Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2014"
TL;DR: The paper surveys mathematical tools required for stability and convergence analysis of modern sliding mode control systems and the generalized Lyapunov theorems for stability analysis and convergence time estimation are presented.
Abstract: The paper surveys mathematical tools required for stability and convergence analysis of modern sliding mode control systems. Elements of Filippov theory of differential equations with discontinuous right-hand sides and its recent extensions are discussed. Stability notions (from Lyapunov stability (1982) to fixed-time stability (2012)) are observed. Concepts of generalized derivatives and non-smooth Lyapunov functions are considered. The generalized Lyapunov theorems for stability analysis and convergence time estimation are presented and supported by examples from sliding mode control theory.
303 citations
TL;DR: An adaptive second order terminal sliding mode (SOTSM) controller is proposed for controlling robotic manipulators where instead of the normal control input, its time derivative is used in the proposed controller.
Abstract: In this paper an adaptive second order terminal sliding mode (SOTSM) controller is proposed for controlling robotic manipulators. Instead of the normal control input, its time derivative is used in the proposed controller. The discontinuous sign function is contained in the derivative control and the actual control obtained after integration is continuous and hence chatterless. An adaptive tuning method is utilized to deal with the system uncertainties whose upper bounds are not required to be known in advance. The performance of the proposed control strategy is evaluated through the control of a two-link rigid robotic manipulator. Simulation results demonstrate the effectiveness of the proposed control method.
222 citations
TL;DR: An overview of recent developments in modeling and control methods of microgrid as well as presenting the reason towards incorporating MG into the existing grid are presented.
Abstract: A microgrid (MG) is a building block of future smart grid, it can be defined as a network of low voltage power generating units, storage devices and loads. System of systems (SoS) is another concept involving large scale integration of various systems. In this paper, we provide an overview of recent developments in modeling and control methods of microgrid as well as presenting the reason towards incorporating MG into the existing grid. Various SoS control strategies when applied to MG are discussed.
222 citations
TL;DR: Within this framework, most of the popular high-order sliding mode control schemas are analysed and some recently obtained results about homogeneity for differential inclusions and robustness with respect to perturbations in the context of input-to-state stability are stressed.
Abstract: The paper is reviewing the tools to handle high-order sliding mode design and robustness. The main ingredient is homogeneity which can be checked using an algebraic test and which helps us in obtaining one of the most desired properties in sliding mode control that is finite-time stability. This paper stresses some recently obtained results about homogeneity for differential inclusions and robustness with respect to perturbations in the context of input-to-state stability. Lastly within this framework, most of the popular high-order sliding mode control schemas are analysed.
178 citations
TL;DR: The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses.
Abstract: In this paper, the pth moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching is investigated. Based on the Lyapunov function, Dynkin formula and Razumikhin technique with stochastic version as well as stochastic analysis theory, many new sufficient conditions are derived to ensure the pth moment exponential stability of the trivial solution. The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses. Moreover, our results generalize and improve some results obtained in the literature. Finally, a numerical example and its simulations are given to illustrate the theoretical results.
161 citations
TL;DR: Based on Lyapunov stability theory and linear matrix inequalities method, some new stability criteria are presented and the lower bounds and upper bounds of the neutral-delay and discrete-delay are considered, which will obtain some less conservative stability analysis results.
Abstract: This paper investigates the problem of robust stability for neutral type system with mixed delays and time-varying structured uncertainties. Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method, some new stability criteria are presented. The difference between this paper and other existing results is that the lower bounds and upper bounds of the neutral-delay and discrete-delay are considered, which will obtain some less conservative stability analysis results. Several numerical examples are given to demonstrate the effectiveness and merit of the proposed results.
124 citations
TL;DR: Improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms.
Abstract: In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.
123 citations
TL;DR: An approach based on non-quadratic Lyapunov functions and S-procedure is proposed in terms of strict LMI for uncertain T–S fuzzy models in order to reduce the conservatism of results developed using quadratic method.
Abstract: This paper deals with the problem of robust stability and robust stabilization for a class of continuous-time singular Takagi–Sugeno fuzzy systems. Sufficient conditions on stability and stabilization are proposed in terms of strict LMI (Linear Matrix Inequality) for uncertain T–S fuzzy models. In order to reduce the conservatism of results developed using quadratic method, an approach based on non-quadratic Lyapunov functions and S-procedure is proposed. Illustrative examples are given to show the effectiveness of the given results.
