Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2018"

A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

Abstract: Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.

Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems

Abstract: In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H∞, L 2 − L ∞ , Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods.

Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers

Abstract: In this paper, the globally exponential synchronization problem of dynamical networks with nonlinearly coupling function is considered. Hybrid pinning control strategies are established to force the states of the network to follow some objective trajectory. The impulsive pinning controllers are used to control a fringe of nodes at the impulsive instants, while during the impulsive instants, pinning state-feedback controllers are designed to achieve the control objective. Finally, the validity of the developed techniques is evidenced by an illustrative example.

Adaptive fractional order sliding mode controller with neural estimator

Abstract: In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.

Combined state and parameter estimation for a bilinear state space system with moving average noise

Abstract: This paper considers the identification problem of bilinear systems with measurement noise in the form of the moving average model. In particular, we present an interactive estimation algorithm for unmeasurable states and parameters based on the hierarchical identification principle. For unknown states, we formulate a novel bilinear state observer from input-output measurements using the Kalman filter. Then a bilinear state observer based multi-innovation extended stochastic gradient (BSO-MI-ESG) algorithm is proposed to estimate the unknown system parameters. A linear filter is utilized to improve the parameter estimation accuracy and a filtering based BSO-MI-ESG algorithm is presented using the data filtering technique. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system

Abstract: This article presents a novel tuning design of Proportional-Integral-Derivative (PID) controller in the Automatic Voltage Regulator (AVR) system by using Cuckoo Search (CS) algorithm with a new time domain performance criterion. This performance criterion was chosen to minimize the maximum overshoot, rise time, settling time and steady state error of the terminal voltage. In order to compare CS with other evolutionary algorithms, the proposed objective function was used in Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) algorithms for PID design of the AVR system. The performance of the proposed CS based PID controller was compared to the PID controllers tuned by the different evolutionary algorithms using various objective functions proposed in the literature. Dynamic response and a frequency response of the proposed CS based PID controller were examined in detail. Moreover, the disturbance rejection and robustness performance of the tuned controller against parametric uncertainties were obtained, separately. Energy consumptions of the proposed PID controller and the PID controllers tuned by the PSO and ABC algorithms were analyzed thoroughly. Extensive simulation results demonstrate that the CS based PID controller has better control performance in comparison with other PID controllers tuned by the PSO and ABC algorithms. Furthermore, the proposed objective function remarkably improves the PID tuning optimization technique.

Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design

Abstract: This paper is concerned with the finite-time and fixed-time synchronization of complex networks with discontinuous nodes dynamics. Firstly, under the framework of Filippov solution, a new theorem of finite-time and fixed-time stability is established for nonlinear systems with discontinuous right-hand sides by using mainly reduction to absurdity. Furthermore, for a class of discontinuous complex networks, a general control law is firstly designed. Under the unified control framework and the same conditions, the considered networks are ensured to achieve finite-time or fixed-time synchronization by only adjusting the value of a key control parameter. Based on the similar discussion, a unified control strategy is also provided to realize respectively asymptotical, exponential and finite-time synchronization of the addressed networks. Finally, the derived theoretical results are supported by an example with numerical simulations.

Recursive parameter estimation algorithm for multivariate output-error systems

Abstract: In this paper, we consider the parameter estimation issues of a class of multivariate output-error systems. A decomposition based recursive least squares identification method is proposed using the hierarchical identification principle and the auxiliary model idea, and its convergence is analyzed through the stochastic process theory. Compared with the existing results on parameter estimation of multivariate output-error systems, a distinct feature for the proposed algorithm is that such a system is decomposed into several sub-systems with smaller dimensions so that parameters to be identified can be estimated interactively. The analysis shows that the estimation errors converge to zero in mean square under certain conditions. Finally, in order to show the effectiveness of the proposed approach, some numerical simulations are provided.

Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping

Abstract: In this paper, the trajectory tracking control problem of a six-degree of freedom (6-DOF) quadrotor unmanned aerial vehicle (UAV) with input saturation is studied. Applying a hierarchical control structure, a priori-bounded control thrust and the desired orientations are derived to stabilize the translational subsystem without singularities. By using a backstepping approach with a Nussbaum function, a priori-bounded control torque for the rotational subsystem is designed to track the desired orientations generated by the translational subsystem. With the proposed control scheme, the latent singularities in the attitude extraction process caused by saturation nonlinearities are avoided, and globally uniformly ultimately bounded (UUB) stability of the closed-loop system is achieved. The tracking error bound is further determined which can be made arbitrarily small by tuning certain control gains. Numerical simulation results are provided to show the effectiveness of the proposed control scheme.

