Dead-zone Input Nonlinearity Research Articles

Two-dimensional identification of time-varying batch nonlinear processes with input dead-zone nonlinearity

ABSTRACT In the time dimension, the batch process with input dead-zone nonlinearity often has the characteristics of short operation time and time-varying process parameters. A two-dimensional recursive least squares (2D-RLS) identification method for time-varying nonlinear systems with input dead zone is proposed. By mining system dynamic information from the time direction of the same batch and different batch directions, the identification parameters are updated. The proposed two-dimensional identification strategy converts the time-varying parameter estimation problem of time dimension into the equivalent time-invariant parameter estimation problem of batch dimension. Sufficient production data in batch dimension ensure that the proposed identification algorithm can eliminate the influence of random measurement noise. The identification strategy with unequal length of batch data is also given. The convergence of the proposed algorithm is analysed. Finally, numerical simulation and experimental tests are used to verify the effectiveness and superiority of the proposed algorithm.

Adaptive neural network anti-disturbance control of a cable-driven flexible-joint-based underwater vehicle manipulator system with dead-zone input nonlinearities via multiple neural observers

To achieve the requirements of lightweight, low energy consumption, and low inertia of an underwater vehicle manipulator system, a cable-driven manipulator is installed on the underwater vehicle to form a cable-driven flexible-joint-based underwater vehicle manipulator system (CDFJ–UVMS). The CDFJ–UVMS is a complex nonlinear system subject to model uncertainties, complex marine environment disturbances, and actuator dead-zone nonlinearity. To design track controllers, the CDFJ–UVMS dynamics is divided into two parts: known and unknown. Subsequently, a radial basis function neural network is adopted to approximate the unknown nonlinearity. A neural network performance observer is constructed, whose estimation error is then used to design a novel neural disturbance observer (NDO) to estimate the total disturbance. Finally, an adaptive neural network control method is proposed for the CDFJ–UVMS based on the NDO, neural network compensator, and neural performance observer. The stability of the closed-loop system is analyzed using the Lyapunov method. The proposed control algorithm is applied to a CDFJ–UVMS with two cable-driven joints and compared with other control methods to show the effectiveness of the proposed control algorithm.

Adaptive Fuzzy Position and Force Control for Cooperative Multi-Manipulators With System Uncertainties and Input Dead-Zone Nonlinearities

Adaptive Fuzzy Position and Force Control for Cooperative Multi-Manipulators With System Uncertainties and Input Dead-Zone Nonlinearities

Fuzzy Adaptive Control for Vehicular Platoons With Constraints and Unknown Dead-Zone Input

In this paper, an adaptive fuzzy control problem is studied for a connected automated vehicles platoon subject to unknown dead-zone input and constraints. To better handle the unknown nonlinear dynamical functions and disturbances, the nonlinear dynamics model is transformed to a new model. Then, the fuzzy logic system (FLS) is used to identify the unknown nonlinear functions. A dead-zone inverse technique is introduced to eliminate the negative effects of the unknown dead-zone input nonlinearity. In the framework of backstepping, the tangent barrier Lyapunov function (BLF) is introduced in this paper, and a distributed adaptive fuzzy control scheme is designed so that the position, velocity and acceleration of the vehicle platoon do not violate the given constrained boundaries. Finally, based on the Lyapunov stability theory, it is noted that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is validated by simulation results.

Identification Modelling and Fault-Tolerant Predictive Control for Industrial Input Nonlinear Actuator System

Industrial actuator systems play an important role in mechanical manufacture, chemical production and other industrial processes. There is important theoretical research significance and engineering application value in accurately modeling and accurately controlling for an industrial actuator system with dead-zone input nonlinearity. The structure and order of the system are determined by the mechanism relationship of the system. Based on sampled data, an identification algorithm is proposed to describe the main dynamic characteristics of the system output. The convergence property of the proposed identification algorithm is also analyzed. Process faults may reduce the tracking control accuracy of the industrial actuator system. By using an intermediate observer to estimate the faults, a fault-tolerant synchronous control feedback rate is designed to compensate faults. The input dead-zone block may weaken the feedback control performance of the input signal and reduce the control precision. According to the dead-zone input nonlinearity model parameter, a compensator is introduced to transform the dead-zone function into a linear function passing through the origin of coordinates. The transformed and dynamic linear segment of the system constitute the generalized linear system. The model predictive control (MPC) strategy is designed to achieve robust and precise control by eliminating the effects of measurement noise. The results of numerical simulation and experimental test verify the superiority and merit of the modeling and fault-tolerant control strategy. The research results of this paper can provide a good reference and guidance for other complex systems in theoretical research and engineering applications.

