are also given, and no matrix decomposition is required. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.

Controllability of Volterra-Fredholm type systems in Banach spaces

Abstract: We show the results in Chalishajar [Controllability of mixed Volterra–Fredholm-type integro-differential systems in Banach space, J. Franklin Inst. 344(1) (2007) 12–21] and Chang and Chalishajar [Controllability of mixed Volterra–Fredholm type integro-differential systems in Banach space, J. Franklin Inst., doi: 10.1016/j.jfranklin.2008.02.002 ] are only valid for ordinary differential control systems. As a result the examples provided cannot be recovered as applications of the abstract results.

New techniques for initial alignment of strapdown inertial navigation system

Abstract: Some new techniques for initial alignment of strapdown inertial navigation system are proposed in this paper. A new solution for the precise azimuth alignment is given in detail. A new prefilter, which consists of an IIR filter and a Kalman filter using hidden Markov model, is designed to attenuate the influence of sensor noise and outer disturbance. Navigation algorithm in alignment is modified to feedback continuously for the closed-loop system. It is shown that the initial estimated variance setting of azimuth angle error can influence the speed of initial alignment significantly. At the beginning of alignment, Kalman filter must make a very conservative guess at the initial value of azimuth angle error to get a high convergent speed of the azimuth angle. It is pointed out that the low signal to noise ratio makes the ordinary setting of the estimated azimuth variance slow down the convergent speed of the azimuth angle. Also is shown that the large azimuth angle error problem can be solved well by our solution. The feasibility of these new techniques is verified by simulation and experiment.

Robust H∞ control of delayed singular systems with linear fractional parametric uncertainties

Abstract: This paper deals with the problem of robust H ∞ control for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is feasible, a desired robust state feedback control law can be constructed, which guarantees that, for all admissible uncertainties, the resulting closed-loop system is not only regular, impulse free and stable, but also meets an H ∞ -norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the application of the proposed method.

Cyclic DNA codes over the ring F2[u]/(u2 - 1) based on the deletion distance

Abstract: We study the structure of cyclic DNA codes over the ring F 2 [ u ] / ( u 2 - 1 ) . We employ the deletion similarity distance on the set of codewords. A set of generators for this type of codes is found. We also study the CG -content of these type of codes and their deletion distance. Examples of cyclic DNA codes are constructed with their CG -content and their corresponding deletion distance.

Delay-dependent exponential stability for a class of neural networks with time delays and reaction–diffusion terms☆

Abstract: In this paper, the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type has been studied. By constructing appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained ensuring the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks. These conditions are dependent on the size of the time delay and the measure of the space, which is usually less conservative than delay-independent and space-independent ones. And, these networks are generalized without assuming the boundedness and differentiability of the activate functions. The proposed LMI condition can be checked easily by recently developed algorithms. The results are new and improve the earlier work. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.

Stochastic fault tolerant control of networked control systems

Abstract: A problem of stabilization about uncertain networked control systems (NCSs) with random but bounded delays is discussed in this paper By using augmented state-space method, this class of problems can be modeled as discrete-time jump linear systems governed by finite-state Markov chains A new switched model based on probability is proposed to research problems of reliable control when actuators become ageing or partially disabled Using improved V–K iteration algorithm, a class of reliable controllers are designed to make systems asymptotically mean square stable under several stochastic disturbances such as random time-delay and stochastic actuator failure and the maximal redundancy degree is given through this method

Dynamical behavior in a harvested differential-algebraic prey–predator model with discrete time delay and stage structure

Abstract: A differential-algebraic model system which considers a prey–predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed model system with and without discrete time delay are investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; on the other hand, the local stability of the model system with discrete time delay is also studied. The theoretical analysis shows that the discrete time delay has a destabilizing effect in the model of population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Numerical simulations are carried out to show the consistency with theoretical analysis.

PID controller tuning rules for integrating processes with varying time-delays

Abstract: This paper discusses PID controller tuning for integrating processes with varying time-delays. Most of the existing tuning rules for the first-order lag plus integrator plus delay (FOLIPD) processes that we mainly focus on have the same general structure, and the properties of these rules are discussed in conjunction with varying time-delays. The analysis leads to novel tuning rules, where the maximum amplitude of an arbitrarily varying time-delay can be given as a parameter, which makes the use of the rules attractive in several applications. We will also extend the analysis to integrating processes with second-order lag and apply the design guidelines for a networked control application. In addition, we propose a novel tuning method that optimizes the closed-loop performance with respect to certain robustness constraints while also providing robustness to delay variance via jitter margin maximization. Further, we develop new PID controller tuning rules for a wide range of processes based on the proposed method. The new tuning rules are discussed in detail and compared with some of the recently published results. The work was originally motivated by the need for robust but simultaneously well-performing PID parameters in an agricultural machine case process. We also demonstrate the superiority of the proposed tuning rules in the case process.

Auto-structuring fuzzy neural system for intelligent control

Abstract: An auto-structuring fuzzy neural network-based control system (ASFNS), which includes the auto-structuring fuzzy neural network (ASFNN) controller and the supervisory controller, is proposed in this paper. The ASFNN is used as the main controller to approximate the ideal controller and the supervisory controller is incorporated with the ASFNN for coping with the chattering phenomenon of the traditional sliding-mode control. In the ASFNS, an automatic structure learning mechanism is proposed for network structure optimization, where two criteria of node-adding and node-pruning are introduced. It enables the ASFNN to determine the nodes autonomously while ensures the control performance. In the ASFNS, all the parameters are evolved by the means of the Lyapunov theorem and back-propagation to ensure the system stability. Thus, an intelligent control approach for adaptive control is presented, where the structure and parameter can be evolved simultaneously. The proposed ASFNS features the following salient properties: (1) on-line and model-free control, (2) relax design in controller structure, (3) overall system stability. To investigate the capabilities, the ASFNS is applied to a kind of nonlinear system control. Through the simulation results the advantages of the proposed ASFNS can be validated.

Bayesian and frequentist estimation of the performance of free space optical channels under weak turbulence conditions

Abstract: Approximate mathematical form expressions were derived for the estimation of the average (ergodic) capacity and the average bit error rate of a log-normal free space optical channel in the cases of weak to moderate atmospheric turbulence conditions. We investigate the average capacity, the average bit error rate and the outage probability of free space optical communication channels using the frequentist and the Bayesian approach. Emphasis is given on the cases of weak to moderate atmospheric turbulence leading to channels modeled by log-normal distributed intensity fading. Furthermore, accurate approximate closed-form expressions and estimation procedures for their achievable capacity as well as their bit error rate and the important parameters of interest are derived. The derived approximate analytical expressions are verified by various numerical examples and simulations. Moreover, each methodology is reviewed in terms of their analytic convenience and their accuracy is also discussed.

Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model

Abstract: This paper is concerned with the problem of delay-dependent guaranteed cost control for uncertain two-dimensional (2-D) state delay systems described by the Fornasini and Marchesini (FM) second state-space model. Given a scalar α ∈ ( 0 , 1 ) , a sufficient condition for the existence of delay-dependent guaranteed cost controllers is given in terms of a linear matrix inequality (LMI) based on a summation inequality for 2-D discrete systems. A convex optimization problem is proposed to design a state feedback controller stabilizing the 2-D state delay system as well as achieving the least guaranteed cost for the resulting closed-loop system. Finally, the simulation example of thermal processes is given to illustrate the effectiveness of the proposed result.

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

Abstract: In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H ∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.