Automatic generation control of two-area electrical power systems via optimal fuzzy classical controller

Abstract: The interconnected large-scale power systems are liable to performance degradation under the presence of sudden small load demands, parameter ambiguity and structural changes. Due to this, to supply reliable electric power with good quality, robust and intelligent control strategies are extremely requisite in automatic generation control (AGC) of power systems. Hence, this paper presents an output scaling factor (SF) based fuzzy classical controller to enrich AGC conduct of two-area electrical power systems. An implementation of imperialist competitive algorithm (ICA) is made to optimize the output SF of fuzzy proportional integral (FPI) controller employing integral of squared error criterion. Initially the study is conducted on a well accepted two-area non-reheat thermal system with and without considering the appropriate generation rate constraint (GRC). The advantage of the proposed controller is illustrated by comparing the results with fuzzy controller and bacterial foraging optimization algorithm (BFOA)/genetic algorithm (GA)/particle swarm optimization (PSO)/hybrid BFOA-PSO algorithm/firefly algorithm (FA)/hybrid FA-pattern search (hFA-PS) optimized PI/PID controller prevalent in the literature. The proposed approach is further extended to a newly emerged two-area reheat thermal-PV system. The superiority of the method is depicted by contrasting the results of GA/FA tuned PI controller. The proposed control approach is also implemented on a multi-unit multi-source hydrothermal power system and its advantage is established by Correlating its results with GA/hFA-PS tuned PI, hFA-PS/grey wolf optimization (GWO) tuned PID and BFOA tuned FPI controllers. Finally, a sensitivity analysis is performed to demonstrate the robustness of the proposed method to broad changes in the system parameters and size and/or location of step load perturbation.

Improved stability conditions of time-varying delay systems based on new Lyapunov functionals

Abstract: This paper is concerned with the stability analysis of time-varying delay systems. Unlike the construction of augmented Lyapunov functional and multiple integral Lyapunov functional, novel three Lyapunov functionals are suggested which are delay product type functions and lead to less conservative results. Based on newly developed Lyapunov functionals, three stability criteria are derived and their superiority is described by three numerical examples.

Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation

Abstract: This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.

Periodic event-triggered resilient control for cyber-physical systems under denial-of-service attacks

Abstract: This paper studies the problem of designing a resilient control strategy for cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. By constructing an H∞ observer-based periodic event-triggered control (PETC) framework, the relationship between the event-triggering mechanism and the prediction error is obtained. Then, inspired by the maximum transmission interval, the input-to-state stability of the closed-loop system is proved. Compared with the existing methods, a Zeno-free periodic PETC scheme is designed for a continuous-time CPS with the external disturbance and measurement noise. In particular, the objective of maximizing the frequency and duration of the DoS attacks is achieved without losing robustness. Finally, two examples are given to verify the effectiveness of the proposed approach.

Robust fault estimation and fault-tolerant control for Markovian jump systems with general uncertain transition rates

Abstract: This paper is concerned with the problems on simultaneous actuator and sensor fault estimation as well as the fault-tolerant control for a class of Markovian jump systems subjected to faults and disturbances. Firstly, the original system is converted into a descriptor system by extending the sensor faults as auxiliary states. Secondly, an adaptive observer is designed for the descriptor system, in which the actuator faults are adjusted by the designed adaptive law. Based on the estimations of the actuator faults, a fault-tolerant control strategy is therefore proposed to stabilize the closed-loop system against actuator faults, sensor faults and disturbances. Sufficient conditions for the existence of the observer and controller are derived in accordance with linear matrix inequalities. Finally, some practical examples are delivered to illustrate the validation and effectiveness of the proposed method.

Finite-time consensus of linear multi-agent system via distributed event-triggered strategy

Abstract: In this paper, we mainly investigate the finite-time consensus problem of general linear multi-agent systems. The paper proposed a suitable event-triggered control strategy. The strategy has some desirable properties including: distributed, independent, and asynchronous. It is theoretical demonstrated that the multi-agent system can achieve consensus in a certain time regardless of the initial condition under this event-triggered control scheme. In addition, without finding singular triggering problem, we prove the feasibility of this proposed event-triggered control protocol. Finally, we put forward some simulation graphs for the sake of showing the availability of our conclusions.