113 citations
TL;DR: The proposed control scheme is designed for the follower quadcopter to keep the specified formation shape and avoid the obstacles during flight and is proved to be stable, computationally feasible and able to reach the desired formation configuration in finite time.
Abstract: This paper presents an integrated and practical control strategy to solve the leader–follower quadcopter formation flight control problem. To be specific, this control strategy is designed for the follower quadcopter to keep the specified formation shape and avoid the obstacles during flight. The proposed control scheme uses a hierarchical approach consisting of model predictive controller (MPC) in the upper layer with a robust feedback linearization controller in the bottom layer. The MPC controller generates the optimized collision-free state reference trajectory which satisfies all relevant constraints and robust to the input disturbances, while the robust feedback linearization controller tracks the optimal state reference and suppresses any tracking errors during the MPC update interval. In the top-layer MPC, two modifications, i.e. the control input hold and variable prediction horizon, are made and combined to allow for the practical online formation flight implementation. Furthermore, the existing MPC obstacle avoidance scheme has been extended to account for small non-apriorily known obstacles. The whole system is proved to be stable, computationally feasible and able to reach the desired formation configuration in finite time. Formation flight experiments are set up in Vicon motion-capture environment and the flight results demonstrate the effectiveness of the proposed formation flight architecture.
110 citations
TL;DR: A novel control scheme combining disturbance observer technique and back-stepping method is proposed for a class of nonlinear system with multiple mismatched disturbances and it is shown that the system output asymptotically converges to zero in spite of existing multiple mismatchatched disturbances.
Abstract: A novel control scheme combining disturbance observer technique and back-stepping method is proposed for a class of nonlinear system with multiple mismatched disturbances. The uncertain multiple mismatched disturbances contain not only single harmonic or constant disturbances but also another unexpected nonlinear signal presented as a nonlinear function. The composite adaptive disturbance observers are designed to estimate the disturbances with partial known information. By integrating disturbance observer based control with back-stepping method, a composite controller is designed. Here, the disturbance estimations are introduced into the design of virtual control laws in each step to compensate the mismatched disturbances. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in spite of existing multiple mismatched disturbances. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed method.
99 citations
TL;DR: This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control and proposes some consensus criteria to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently.
Abstract: This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.
TL;DR: An active fault-tolerant control system (AFTCS) is developed as an extension of the gain-scheduled proportional-integral control system based on fuzzy gain scheduling (FGS) technique for multi-input and multi-output wind turbine system.
Abstract: Advanced fault detection and accommodation schemes are required for ensuring efficient and reliable operation of modern wind turbines. This paper presents a novel approach in designing a fault detection and diagnosis (FDD) and fault-tolerant control (FTC) scheme for a wind turbine using fuzzy modeling, identification and control techniques. First, an improved gain-scheduled proportional-integral (PI) control system based on fuzzy gain scheduling (FGS) technique for multi-input and multi-output wind turbine system is designed. Then, to accommodate sensor faults and based on a signal correction algorithm, an active fault-tolerant control system (AFTCS) is developed as an extension of the gain-scheduled PI control system. The AFTCS exploits the fault information from a model-based FDD scheme developed using fuzzy modeling and identification method. The proposed schemes are evaluated by a series of simulations on a well-known large off-shore wind turbine benchmark in the presence of wind turbulences, measurement noises, and different realistic fault scenarios. All results indicate high effectiveness and robustness of the designed control systems in both fault-free and faulty operations of the wind turbine.
TL;DR: The proposed controller is designed based on strict-positive-real (SPR) Lyapunov stability theory to ensure the asymptotic stability of the closed-loop system.
Abstract: This paper deals with the problem of adaptive output feedback neural network controller design for a SISO non-affine nonlinear system. Since in practice all system states are not available in output measurement, an observer is designed to estimate these states. In comparison with the existing approaches, the current method does not require any information about the sign of control gain. In order to handle the unknown sign of the control direction, the Nussbaum-type function is utilized. In order to approximate the unknown nonlinear function, neural network is firstly exploited, and then to compensate the approximation error and external disturbance a robustifying term is employed. The proposed controller is designed based on strict-positive-real (SPR) Lyapunov stability theory to ensure the asymptotic stability of the closed-loop system. Finally, two simulation studies are presented to demonstrate the effectiveness of the developed scheme.
