Nonlinear and Robust Control Schemes for Offshore Steel Jacket Platforms

This paper presents two control schemes to control the dynamicresponse of an offshore steel jacket platform due to wave-inducedforces. The objective of the controllers is to greatly reduce theinternal system oscillations and to obtain a smooth response ofthe steel jacket platform when subjected to nonlinear self-excitedhydrodynamic forces. The first controller is a nonlinearcontroller whose design is based on Lyapunov theory. The secondcontroller is a robust state feedback linear controller whosedesign is based on an optimal control approach. Both controlschemes guarantee the asymptotic stability of the system. Thetheoretical developments are illustrated through simulationresults of the proposed control schemes. Furthermore, theperformance of the offshore steel jacket platform is presentedwhen a direct velocity feedback controller is applied to thesystem. It is found that the performance of the system with theproposed controllers is better than the performance of the systemwith the direct velocity feedback controller.     

Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.     

Truncated predictor stabilization control for interconnected nonlinear systems with time-varying input delay

This paper deals with control design for interconnected nonlinear systems with time-varying input delay. Based on the truncated prediction of the system state over the delay period, the state feedback control law is constructed. In the framework of the Lyapunov–Krasovskii function, the stability equations of closed-loop system under state feedback law are established, and the feasibility of the controller is transformed into the problem of establishing a set of linear matrix inequality (LMI) conditions. Based on the Lyapunov stability theorem, it is proved that the closed-loop system is asymptotically stable. Finally, a simulation example is provided to demonstrate the effectiveness of the control scheme.

     

Fuzzy adaptive output feedback control for robotic systems based on fuzzy adaptive observer

In this paper, a fuzzy adaptive output feedback control scheme based on fuzzy adaptive observer is proposed to control robotic systems with parameter uncertainties and external disturbances. It is supposed that only the joint positions of the robotic system can be measured, whereas the joint velocities are unknown and unmeasured. First, a fuzzy adaptive nonlinear observer is presented to estimate the joint velocities of robotic systems, and the observation errors are analyzed using strictly positive real approach and Lyapunov stability theory. Next, based on the observed joint velocities, a fuzzy adaptive output feedback controller is developed to guarantee stability of closed-loop system and achieve a certain tracking performance. Based on the Lyapunov stability theorem, it is proved that all the signals in closed-loop system are bounded. Finally, simulation examples on a two-link robotic manipulator are presented to show the efficiency of the proposed method.     

Discrete adaptive fuzzy control for asymptotic tracking of robotic manipulators

This paper presents a novel discrete adaptive fuzzy controller for electrically driven robot manipulators. It addresses how to overcome the nonlinearity, uncertainties, discretizing error and approximation error of the fuzzy system for asymptotic tracking control of robotic manipulators. The proposed controller is model-free in the form of discrete Mamdani fuzzy controller. The parameters of fuzzy controller are adaptively tuned using an adaptive mechanism derived by stability analysis. A robust control term is used to compensate the approximation error of the fuzzy system for asymptotic tracking of a desired trajectory. The controller is robust against all uncertainties associated with the robot manipulator and actuators. It is easy to implement since it requires only the joint position feedback. Compared with fuzzy controllers which employ all states to guarantee stability, the proposed controller is very simpler. Stability analysis and simulation results show its efficiency in the tracking control.     

Backstepping-based Lyapunov redesign control of hysteretic single degree-of-freedom structural systems

This paper considers the problem of active control design for a hysteretic single-degree-of-freedom (SDOF) structural system which is exposed to an earthquake excitation. First, backstepping-based control is used to design a controller for the structural system neglecting the effect of the earthquake disturbance. Then, Lyapunov redesign is utilized to design a robust controller for the system in the presence of the earthquake excitation. The hysteretic part of the structural system is modeled by the well-known Bouc–Wen equation, and this equation is directly utilized in the controller design. The controller is proposed for two cases: (a) when the parameters of the structure and the Bouc–Wen model are known, and (b) when these parameters are uncertain. A Lyapunov function is introduced for the closed-loop system, which guarantees the stability of the system equilibrium point. Since the controllers use the nominal and/or minimum and maximum values of the system parameters, the proposed methods are model based. Numerical evaluations are conducted to show the effectiveness of the proposed method. Seven different earthquakes are considered as the external excitations. Simulation results show that the displacement, velocity, and acceleration responses of the controlled structure are reduced significantly compared to the uncontrolled structure.     