Finite-time non-fragile l2−l∞ control for jumping stochastic systems subject to input constraints via an event-triggered mechanism

Abstract: In the work, the finite-time non-fragile l 2 − l ∞ control problem for jumping stochastic systems with input constraints is addressed. An event-triggered mechanism is introduced to reduce the burden of the data communications. Our goal is to design a controller which makes sure that the underlying closed-loop system could be stochastically finite-time bounded at a specified level of l 2 − l ∞ performance. By using the finite-time analysis theory, some sufficient conditions are proposed for the existence of such a desired controller. The availability of the developed method is finally explained by an illustrated example.

Graph theory-based finite-time synchronization of fractional-order complex dynamical networks

Abstract: This paper considers the finite-time synchronization problem for a class of fractional-order complex dynamical networks (FOCDNs). By utilizing the properties of fractional calculus and fractional-order comparison principle, we propose a new lemma. Base on the new lemma, some analysis techniques and algebraic graph theory method, some novel criteria are given to ensure finite-time synchronization of FOCDNs, and the upper bound of the setting time for synchronization is estimated. At last, numerical simulations are given to verify the effectiveness of the obtained results.

Robust finite-time stability of singular nonlinear systems with interval time-varying delay

Abstract: The problem of robust finite-time stability (RFTS) for singular nonlinear systems with interval time-varying delay is studied in this paper. Some delay-dependent sufficient conditions of RFTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii functional (LKF) method and singular analysis technique. Two examples are provided to show the applications of the proposed criteria.

A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks

Abstract: This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from r ( t − τ ¯ ) to r ( t k − τ ¯ ) and from r ( t − τ ¯ ) to r ( t k + 1 − τ ¯ ) . Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.

AGC of two-area electric power systems using optimized fuzzy PID with filter plus double integral controller

Abstract: The incessant swell in size, complexity, nonlinearity and structural variations in modern electric power systems, as well as rise in power demand has entailed the use of intelligent control strategies for the real-time satisfactory operation of power system. Hence, in this paper, a novel fuzzy PID with filter plus double integral (FPIDF-II) controller is proposed for automatic generation control (AGC) of two-area interconnected power systems. Initially, a well accepted two-area non-reheat thermal system is considered and the output scaling factors (SF) of FPIDF-II controller are optimized using imperialist competitive algorithm (ICA) employing an integral squared error (ISE) criterion. The supremacy of the proposed approach is demonstrated by contrasting the results with recently published optimal and various modern heuristic optimization techniques based controllers. To demonstrate the efficacy and scalability of the approach over other prevalent intelligent control techniques, the study is further extended to two-area non-reheat thermal system with governor deadband nonlinearity, two-area reheat thermal system, recently appeared two-area photovoltaic (PV)-reheat thermal system and two-area multi-source hydrothermal system. Finally, a sensitivity analysis is carried out to demonstrate the robustness of the proposed controller under broad variations in the system parameters from their nominal values.

Stability analysis of continuous-time systems with time-varying delay using new Lyapunov–Krasovskii functionals

Abstract: This paper studies the stability of linear continuous-time systems with time-varying delay by employing new Lyapunov–Krasovskii functionals. Based on the new Lyapunov–Krasovskii functionals, more relaxed stability criteria are obtained. Firstly, in order to coordinate with the use of the third-order Bessel-Legendre inequality, a proper quadratic functional is constructed. Secondly, two couples of integral terms { ∫ t − h t s x ( s ) d s , ∫ s t x ( s ) d s } and { ∫ t − h M s x ( s ) d s , ∫ s t − h t x ( s ) d s } are involved in the integral functionals ∫ t − h t t ( · ) d s and ∫ t − h M t − h t ( · ) d s , respectively, so that the coupling information between them can be fully utilized. Finally, two commonly-used numerical examples are given to demonstrate the effectiveness of the proposed method.