TL;DR: A new Fault Tolerant Control methodology for a class of LPV descriptor systems that are represented under a polytopic LPV form to compensate the effects of time-varying or constant actuator faults by designing an Adaptive Polytopic Observer (APO) which is able to estimate both the states of the system and the magnitude of the actuators faults.
Abstract: This paper presents a new Fault Tolerant Control (FTC) methodology for a class of LPV descriptor systems that are represented under a polytopic LPV form. The aim of this FTC strategy is to compensate the effects of time-varying or constant actuator faults by designing an Adaptive Polytopic Observer (APO) which is able to estimate both the states of the system and the magnitude of the actuator faults. Based on the information provided by this APO, a new state feedback control law is derived in order to stabilize the system. Stability conditions of the designed observer and the state-feedback control are provided and solved through a set of Linear Matrix Inequalities (LMI) under equality constraints. The performance of the proposed Fault Tolerant Control scheme is illustrated using a two-phase flash system.
TL;DR: In this article, an active disturbance rejection control (ADRC) scheme is applied to guarantee the state variables of the closed loop system to converge to the reference state with the help of the extended state observer by estimating the inertia uncertainty and external disturbance.
Abstract: The problem of position tracking for a tank gun control system with inertia uncertainty and external disturbance is investigated in this paper. The tank gun control system, demanding high tracking precision and stabilization precision, is a nonlinear system. Classical control methods are commonly used in the actual system, which is difficult to ensure high precision and high disturbance rejection capability. An active disturbance rejection control (ADRC) scheme is applied to guarantee the state variables of the closed loop system to converge to the reference state with the help of the extended state observer by estimating the inertia uncertainty and external disturbance. The basic theory of the ADRC is introduced here. According to the mathematical model, the parameters of ADRC are designed. Also, simulation results show that ADRC controller has advantages of high precision and high disturbance rejection ability. A comparison between ADRC and PID is also presented to show the effectiveness of the ADRC control strategy.
TL;DR: It is shown that separate design of the state feedback and the estimator results in the stability of the overall closed-loop system, and the input-to-state stability (ISS) gain for the closed- loop system is obtained and a procedure for minimizing it is given.
Abstract: In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the estimate of fault is used to compensate for the effect of the fault. By using the estimate of fault and the states, a fault tolerant controller using a PWL state feedback is designed. The observer-based fault-tolerant controller is obtained by the interconnection of the estimator and the state feedback controller. We show that separate design of the state feedback and the estimator results in the stability of the overall closed-loop system. In addition, the input-to-state stability (ISS) gain for the closed-loop system is obtained and a procedure for minimizing it is given. All of the design conditions are formulated in terms of linear matrix inequalities (LMI) which can be solved efficiently. Also, performance of the estimator and the state feedback controller are minimized by solving convex optimization problems. The efficiency of the method is demonstrated by means of a numerical example.
TL;DR: The problem of how to design a controller such that the state of the resulting closed-loop system is contained in a prescribed ellipsoid is studied and sufficient conditions for the solvability of the control synthesis problem are obtained.
Abstract: This paper is concerned with the problems of reachable set estimation and state-feedback controller design for linear systems with distributed delays and bounded disturbance inputs. The disturbance inputs are assumed to be either unit-energy bounded or unit-peak bounded. First, based on the Lyapunov–Krasovskii functional approach and the delay-partitioning technique, delay-dependent conditions for estimating the reachable set of the considered system are derived. These conditions guarantee the existence of an ellipsoid that contains the system state under zero initial conditions. Second, the reachable set estimation is taken into account in the controller design. Here, the purpose is to determine an ellipsoid and find a state-feedback controller such that the determined ellipsoid contains the reachable set of the resulting closed-loop system. Sufficient conditions for the solvability of the control synthesis problem are obtained. Based on these results, the problem of how to design a controller such that the state of the resulting closed-loop system is contained in a prescribed ellipsoid is studied. Finally, numerical examples and simulation results are provided to show the effectiveness of the proposed analysis and design methods.
TL;DR: The finite-time synchronization between two complex dynamical networks via the periodically intermittent adaptive control and the intermittently intermittent feedback control is studied.
Abstract: In this paper, the finite-time synchronization between two complex dynamical networks via the periodically intermittent adaptive control and the periodically intermittent feedback control is studied. The finite-time synchronization criteria are derived based on finite-time stability theory, the differential inequality and the analysis technique. Since the traditional synchronization criteria for some models are improved in the convergence time by using the novel periodically intermittent adaptive control and periodically intermittent feedback control, the results of this paper are important. Numerical examples are finally presented to illustrate the effectiveness and correctness of the theoretical results.