Adaptive neural network-based saturated control of robotic exoskeletons

In this paper, novel adaptive neural network (NN) controllers with input saturation are presented for n-link robotic exoskeletons. The controllers consist of a state feedback controller and an output feedback controller. Through utilizing auxiliary dynamics, the controllers provide a new framework for input saturated control of these robotic systems which can feature the global stability for state feedback control. To compensate for the unknown dynamics of the system, adaptive schemes based on NNs are exploited. Furthermore, adaptive robust terms are utilized to deal with unknown external disturbances. Stability studies show that the closed-loop system is globally uniformly ultimately bounded (UUB) with the state feedback controller, where the global property of the NN-based controller is achieved exploiting a smooth switching function and a robust control term. Also, the system is semi-globally UUB with the output feedback controller. Effectiveness of the controllers is validated by simulations and experimental tests.     

Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics

This paper addresses the problems of observer design and output feedback stabilization for a class of nonlinear multivariable systems, where the nonlinear system dynamics are described by ordinary differential equations (ODEs), and the sensor dynamics are governed by diffusion partial differential equations (PDEs). Based on the Luenberger observer theory, a Luenberger-type PDE-ODE cascaded observer is derived to estimate the state variables of the system. Then, an observer-based output feedback stabilizing controller is developed. The exponential stability of both the observer error system and closed-loop control system is proven via the Lyapunov direct method. Finally, numerical examples are provided to illustrate the effectiveness of the proposed design methods.     

Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology

For the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults, a fuzzy controller based on command filtered and event-triggered technology is designed to improve the tracking error of the system. Concurrently, a fault-tolerant control scheme is introduced to effectively solve the problem of sudden output sensor failure. Additionally, the proposed controller can also greatly avoid complexity explosion problem of derivations of virtual control laws, which makes the design of the controller simpler. Furthermore, an effective observer is designed to solve the problem of system state immeasurability. Therefore, the proposed control scheme makes the design of the controller more convenient and flexible. According to Lyapunov stability theory, it is proved that all closed-loop signals are uniformly and ultimately bounded. Finally, two simulation examples of second-order nonlinear system and single-link robot show the effectiveness of the proposed scheme.

     

Control and synchronization for a class of new chaotic systems via linear feedback

This paper presents a class of new chaotic systems containing two system parameters and a nonlinear term. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and spectrum of Lyapunov exponents. Based on Lyapunov stability criteria, the simple sufficient conditions for the design of appropriate linear state feedback controllers to stabilize and synchronize globally the new chaotic systems are presented.     

A novel adaptive fuzzy sliding-mode controller for uncertain chaotic systems

This paper is concerned with the stabilization problem for a class of uncertain chaotic systems. Based on a set of linguistic rules, a novel variable universe fuzzy sliding-mode control approach is designed to improve the robustness and the stability of system. Based on Lyapunov stability theory, the overall closed-loop system is shown to be stable. The designed controller not only can control the uncertain chaotic system to a desired state, but also the control action is smooth without chattering. Simulation examples are presented to further illustrate the advantage of the proposed method.     

Control of friction oscillator by Lyapunov redesign based on delayed state feedback

Abstract The stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated by proposing a controller design method. Firstly a sufficient condition of the stability for the nominal system with delayed state feedback is derived by constructing a Lyapunov-Krasovskii function. The delayed feedback gain matrix is calculated by applying linear matrix inequality method. Secondly on the basis of the delayed state feedback, a continuous function is designed by Lyapunov redesign to ensure that the solutions of the friction oscillator system are ultimately bounded under the overall control. Moreover, the ultimate bound can be adjusted in practice by choosing appropriate parameter. Accordingly friction-induced vibration or instability can be controlled effectively. Numerical results show that the pro- posed method is valid.     

A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems

In this paper, a projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive controller is investigated for a projective synchronization of uncertain multivariable chaotic systems. The adaptive fuzzy-logic systems are used to approximate the unknown functions. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the synchronization errors to an adjustable region. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.     

Chaotic synchronization of Rikitake system based on T-S fuzzy control techniques

This paper studies the chaos synchronization of the Rikitake system based on Takagi–Sugeno fuzzy control techniques. By employing the Lyapunov function and linear matrix inequality approach, the fuzzy controller design is presented to synchronize the two identical Rikitake systems. Finally, numerical results and simulations are given to demonstrate the advantages of the proposed results.     

