Unknown Dead-zone Nonlinearity Research Articles

Control of state constrained nonlinear systems with unknown dead-zone nonlinearity: A unified fuzzy dynamic surface control approach

In this paper, we focus on the tracking control issue of state constrained nonlinear systems with unknown dead-zone nonlinearity. The systems also take into account unknown virtual control coefficients as well as external disturbances. The utilization of feasibility nonlinear transformed functions not only converts original constrained nonlinear systems into unconstrained systems, but also eliminates the difficulty of parameter selection of the barrier Lyapunov function. Under the premise of relaxing the limitation of systems, the property of the hyperbolic tangent function and adaptive estimated parameters are used to design controller to improve the robustness of control strategy. Through the combination of dynamic surface control and adaptive backstepping technology, an adaptive fuzzy dynamic surface control strategy is developed so that all signals of the closed-loop unconstrained system and original system are bounded, and states of the original system do not break predetermined constraints. Two examples are provided to illustrate that control strategy is effective.

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.

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.

Modeling and parametric identification of Hammerstein systems with time delay and asymmetric dead-zones using fractional differential equations

The parametric identification of Hammerstein structured nonlinear systems with discontinuous asymmetric (two segment piecewise-linear with a dead-zone) nonlinearity and input time delay is presented using a fractional-order modeling technique. The effect of the unknown dead-zone nonlinearity is separated from the linear dynamics using special excitation signals to simplify the identification process. The use of fractional calculus permits reduced order modeling of the linear dynamics. An interactive block-based strategy is then introduced to simultaneously estimate the separated nonlinear and linear parameters, including the fractional differentiation order(s) and input time delay, which usually require separate algorithms in such cases. The proposed method utilizes block pulse functions to mitigate the computational complexity of fractional differential operations. Numerical examples are provided to validate the efficacy in comparison to existing methods. A DC servo motor application is used to demonstrate the proposed nonlinear modeling approach.

Adaptive generation of limit cycles in a class of nonlinear systems with unknown parameters and dead-zone nonlinearity

This paper presents a new method to design an adaptive controller for generating stable limit cycles in a class of nonlinear systems subject to unknown dead-zone nonlinearity and unknown parameters. In this regard, the set stabilisation-based approach is utilised and the proper Lyapunov function is taken concerning the geometric shape of the desired limit cycle. Firstly, the state feedback control is designed to create the desired limit cycle in the second-order subsystem and then, extended to the arbitrary order system through the adaptive backstepping technique. Besides, the explosion of a complex problem, which happens during the backstepping implementation in high-order systems, is handled. In the final stage, the boundedness of all the closed-loop signals is guaranteed via Lyapunov analysis. The effectiveness of the proposed control algorithm is demonstrated by a simulation example.

Quantized controller for a class of uncertain nonlinear systems with dead-zone nonlinearity

In this paper, a quantized controller is designed for a class of uncertain nonlinear systems subjected to unknown disturbances and unknown dead-zone nonlinearity. A general class of strict feedback nonlinear systems is taken as the plant to design the controller. Here, each differential equation of the system is considered to have unknown parameters and time-varying disturbances. The maximum upper bound of the disturbances is estimated instead of estimating each disturbance. This novel idea reduces the computational cost in handling the disturbances in uncertain systems. The tuning functions are constructed to estimate the unknown system parameter and maximum upper bound of the disturbances. It is considered that the actuator dead-zone nonlinearity is bounded by an unknown parameter and incorporated to design the final quantized controller. A backstepping technique is applied to design the tuning functions and controller that stabilizes the uncertain system. The stability of the proposed controller is proved using the Lyapunov stability based theory. The obtained MATLAB simulation test results verify the designed proposed controller.

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 Control of a Hose and Drogue System with Input Nonlinearities and Partial State Constraints

This paper proposes a novel multi-objective controller for the hose and drogue system, to address the input nonlinearities of dead-zone and constraint as well as partial state constraints. Based upon a smooth auxiliary function, a new dead-zone compensation method is developed to offset the unknown dead-zone nonlinearity, and the obtained controller can also deal with the input constraint by employing the Nussbaum-function-based method. Subsequently, based upon a new barrier Lyapunov function and the parameter projection method, the proposed controller can enforce the partial state constraints in the presence of the partial differential characteristics of the hose and drogue system. A simulation example is presented to illustrate the effectiveness of the proposed controller.

Adaptive fuzzy control for pure-feedback systems with full state constraints and unknown nonlinear dead zone

In this paper, an adaptive control problem for a class of pure-feedback time-varying delay nonlinear systems with full state constraints and unknown dead zone is investigated. Differing from the full state constraints without considering the time-varying delay in nonlinear systems, a well defined Barrier Lyapunov-Krasovskii functional is designed to address the difficult in this paper. By defining a continuous function and combining with mean value theorem, system is modeled with dead zone. Furthermore, a novel adaptive control scheme is developed based on recursive backstepping method. It is proved that the proposed approach can guarantee a desired tracking performance and semi-global asymptotically stability of the closed-loop system. Finally, some simulation results are given to verify the effectiveness of the proposed strategy.

Extremum seeking dead-zone pre-compensator for an industrial control system

Abstract PID type industrial controllers such as PI, PD, PID are mature control algorithms and they are intensively used in industry due to their simplicity and easily implementability. However, they start to fail when there is an unknown or unpredictable nonlinear behavior in the plant or actuator. In this paper, a novel compensation algorithm is proposed for PD type industrial control systems, which possess an unknown dead-zone nonlinearity. An extremum-seeking technique is utilized in the compensation algorithm. The aim is to propose a new, effective and robust compensator which can be added easily to an existing industrial controller without any need to change/retune the controller settings/parameters. It is shown that by adding the compensator to an existing PD control system, the sensitivity of the controller to the dead-zone nonlinearity is removed.