TL;DR: Several new results are established to express the structures and bounds of the eigenvalues related to the symmetric positive definite matrices and a family of iterative algorithms are presented for the matrix equation AX=F and the coupled Sylvester matrix equations.
Abstract: In this paper, we discuss the properties of the eigenvalues related to the symmetric positive definite matrices Several new results are established to express the structures and bounds of the eigenvalues Using these results, a family of iterative algorithms are presented for the matrix equation AX=F and the coupled Sylvester matrix equations The analysis shows that the iterative solutions given by the least squares based iterative algorithms converge to their true values for any initial conditions The effectiveness of the proposed iterative algorithm is illustrated by a numerical example
TL;DR: Finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates by constructing the suitable stochastic Lyapunov–Krasovskii functional using finite-time stability theorem, inequality techniques and the pinning control technique.
Abstract: In this paper, finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite-time stability theorem, inequality techniques and the pinning control technique, several sufficient criteria have been proposed to ensure the finite-time synchronization for the MJCNs with or without time delays. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, this paper has important theory significance and practical application value. Finally, numerical simulations illustrated by mode jumping from one mode to another according to a Markovian chain with partially unknown transition probability verify the effectiveness of the proposed results.
TL;DR: An adaptive compensation control scheme is developed via disturbance observer and quantum information technology for the four-rotor helicopter, which can handle the control problems of helicopter's attitude with the unknown actuator failures and external disturbance effectively.
Abstract: In this paper, an adaptive compensation control scheme is developed via disturbance observer and quantum information technology for the four-rotor helicopter, which can handle the control problems of helicopter's attitude with the unknown actuator failures and external disturbance effectively. Both the digital simulations and the semi-physical simulations in a Quanser 3-DOF hover platform illustrate the effectiveness of the proposed compensation control scheme.
TL;DR: A high gain observer with multiple sliding modes for simultaneous state and fault estimations for MIMO nonlinear systems and does not impose the small-Lipschitz-constant condition on the system nonlinearity.
Abstract: This paper develops a high gain observer with multiple sliding modes for simultaneous state and fault estimations for MIMO nonlinear systems. The novelty lies in the observer design that employs the combination of high-gain observer and sliding mode observer. The proposed observer does not impose the small-Lipschitz-constant condition on the system nonlinearity. By imposing a structural assumption on the nonlinear fault distribution matrix, the observability of the faults/unknown inputs w.r.t. the outputs is safeguarded and sliding modes are utilized for their reconstruction. The reconstruction of the faults from the sliding mode only relies on the output estimation error and thus can be implemented online together with the state estimation. Finally, an application to flexible joint robotic arm is used to illustrate the proposed method.
TL;DR: This work investigates the existence of solutions for a nonlinear fractional q-difference integral equation (q-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions.
Abstract: We investigate the existence of solutions for a nonlinear fractional q-difference integral equation (q-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions. Our results are based on some classical fixed point theorems. An illustrative example is also presented.
TL;DR: To decrease the feedback control gains, the idea of adaptive control scheme and the improved Halanay inequality are combined together, and the verified conditions are further weakened, to guarantee the asymptotic synchronization of the complex network under study.
Abstract: In this paper, the synchronization control problem is considered for the delayed hybrid-coupled heterogeneous networks, i.e., complex networks with nonidentical dynamical nodes. Some effective control schemes are designed under which the whole network is globally asymptotically synchronized to an arbitrary objective trajectory. By imposing the open-loop control on the whole network together with the feedback control only on a small fraction of the nodes, an easy-to-verify sufficient condition is derived to guarantee the asymptotic synchronization of the complex network under study. Furthermore, to decrease the feedback control gains, the idea of adaptive control scheme is combined together, and the verified conditions are further weakened. Finally, by introducing the impulses to the open-loop network and using the improved Halanay inequality, other novel synchronization criteria are developed for the complex network. Comparisons of the obtained theoretical results as well as the detail pinning schemes are also given. Numerical examples of the undirected scale-free network and the directed small-world network are illustrated to demonstrate the applicability and efficiency of the proposed theoretical results.