A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems

Abstract: In this paper, a new direct method based on the Chebyshev cardinal functions is proposed to solve a class of variable-order fractional optimal control problems (V-OFOCPs). To this end, a new operational matrix (OM) of variable-order (V-O) fractional derivative in the Caputo sense is derived for these basis functions and is used to obtain an approximate solution for the problem under study. In the proposed method, the state and the control variables are expanded in terms of the Chebyshev cardinal functions with unknown coefficients, at first. Then, the OM of V-O fractional derivative and some properties of the Chebyshev cardinal functions are employed to achieve a nonlinear algebraic equation corresponding to the performance index and a nonlinear system of algebraic equations corresponding to the dynamical system in terms of the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations derived from the given dynamical system and the initial conditions to the performance index by a set of undetermined Lagrange multipliers. As a result, the necessary conditions of optimality are derived as a system of algebraic equations in the unknown coefficients of the state variable, control variable, and Lagrange multipliers. Furthermore, some numerical examples of different types are demonstrated with their approximate solutions for confirming the high accuracy and applicability of the proposed method.

A new approach for the nonlinear fractional optimal control problems with external persistent disturbances

Abstract: The aim of this manuscript is to investigate an efficient iterative approach for the nonlinear fractional optimal control problems affected by the external persistent disturbances. For this purpose, first the internal model principle is employed to transform the fractional dynamic system with disturbance into an undisturbed system with both integer- and fractional-order derivatives. The necessary optimality conditions are then reduced into a sequence of linear algebraic equations by using a series expansion approach and the Grunwald–Letnikov approximation for the fractional derivatives. The convergence of the latter sequence to the optimal solution is also studied. In addition, an iterative algorithm designing the suboptimal control law is presented. Numerical simulations confirm that the new approach is efficient to reject the external disturbance and provides satisfactory results compared to the other existing methods.

Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense

Abstract: In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.

Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty

Abstract: In this paper, we investigate the problem of finite-time stabilization of time-varying delayed neural networks with uncertainty. By employing the Lyapunov approach and linear matrix inequalities (LMIs), two different memory controllers are derived to achieve the finite-time stabilization of the addressed neural networks. Moreover, the upper bound of the setting-time for stabilization can be estimated via different Lyapunov functions. Our results improve and extend some recent works. Finally, the effectiveness and feasibility of the proposed controllers are demonstrated by numerical simulations.

Advanced stability criteria for linear systems with time-varying delays

Abstract: This paper investigates a stability problem for linear systems with time-varying delays. By constructing suitable augmented Lyapunov–Krasovskii functionals, improved stability criteria under various conditions of time-varying delays are derived within the framework of linear matrix inequalities (LMIs). Moreover, to reduce the computational burden caused by the non-convex term including h2(t), how to deal with it is applied by estimating it to the convex term including h(t). Finally, three illustrative examples are given to show the effectiveness of the proposed criteria.

Robust H∞ control of an observer-based repetitive-control system

Abstract: This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.

Lag synchronization for fractional-order memristive neural networks with time delay via switching jumps mismatch

Abstract: This paper studies drive-response synchronization in fractional-order memristive neural networks (FMNNs) with switching jumps mismatch. A comparison theorem for fractional-order systems with variable order is provided first. Theories of fractional order Filippov differential inclusions are used to treat FMNNs because the parameters of FMNNs are state dependent and the FMNNs has discontinuous right hand sides. Based on Laplace transform and linear feedback control, some lag quasi-synchronization conditions are obtained with variable order α: 0

Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects

Abstract: In this paper, we investigate the asymptotic stability of fractional-order fuzzy neural networks with fixed-time impulse and time delay. According to the fractional Barbalat’s lemma, Riemann–Liouville operator and Lyapunov stability theorem, some sufficient conditions are obtained to ensure the asymptotic stability of the fractional-order fuzzy neural networks. Two numerical examples are also given to illustrate the feasibility and effectiveness of the obtained results.

Event-triggered time-varying formation control for general linear multi-agent systems

Abstract: This paper investigates event-triggered formation control problems for general linear multi-agent systems. The time-varying formation this paper studied can be described by a bounded piecewise differentiable vector-valued function. Firstly, a time-varying formation control protocol based on event-triggered scheme is constructed by the states of the neighboring agents. Each agent broadcasts its state information to neighbor nodes if the triggering condition is satisfied, and the communication load is decreased significantly. Then, an algorithm consisting of three steps is proposed to design the event-triggered formation control protocol. Moreover, it is proven that under the designed event-triggered formation protocol, the multi-agent systems can achieve the desired time-varying formation which belongs to the feasible formation set with the bounded formation error and the closed systems do not exhibit Zeno behavior. Finally, simulation results are given to demonstrate the effectiveness of the theoretical analysis.