Dead-zone Input Nonlinearity Research Articles

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.

Formula omitted] non-fragile observer-based dynamic event-triggered sliding mode control for nonlinear networked systems with sensor saturation and dead-zone input

This paper considers the problem of robust non-fragile observer-based dynamic event-triggered sliding mode control (SMC) for a class of discrete-time Lipschitz nonlinear networked control systems subject to sensor saturation and dead-zone input nonlinearity. First, an improved dynamic event-triggered scheme (DETS) in consideration of sensor saturation is proposed to reduce the number of data transmission. Next, a non-fragile observer is designed to estimate the system state, which facilitates the construction of the discrete sliding surface. By using a reformulated Lipschitz property, the error dynamics and sliding mode dynamics are modeled as a unified linear parameter varying (LPV) networked system with time-varying delays. Then, based on this model, sufficient conditions are established to guarantee the resulting closed-loop system to be asymptotically stable with a given disturbance attenuation level. Furthermore, an observer-based event-triggered SMC law is designed to drive the trajectories of the observer system onto a region near equilibrium point in a finite time in the presence of dead-zone input nonlinearity. Finally, two practical examples are employed to demonstrate the effectiveness of the proposed method.

Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics

This paper investigates adaptive finite-time practical consensus protocols for a class of second-order multiagent systems with a positive odd power, nonsymmetric input dead zone and uncertain dynamics under a directed communication topology. In this study, three major steps are employed to address the existence of the positive odd power, nonsymmetric input dead zone and uncertain dynamics. Overall, based on the technique of adding one power integrator, useful preliminary results are obtained by configuring a suitable fraction power. Furthermore, to circumvent input dead-zone nonlinearity, an adaptive fuzzy logic (FL) method is used to estimate the width of the dead zone. Finally, the difficulty in designing finite-time practical consensus protocols for the multiagent systems with uncertain dynamics is handled by using radial basis function neural networks (RBFNNs) to approximate the related unknown nonlinear functions. Then, given some reasonable assumptions, it is shown that finite-time practical consensus of the second-order multiagent systems is obtained by using the proposed distributed control protocols and adaptive laws. In addition, the proper approach for selecting parameters is provided such that the neighborhood position error and parameter estimate errors for each agent converge to predesigned small regions of the origin in a finite time. The effectiveness of the developed algorithm is finally validated through a numerical simulation.

Observer-based fractional-order adaptive type-2 fuzzy backstepping control of uncertain nonlinear MIMO systems with unknown dead-zone

A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input nonlinearity is considered in the presence of model uncertainties and external disturbances where the control scheme is constructed by combining the backstepping dynamic surface control (DSC) and fractional adaptive type-2 fuzzy technique. First, a linear state observer estimates immeasurable states. Second, the unknown nonlinear functions of the uncertain system are approximated with interval type-2 fuzzy logic systems. Third, to avoid the complication of backstepping design process, the DSC is used. Fourth, by using the fractional adaptive backstepping, fractional adaptive laws are constructed, the proposed method is applied to a class of uncertain fractional-order nonlinear MIMO system. In order to have a better control performance in reducing tracking error, the controller parameters are tuned by using the PSO algorithm. Stability of the system is proven by the Mittag-Leffler method. It is presented that the proposed design guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the zero. The simulation examples are given to show the efficiency of the proposed controller.

Adaptive type-2 fuzzy backstepping control of uncertain fractional-order nonlinear systems with unknown dead-zone

A new problem of adaptive type-2 fuzzy fractional control with pseudo-state observer for commensurate fractional order dynamic systems with dead-zone input nonlinearity is considered in presence of unmatched disturbances and model uncertainties; the control scheme is constructed by using the backstepping and adaptive technique. To avoid the complexity of backstepping design process, the dynamic surface control is used. Also, Interval type-2 Fuzzy logic systems (IT2FLS) are used to approximate the unknown nonlinear functions. By using the fractional adaptive backstepping, fractional control laws are constructed; this method is applied to a class of uncertain fractional-order nonlinear systems. In order to better control performance in reducing tracking error, the PSO algorithm is utilized for tuning the controller parameters. Stability of the system is proven by the Mittag–Leffler method. It is shown that the proposed controller guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the origin. The efficiency of the proposed method is illustrated with simulation examples.