Adaptive output feedback asymptotic tracking for uncertain nonlinear systems with dead-zone input

In this paper, the adaptive output feedback asymptotic tracking problem is investigated for nonlinear systems with dead-zone input and unknown nonlinearities, where only system output is available. First, an observer is constructed to estimate unavailable states. Then, by the observer and barrier Lyapunov function, an adaptive output feedback controller is designed, which compensates the influence of dead-zone input and unknown nonlinearities. Furthermore, based on the proposed controller and tuning function, the global boundedness of all signals in closed-loop system is achieved, and the tracking error can asymptotically converge to zero. Particularly, it should be noted that there is no need to calculate the derivatives of virtual control laws in controller design, thus reducing the computational complexity. Finally, two numerical examples are taken to verify the effectiveness of the designed controller.

Distributed Nash Equilibrium Seeking Under Input Dead Zone

This article investigates the Nash equilibrium (NE) seeking problem for games in the presence of input dead-zone nonlinearity. The purpose of each player is to minimize its own cost function, which depends not only on its own decision variable, but also on decision variables of the other players. To obtain an NE, a novel two-time-scale distributed algorithm is designed. This new strategy consists of two parts: one is the fast compensating dynamics, which can rapidly compensate the effect of input dead zone; the other is the optimization dynamics that can distributively drive the players’ decision variables to achieve the NE. Since the proposed algorithm has a two-time-scale structure, singular perturbation techniques are used to prove that the players’ actions semiglobally practically asymptotically converge to the NE. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed strategy.

Distributed Control Design for Uncertain Multiagent Systems with Heterogenous High Powers

In this paper, a distributed asymptotic tracking control strategy is investigated by establishing filters and barrier function-based consensus control scheme to address the control of heterogenous power-chained multiagent systems (MASs) under a directed graph subject to the unknown input deadzone nonlinearities and unknown control coefficients. First, to generate estimation information from the leader, a two-order filter is exploited for every agent which solves the difficultly of the time-varying control coefficients in multiagent systems with a directed topology. Then, based on the two-order filters, prescribed performance method and barrier functions are utilized to establish the distributed tracking protocol to handle the power-chained deadzone input nonlinearities, such that the MAS can reach the global consensus while guaranteeing the prescribed tracking error performance. Using the Lyapunov stability theorem, the proof of the convergence is accomplished rigorously. Ultimately, the efficacy and advantage of the devised method are validated by two simulation examples.

A receptance-based vibration control with dead-zone compensation for systems with input delay

This paper presents a novel compensation approach for receptance-based second-order systems with long input delay and unknown dead-zone input nonlinearity. The approach is based on a filtered Smith predictor for systems with long input delay based on the receptance model. An innovative discrete-time adaptive strategy approach for dealing with unknown input dead-zone is also based on a receptance model realization. The receptance-based second-order model is used on several fundamental applications, including active control vibration of mechanical vibrating systems. In the proposed approach, a filtered prediction error that considers the effects of time delay can be applied to pursue state feedback design for active vibration control purposes. The dead-zone compensation is treated by a discrete-time state observer, which is based on displacement, velocity, and control effort signals to estimate the unknown parameters to be used on an adaptive algorithm. The main contribution of this work is to combine unknown dead-zone adaptive mechanism and a receptance-based time delay compensation in a unified design. Some numerical examples illustrate the effectiveness of the innovative proposed approach.