TL;DR: A robust quasi-min–max model predictive control algorithm for a class of nonlinear systems described by linear parameter varying (LPV) systems subject to input constraints and unknown but bounded disturbances is presented.
Abstract: This paper presents a robust quasi-min–max model predictive control algorithm for a class of nonlinear systems described by linear parameter varying (LPV) systems subject to input constraints and unknown but bounded disturbances. The proposed control algorithm solves a semi-definite programming problem that explicitly incorporates a finite horizon cost function and linear matrix inequalities (LMI) constraints. For the purpose of the recursive feasibility of the optimization, the dual-mode approach is implied. Input-to-state stability (ISS) and quasi-min–max MPC are combined to achieve the closed-loop ISS of the controller with respect to the disturbance in LMI paradigm. Two examples of continuous stirred tank reactor (CSTR) and couple-mass-spring system are used to demonstrate the effectiveness of the proposed results.
TL;DR: The proposed adaptive SMC does not require any a priori knowledge of the uncertainty bounds and therefore offers significant advantages over the non-adaptive schemes of SMC design.
Abstract: This paper proposes an adaptive scheme of designing sliding mode control (SMC) for affine class of multi-input multi-output (MIMO) nonlinear systems with uncertainty in the systems dynamics and control distribution gain. The proposed adaptive SMC does not require any a priori knowledge of the uncertainty bounds and therefore offers significant advantages over the non-adaptive schemes of SMC design. The closed loop stability conditions are derived based on Lyapunov theory. The effectiveness of the proposed approach is demonstrated via simulations considering an example of a two-link robot manipulator and has been found to be satisfactory.
TL;DR: New less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay are presented and the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions.
Abstract: This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.
TL;DR: In this paper, a mode-dependent average dwell time (MDADT) method was used for finite-time H ∞ control problem for a class of switched linear systems.
Abstract: This paper is concerned with finite-time H ∞ control problem for a class of switched linear systems by using a mode-dependent average dwell time (MDADT) method. The switching signal used in this paper is more general than the average dwell time (ADT), in which each mode has its own ADT. By combining the MDADT and Multiple Lyapunov Functions (MLFs) technologies, some sufficient conditions, which can guarantee that the corresponding closed-loop system is finite-time bounded with a prescribed H ∞ performance, are derived for the switched systems. Moreover, a set of mode-dependent dynamic state feedback controllers are designed. Finally, two examples are given to verify the validity of the proposed approaches.
TL;DR: A fuzzy sliding mode governor based on the sliding mode control (SMC) and the fuzzy logic and series of numerical simulations prove that the hydro-turbine governing system can maintain a better operation station under the designed governor.
Abstract: In this paper, we introduce a novel model of a hydro-turbine system with the effect of surge tank based on state-space equations to study the nonlinear dynamical behaviors of the hydro-turbine system. The critical points of Hopf bifurcation and the relationship of the stability satisfying with the adjustment coefficients are obtained from direct algebraic criterion. Furthermore, the bifurcation diagrams and Lyapunov exponents are presented and analyzed. The dynamical behaviors of the points with representative characteristics are identified and studied in detail. Both theoretical analysis and numerical simulations show that chaotic oscillations, which cannot stabilize the system, may occur with the changes of adjustment coefficients. To control the undesirable chaotic behaviors in this system, fuzzy sliding mode governor based on the sliding mode control (SMC) and the fuzzy logic are designed, and considering the bounded disturbance. Finally, series of numerical simulations are presented to verify the effectiveness of the proposed governor, which prove that the hydro-turbine governing system can maintain a better operation station under the designed governor.
TL;DR: By combining adaptive controller and PD controller together, a protocol for the heterogeneous system with unknown parameters (in the nonlinear EL dynamics) is designed and the stability of the controllers is proved.
Abstract: In this paper, we consider the consensus problem of a class of heterogeneous multi-agent systems composed of the linear first-order and second-order integrator agents together with the nonlinear Euler–Lagrange (EL) agents. First, we propose a distributed consensus protocol under the assumption that the parameters of heterogeneous system are exactly known. Sufficient conditions for consensus are presented and the consensus protocol accounting for actuator saturation is developed. Then, by combining adaptive controller and PD controller together, we design a protocol for the heterogeneous system with unknown parameters (in the nonlinear EL dynamics). Based on graph theory, Lyapunov theory and Barbalat's Lemma, the stability of the controllers is proved. Simulation results are also provided to illustrate the effectiveness of the obtained results.