Adaptive Neural Command Filtered Tracking Control for Flexible Robotic Manipulator With Input Dead-Zone

In this paper, an adaptive neural network (NN) command filtered tracking control method is developed for a flexible robotic manipulator with dead-zone input. To deal with the input dead-zone nonlinearity, it is viewed as a combination of a linear part and bounded disturbance-like term. The Neural networks (NNs) are used to estimate the uncertain nonlinearities appeared in the control system. By using the command filter technique, the problem of `explosion of complexity' is overcome. The proposed controller guarantees that all the closed-loop signals are bounded and the system output can track the given reference signal. The simulation results are provided to demonstrate the effectiveness of the proposed controller.

Adaptive Fuzzy Finite-time Control for Uncertain Nonlinear Systems with Dead-zone Input

This paper presents a novel adaptive finite-time tracking control scheme for nonlinear systems. During the design process of control scheme, dead-zone input nonlinearity phenomena existing in the actuator is taken into account. Fuzzy logic systems are adopted to approximate the unknown nonlinear functions. This paper provides a new finite-time stability criterion, making the adaptive tracking control scheme more suitable in the practice than traditional methods. Under the presented controller, the desired system performance is realized in finite time. Finally, the validity and effectiveness of the proposed control method is validated by two examples.

Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

This paper considers the problem of global fixed-time stabilization for a class of uncertain high-order nonlinear systems. One distinct characteristic of this work is that the system under consideration possesses the dead-zone input nonlinearity. By delicately combining the sign function with a power integrator technique, a state feedback controller is designed such that the states of the resulting closed-loop system converge to the origin within a fixed time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Improved prescribed performance control for air-breathing hypersonic vehicles with unknown deadzone input nonlinearity

An improved prescribed performance controller is proposed for the longitudinal model of an air-breathing hypersonic vehicle (AHV) subject to uncertain dynamics and input nonlinearity. Different from the traditional non-affine model requiring non-affine functions to be differentiable, this paper utilizes a semi-decomposed non-affine model with non-affine functions being locally semi-bounded and possibly in-differentiable. A new error transformation combined with novel prescribed performance functions is proposed to bypass complex deductions caused by conventional error constraint approaches and circumvent high frequency chattering in control inputs. On the basis of backstepping technique, the improved prescribed performance controller with low structural and computational complexity is designed. The methodology guarantees the altitude and velocity tracking error within transient and steady state performance envelopes and presents excellent robustness against uncertain dynamics and deadzone input nonlinearity. Simulation results demonstrate the efficacy of the proposed method.

Adaptive prescribed performance control of half-car active suspension system with unknown dead-zone input

Abstract This paper proposes a novel adaptive control scheme for half-car active suspension system (HCASS) with unknown dead-zone input. Under the proposed control framework, the overall HCASS is divided into two subsystems. The proposed controller is designed based on the first subsystem, and the second subsystem is regarded as zero dynamics of HCASS. For the first subsystem, a new robust adaptive strategy is first constructed to compensate the adverse effects of unknown dead-zone input nonlinearities. Further, in order to ensure some important state variables within the given restrictive conditions all the time, a novel prescribed performance control strategy (PPC, for short) is designed. For the second subsystem, the corresponding stability analysis of zero dynamics is presented. Finally, the solution of the resulting closed-loop system is ensured to be uniformly ultimately bounded, and the effectiveness of the proposed approach is illustrated by a strict and complete simulation analysis.

Finite-time sliding mode joint positioning error constraint control for robot manipulator in the presence of unknown deadzone

This paper proposes two tracking error constraint finite-time sliding mode control schemes for unknown manipulator parameters with deadzone input nonlinearity. A transformed filtered tracking error surface was first constructed as a separated form to guarantee the predefined tracking performance. Next, a simple transformed prescribed error surface was considered to obtain the same predefined tracking performance. Both proposed controls adopt Finite-time sliding mode control (FSMC) with a non-model-based manipulator feedforward method to achieve rapid error convergence and fast control design. Unlike conventional controls with deazone compensation, the proposed controls are robust to deadzone nonlinearity without adding extra compensators. The effectiveness of the proposed scheme was proven by simulation and experimental evaluations for an articulated manipulator system with unknown deadzone and friction.