Adaptive Robust Control for a Spatial Flexible Timoshenko Manipulator Subject to Input Dead-Zone

This article investigates the adaptive robust spatial vibration control for a flexible Timoshenko manipulator subject to input dead-zone nonlinearity characteristic. The “disturbance-like” terms and dead-zone nonlinearity are first incorporated into the context of control design, and the new boundary robust adaptive control laws are constructed to reduce the shear deformation and elastic oscillation, ensure the expected angle orientation, handle the input dead-zone, and estimate the upper bound of compound disturbances. The convergence of states and the stability of the system are analyzed and proven without simplifying the infinite dimensional dynamics. In the end, the effectiveness of the presented scheme is demonstrated by the result of simulation research.

A switching-based state-scaling design for prescribed-time stabilization of nonholonomic systems with actuator dead-zones

Nonholonomic constraint is widespread in many aerospace applications such as space robots, artificial satellites, aircrafts etc. In this paper, the problem of global prescribed-time stabilization is addressed for a category of uncertain nonholonomic constraint systems (namely, nonholonomic systems for short) with actuator dead-zones. To deal with the obstacle that the presence of input dead-zone nonlinearities renders the traditional discontinuous feedback control technique inapplicable to nonholonomic systems, a novel switching-based state-scaling transformation (switching-based-SST) is introduced. This transformation can change the original predefined-time stabilization into the asymptotic stabilization of the transformed one. Under such new framework, a state feedback controller that achieves the prescribed-time convergence performance is developed by using the recursive idea. Finally, a practical application to a unicycle-type mobile robot is presented to confirm the validity of the proposed method.

Fixed-time stabilization for interconnected high-order nonlinear systems with dead-zone input and output constraint

This paper deals with the problem of fixed-time stabilization for a class of high-order nonlinear systems with time-varying output constraint (also known as p-normal form systems). Compared with the existing results, the order of the systems can be less than 1, which is more relaxed. Moreover, each subsystem is with the dead-zone input and interconnected nonlinearity. We design a new decentralized fixed-time controller based on the recursive design method by revamping the technique of adding a power integrator and using the tan-type barrier Lyapunov function. The proposed controller is also effective for the systems with asymmetric output constraints. Based on Lyapunov stability theory, it is proved that the decentralized controller can realize that the outputs are strictly constrained within predefined boundaries and all state variables converge to zero in a fixed time, where the bound of reaching time is independent of the initial conditions. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.

Adaptive Neural Network Tracking Control for Double-Pendulum Tower Crane Systems With Nonideal Inputs

A novel adaptive neural network tracking control method is systematically investigated for a unique double-pendulum tower crane system model in this article. Several critical and practical application-oriented control issues, including robustness, tracking error limitation, double-pendulum effects, and input dead zone nonlinearity, are considered simultaneously, which have never been well addressed in the existing literature. Technically, neural networks are employed to approximate the functions with uncertain/unknown dynamics and nonideal inputs. Several barrier Lyapunov functions are proposed that can circumvent the violation of tracking error limitations in the proposed control method. Importantly, based on the designed adaptive neural network tracking control method, the jib and trolley can track their desired trajectories very fast, and the hook and payload sway can be completely eliminated. The Lyapunov stability theory and Babalat’s lemma are utilized to theoretically prove the convergence and stability of the proposed control system. Finally, well-designed simulation studies are carried out to verify the excellent performance and strong robustness of the control method. This article should be the first work considering a double-pendulum tower crane system with guaranteed convergence and performance without any linearization for the original nonlinear dynamic model.

Online Modeling of the CNC Engraving System With Dead-Zone Input Nonlinearity

This article is concerned with modeling of a class of permanent-magnet-synchronous-motor-based drive systems with dead-zone input nonlinearity. The experimental testing method based on recursive least squares (RLS) is combined with the mechanism analysis method based on physical laws. With the structure of the analytical model first determined by the mechanism analysis method, an online RLS-based data-driven method is then exploited to obtain the unknown parameters of the analytical model. Since the unknown parameters are decoupled in the proposed method, all parameter estimates are available. An auxiliary model and a variable forgetting factor are constructed to ensure the high accuracy and the fast convergence of the proposed method, respectively. Besides, the asymptotic convergence property of the proposed method is analyzed, and the upper bound of the parameter estimation error is also presented. The effectiveness of the proposed method is verified by simulations and experiments on a self-designed computer numerical control engraving system.