Seismic-vibration mitigation of a nonlinear structural system with an ATMD through a fuzzy PID controller

This paper discusses the design of fuzzy PID type controllers (FPIDC) to improve seismic control performance of a nonlinear structural system with an active tuned mass damper (ATMD) against earthquakes. Since structural systems have nonlinearities and uncertainties, fuzzy-based controllers are adequate because of their robust character and satisfactory performance in active structural control. The main advantages of this controller are the ability to handle nonlinearities and uncertainties effectively. In the literature, various structures for fuzzy PID (including PI and PD) controllers have been proposed. In order to obtain proportional, integral and derivative control actions altogether, it is intuitive and convenient to combine PI and PD actions to form a fuzzy PID controller. The simulated system has fifteen degrees of freedom and is modeled using nonlinear behavior of the base–structure interaction. The system is then simulated against the ground motion of the Northridge earthquake (M _w =6.7) in USA on 17 January, 1994. Finally, the time history of the storey displacements, accelerations, ATMD displacements, control voltage and frequency responses of both the uncontrolled and controlled cases are presented. The ground motion recorded of the El-Centro and Kocaeli earthquakes has been used to evaluate the effectiveness of the proposed control algorithm. The robustness of the controller has been checked through the uncertainty in stiffness of the structure. Simulation results exhibit that superior vibration suppression is achieved by the use of designed fuzzy PID type controllers.     

Adaptive control for synchronization of a four-dimensional chaotic system via a single variable

This paper studies the control for synchronization of a four-dimensional system via a single variable, and a linear feedback controller and an adaptive controller are proposed. Based on the Lyapunov stability theory, the correctness of the proposed methods is strictly demonstrated. The numerical simulations further show their effectiveness.     

Synchronization and stabilization of fractional order nonlinear systems with adaptive fuzzy controller and compensation signal

In this paper, a direct adaptive fuzzy controller with compensation signal is presented to control and stabilize a class of fractional order systems with unknown nonlinearities. Based on a Lyapunov function candidate the global Mittag–Leffler stability is proved and a new fractional order adaptation law is derived. The adaptation law adjusts free parameters of the fuzzy controller and bounds them by utilizing a novel fractional order projection algorithm. Furthermore, due to the use of compensation term, the proposed approach does not demand suitable membership functions in the fuzzy system. In addition, the stability of the closed-loop system is guaranteed by utilizing a supervisory controller. Numerical simulations show the validity and effectiveness of the introduced scheme for various fractional order nonlinear models that perturbed by disturbance and uncertainty.     

Adaptive fuzzy H ∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems

In this paper, a fuzzy logic controller equipped with training algorithms is developed such that the H ^?? tracking performance should be satisfied for a model-free nonlinear fractional order time delay system which is infinite dimensional in nature and time delay is a source of instability. In order to deal with the linguistic uncertainties caused from delay terms, the adaptive time delay fuzzy logic system is constructed to approximate the unknown time delay system functions. By incorporating Lyapunov stability criterion with H ^?? tracking design technique, the free parameters of the adaptive fuzzy controller can be tuned on line by output feedback control law and adaptive law. Moreover, the tracking error and external disturbance can be attenuated to arbitrary desired level. The numerical results show the effectiveness of the proposed adaptive H ^?? tracking scheme.     

Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms

Adaptive control of a class of uncertain multi-input/multi-output (MIMO) non-linear systems in block-triangular forms is considered in this paper. By incorporating dynamic surface approach and ??minimal learning parameters?? algorithm, a systematic procedure for the synthesis of stable adaptive fuzzy tracking controllers with less tuning parameters is developed. Takagi?CSugeno (T-S) fuzzy logic systems (FLSs) are used to approximate those unstructured system functions rather than the unknown virtual control gain functions. Consequently, the potential controller singularity problem can be overcome. Moreover, both problems of ??explosion of learning parameters?? and ??explosion of complexity?? are avoided. The computational burden has thus been greatly reduced. The stability in the sense of semi-globally uniform ultimate boundedness (SGUUB) of the closed-loop MIMO systems is established via Lyapunov stability theorem. Finally, simulation results are presented to demonstrate the effectiveness and the advantages of the proposed control approach.