Nussbaum-Based Adaptive Fuzzy Tracking Control of Unmanned Surface Vehicles with Fully Unknown Dynamics and Complex Input Nonlinearities

In this paper, subject to both fully unknown dynamics and complex input nonlinearities including unknown control directions and dead zones, a Nussbaum-based adaptive fuzzy trajectory tracking control scheme of an unmanned surface vehicle is addressed by combining adaptive fuzzy backstepping technique with Nussbaum approach. The dead-zone input nonlinearity is firstly divided into input-dependent functions and time-varying input coefficients which can be treated as system uncertainties. Together with disturbances, unknown dynamics and uncertainties, the lumped nonlinearity is online approximated by employing an adaptive fuzzy approximator. Within the backstepping framework, a Nussbaum gain function is further designed to tackle unknown control directions, and thereby devising an adaptive fuzzy trajectory tracking control scheme which is constructed recursively to deal with complex input nonlinearities and fully unknown dynamics. Theoretical analysis reveals that all signals of the closed-loop tracking system are bounded and tracking errors can converge to an arbitrarily small neighborhood of zero. Simulation studies demonstrate the effectiveness and superiority of the proposed approach.

Decentralized Sliding Mode Control for Multi‐Input Complex Interconnected Systems Subject to non‐smooth Nonlinearities

AbstractMany modern control systems become gradually more complicated and, consequently, the approach to control design approaches is both difficulty and complex. Moreover, if such a complex interconnected system is subjected to non‐smooth nonlinearities in the actuator, then unexpected difficulties, degradation or, even worse, instability will arise in the system performance. Therefore, a new decentralized sliding mode control (DSMC) approach for such a class of complex interconnected systems subjected to non‐smooth (deadzone) nonlinearities is proposed in this paper. Based on sliding mode control (SMC) theory, the proposed DSMC laws guarantee the global reaching condition of the sliding mode in uncertain complex interconnected systems with deadzone nonlinearities, that is, they can ensure that the sliding mode is reached in finite time and with prescribed transient behavior. In the sliding mode, the investigated uncertain complex interconnected system with deadzone nonlinearities in the actuator still are insensitive to system uncertainties and external disturbances. The proposed DSMC laws can work effectively for uncertain complex interconnected systems either with or without deadzone nonlinearities in the actuator. However, this cannot be guaranteed by the traditional DSMC design for systems without input deadzone nonlinearities. Furthermore, the sliding motion can be controlled to converge within a specified exponential speed. Finally, two illustrative examples with a series of computer simulations are presented to demonstrate the effectiveness of the proposed DSMC laws.

Adaptive Neural Control of Nonlinear Systems With Unknown Control Directions and Input Dead-Zone

This paper presents an adaptive neural control approach for nonstrict-feedback nonlinear systems in presence of unmodeled dynamics, unknown control directions and input dead-zone nonlinearity. To handle the difficulty due to uncertain control directions, Nussbaum gain functions are applied. Based on the structural characteristic of radial basis function neural networks, a backstepping-based adaptive neural control algorithm is developed. The main contributions of this paper lie in the fact that a backstepping-based neural control algorithm is developed for nonstrict-feedback nonlinear systems with unmodeled dynamics, unknown control directions and actuator dead-zone, and the total number of adaptive laws is not greater than the order of control system. As a beneficial result, the controller is much easier to be implemented in practice with less computational burden. A simulation example is given to reveal the viability of the presented approach. It is demonstrated by both theoretical analysis and simulation study that the presented control strategy ensures the semiglobally uniform ultimate boundedness of all closed-loop system signals.

Decentralised adaptive robust control schemes of uncertain large‐scale time‐delay systems with multiple unknown dead‐zone inputs

A simple design method is presented such that the decentralised adaptive robust control schemes with a relatively simple structure can be synthesised for a class of uncertain large-scale interconnected time-delay systems with multiple dead-zone inputs. It is supposed that any information on dead-zone input non-linearities is completely unknown. On the basis of adaptive technique, a self-tuning control gain function is introduced for each subsystem to construct a simple local state feedback controller which is structurally linear in the local state variables. The simple design method presented in this study might be well understood by engineering designers, and the resulting simple control schemes can be easily implemented in a number of practical engineering control problems. By combining the presented design method with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain interconnected dynamical systems with completely unknown dead-zone in the actuators. Finally, the simulations of some numerical examples are provided to show the design procedure of the presented method and to demonstrate the validity of the theoretical results.

Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity

This paper is concerned with finite-time stabilization of a class of pure-feedback systems with dead-zone input. A systematic design procedure is established to derive the finite-time controller. Firstly, to circumvent the difficulties arising from the nonaffine properties, through a change of coordinates and incorporating mean value theorem, a system transformation technique is introduced to convert the original nonaffine system into an affine one. Then, based on the strengthened finite-time Lyapunov stability theorem as well as utilizing the bounds of dead-zone parameters, the finite-time stabilizer is explicitly constructed via backstepping design approach. It is proven that the designed controller can ensure all the states of the closed-loop system converge to zero in a finite time and maintain at zero afterwards. The proposed design framework is also extended to finite-time stabilization of uncertain pure-feedback systems and finite-time tracking control of pure-feedback systems. The effectiveness of the theoretical results are finally demonstrated by a numerical example and a realistic example.

Approximation-Free Tracking Error Constraint Control for Lagrangian Systems

This paper proposes an approximation-free adaptive tracking error constraint control scheme for unknown Lagrangian systems. A transformed filtered tracking error surface has been constructed to guarantee the transient and steady-state performance of the position control of the Lagrangian systems combined with adaptive estimation laws for unknown upper bounds of the parameters of the Lagrangian systems. To obtain fast error convergence, a finite-time control has been adopted in the proposed controller. In addition, the proposed controller is effective for the constrained positioning of Lagrangian mechanical systems with unknown deadzone input nonlinearity, without requiring nonlinear approximations or identification processes for unknown parameters of dynamics and deadzone. The effectiveness of the proposed constraint control scheme has been proven by simulation and experimental evaluations for an XY table and an articulated manipulator system in the presence of unknown deadzone.

Output-Feedback Controller Based Projective Lag-Synchronization of Uncertain Chaotic Systems in the Presence of Input Nonlinearities

This paper solves the problem of projective lag-synchronization based on output-feedback control for chaotic drive-response systems with input dead-zone and sector nonlinearities. This class of the drive-response systems is assumed in Brunovsky form but with unavailable states and unknown dynamics. To effectively deal with both dead-zone and sector nonlinearities, the proposed controller is designed in a variable-structure framework. To online learn the uncertain dynamics, adaptive fuzzy systems are used. And to estimate the unavailable states, a simple synchronization error is constructed. To prove the stability of the overall closed-loop system (controller, observer, and drive-response system) and to design the adaptation laws, a Lyapunov theory and strictly positive real (SPR) approach are exploited. Finally, three academic examples are given to show the effectiveness of this proposed lag-synchronization scheme.

Adaptive fuzzy control for full states constrained systems with nonstrict-feedback form and unknown nonlinear dead zone

This paper addresses the problem of direct adaptive fuzzy tracking control design for a class of uncertain nonstrict-feedback systems with nonlinear dead zone and full state constraints. Fuzzy logic systems are used to approximate some unknown nonlinear functions and less adjustable parameters are adopted in each backstepping design process. This advantage is first to take into account the full state constrained nonstrict-feedback systems with input dead zone nonlinearity. To guarantee that the full state constraints are not violated, a novel adaptive fuzzy controller is developed by introducing Barrier Lyapunov Function with the error variables. Furthermore, it is proved that all the closed-loop signals remain semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to verify the effectiveness of the proposed control method.

A modified robust self-tuning controller for Hammerstein nonlinear systems with asymmetric deadzone input nonlinearity

This article presents a novel adaptive control method for a class of uncertain discrete-time Hammerstein nonlinear systems with asymmetric deadzone input nonlinearity and bounded external disturbance. Based on the parameterization model of Hammerstein systems, the unknown parameters are updated by a robust recursive least squares algorithm with a deadzone weighted factor. Then, by introducing an estimate of the unmodeled dynamics as a feedback, the deadzone compensating control law is derived without an adaptive deadzone inverse. Theoretical results show that all the signals in the closed-loop system are bounded and the output tracking error is convergent with a relatively small residue. To show the usefulness of the developed results, simulation examples including an electro-hydraulic servo system and a DC motor subjected to a nonlinear friction are studied.