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

Reinforcement Learning-Based Optimal Tracking Control of an Unknown Unmanned Surface Vehicle.

In this article, a novel reinforcement learning-based optimal tracking control (RLOTC) scheme is established for an unmanned surface vehicle (USV) in the presence of complex unknowns, including dead-zone input nonlinearities, system dynamics, and disturbances. To be specific, dead-zone nonlinearities are decoupled to be input-dependent sloped controls and unknown biases that are encapsulated into lumped unknowns within tracking error dynamics. Neural network (NN) approximators are further deployed to adaptively identify complex unknowns and facilitate a Hamilton-Jacobi-Bellman (HJB) equation that formulates optimal tracking. In order to derive a practically optimal solution, an actor-critic reinforcement learning framework is built by employing adaptive NN identifiers to recursively approximate the total optimal policy and cost function. Eventually, theoretical analysis shows that the entire RLOTC scheme can render tracking errors that converge to an arbitrarily small neighborhood of the origin, subject to optimal cost. Simulation results and comprehensive comparisons on a prototype USV demonstrate remarkable effectiveness and superiority.

Robust tracking and model following of uncertain non‐linear systems with time‐varying delays and dead‐zone inputs

The problem of robust tracking and model following is considered for a class of uncertain non-linear systems with any time-varying delays and completely unknown dead-zone input non-linearity. Here, time-varying delays are assumed to be any continuous and bounded non-negative functions, and any information on their derivatives need not known. In the study, the system uncertainties assumed to be any continuous and bounded non-linear functions, and their non-linear upper bounds do not need also to be known. Based on Wu inequality, a novel design method is presented by which some simple and direct robust tracking control schemes can be easily constructed. It is shown that the tracking error between the output of an actual dynamical system and the dynamical signals of the given reference model can be guaranteed to be uniformly exponentially bounded. A numerical example is also given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.

Adaptive synchronization of two different uncertain chaotic systems with unknown dead-zone input nonlinearities

The present work addresses chaos synchronization between two different general chaotic systems with parametric and structural uncertainties, subject to external disturbances and input dead-zone nonlinearities. In this regard, a novel robust controller has been designed that guarantees asymptotic stability of synchronization errors and boundedness of all closed-loop signals. One advantage of the proposed controller over the existing control algorithms is using only one update law for estimating the structural uncertainties, external disturbances, and unknown characteristics of the dead-zone nonlinearities, which reduces the computational burden considerably. The designed controller is singularity free, and a smooth projection algorithm has been used to make the controller more robust. In addition, a finite-time controller has been designed and its performance has been compared with the robustly designed controller.

Adaptive neural network control for a class of MIMO non-affine uncertain systems with input dead-zone nonlinearity and external disturbance

This paper studies an adaptive tracking control for a class of multi-input multi-output (MIMO) non-affine nonlinear systems, with input dead-zone nonlinearity and external disturbances. By using the mean-value theorem, the system model is transformed into an affine form so as the difficulty in controlling non-affine systems is overcome. In the proposed control design, neural networks (NNs) are used to approximate the unknown nonlinearities based on their universal approximation properties. To compensate for approximation errors and external disturbances, an adaptive robust control term is introduced. In comparison with existing approaches, the structure of the designed controller is considerably simpler, and can handle a wider range of nonlinear systems. The stability of the closed-loop system is investigated by using Lyapunov theory. The simulation results illustrate the proposed method.

Adaptive neural network control for a class of MIMO non-affine uncertain systems with input dead-zone nonlinearity and external disturbance

This paper studies an adaptive tracking control for a class of multi-input multi-output (MIMO) non-affine nonlinear systems, with input dead-zone nonlinearity and external disturbances. By using the mean-value theorem, the system model is transformed into an affine form so as the difficulty in controlling non-affine systems is overcome. In the proposed control design, neural networks (NNs) are used to approximate the unknown nonlinearities based on their universal approximation properties. To compensate for approximation errors and external disturbances, an adaptive robust control term is introduced. In comparison with existing approaches, the structure of the designed controller is considerably simpler, and can handle a wider range of nonlinear systems. The stability of the closed-loop system is investigated by using Lyapunov theory. The simulation results illustrate the proposed method.