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.

Adaptive Practical Finite-Time Stabilization for Uncertain Nonstrict Feedback Nonlinear Systems With Input Nonlinearity

This paper investigates the adaptive practical finite-time stabilization for a class of nonstrict feedback nonlinear systems. The nonlinear systems under consideration contain unknown nonlinearities and control coefficients, and unknown deadzone and saturation input nonlinearities. Without imposing any conditions on the unknown nonlinearities, neural networks are utilized as the approximators to cope with these unknown nonlinear functions. The adding a power integrator technique is employed to construct controller and adaptive laws. The stability of the corresponding closed-loop system is proved with the help of the finite-time Lyapunov theory. Finally, two simulation examples are provided to show the validity of the proposed design method.

Robust adaptive self-organizing neuro-fuzzy tracking control of UUV with system uncertainties and unknown dead-zone nonlinearity

In this paper, a robust adaptive self-organizing neuro-fuzzy control (RASNFC) scheme for tracking of unmanned underwater vehicle with uncertainties and the unknown dead-zone nonlinearity is proposed. The proposed RASNFC scheme comprises an estimation-based adaptive controller (EBAC) using a self-organizing neuro-fuzzy network (SNFN) and a robust controller. The EBAC controller is constructed with a novel sliding mode reaching law control framework, and the unknown dynamic function is identified by the SNFN approximator which is able to online self-construct a neuro-fuzzy network with dynamic structure by generating and pruning fuzzy rule. The robust controller is employed to provide the finite $$L_{2}$$ -gain property to cope with reconstruction errors such that the robustness of the entire closed-loop control system is enhanced. Theoretical analysis shows that tracking errors and their derivatives are asymptotically stable and all signals in the closed-loop system are bounded. Comparative simulation results demonstrate the effectiveness and superiority of the proposed RASNFC scheme.

Barrier Lyapunov function-based adaptive control for hypersonic flight vehicles

This paper presents an adaptive control strategy for hypersonic flight vehicles (HFVs) subject to parametric uncertainties, external disturbances and faulty actuators. Besides the guaranteed tracking performance, the main novelty of this study is to strictly constrain the flight states, which are crucial to hypersonic flights, such as the bounded angle of attack required by the scramjet. To achieve this, the disturbed control-oriented model of HFVs with uncertain parameters and faulty actuators is first rewritten into a parameterized form, based on which novel adaptive controllers are then designed for velocity and altitude subsystems. By introducing barrier Lyapunov functions to design procedures, specific tracking performances of velocity and altitude are guaranteed, while the other flight states of angle of attack, flight path angle, pitch angle and pitch angle rate can be kept within the prescribed ranges. Command filters are employed in the back-stepping design for altitude subsystem to limit the magnitudes of virtual controls and to avoid the complicated analytical calculations. In addition, an adaptive inverse is integrated into the adaptive control scheme to sufficiently compensate for the unknown dead-zone nonlinearity in elevator. It is shown that the developed control system regulates the tracking errors within some neighborhoods of zero, which become sufficiently small by proper adjustments on design parameters. Finally, the numerical simulation is provided for comparison and verification purposes.

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.

Output Consensus Control of Multiagent Systems With Unknown Nonlinear Dead Zone

This paper investigates the output consensus control problem of uncertain second-order nonlinear multiagent systems with unknown nonlinear dead zone, where the communication networks can be described as a directed graph with a fixed topology. The control input in each follower is assumed to be subject to unknown nonlinear dead zone. By the function approximation capability of neural networks (NNs), a distributed adaptive NN-based controller is designed for each follower in the graph such that all the outputs of the followers can asymptotically synchronize to the output of the leader with synchronization errors being semiglobally uniformly ultimately bounded. Based on Lyapunov stability theory and algebraic graph theory, analysis is conducted on stability and parameter convergence of the proposed algorithm. Finally, an example is provided to validate the theoretical results.

Barrier Lyapunov function-based adaptive output feedback failure compensation for a class of non-linear systems with unknown dead-zone non-linearity

In this paper, an adaptive robust output feedback control approach is proposed for a class of uncertain non-linear systems with unknown input dead-zone non-linearity, unknown failures and unknown bounded disturbances. By constructing the dead-zone inverse and applying the backstepping recursive design technique, a robust adaptive backstepping controller is proposed, in which adaptive control law is synthesized to handle parametric uncertainties and a novel robust control law to attenuate disturbances. The robust output feedback control law is developed by integrating a switching function σ algorithm at each step of the backstepping design procedure. In addition, K-filters are designed to estimate the unmeasured states and neural networks are employed to approximate the unknown non-linear functions. By ensuring boundedness of the barrier Lyapunov function, the major feature of the proposed controller is that it can theoretically guarantee asymptotic output tracking performance, in spite of the presence of unknown input dead-zone non-linearity, various actuator failures and unknown bounded disturbances via Lyapunov stability analysis. The effectiveness of the proposed approach is illustrated by the simulation examples.

Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

Direct adaptive controller for uncertain MIMO dynamic systems with time-varying delay and dead-zone inputs

This paper presents an adaptive tracking control method for a class of nonlinearly parameterized MIMO dynamic systems with time-varying delay and unknown nonlinear dead-zone inputs. A new high dimensional integral Lyapunov–Krasovskii functional is introduced for the adaptive controller to guarantee global stability of the considered systems and also ensure convergence of the tracking errors to the origin. The proposed method provides an alternative to existing methods used for MIMO time-delay systems with dead-zone nonlinearities.