Unknown Input Saturation Research Articles

Error-Driven-Based Nonlinear Feedback Recursive Design for Adaptive NN Trajectory Tracking Control of Surface Ships With Input Saturation

In this paper, we investigate the trajectory tracking control problem of surface ship subject to the dynamic uncertainties, unknown time-varying disturbances and input saturation. To handle the non-smooth input saturation nonlinearity and compensate the ship dynamic uncertainties, Gaussian error function and adaptive neural network technique are employed. In control design, to obtain the transient motion reference signal, finite-time nonlinear tracking differentiator is applied to generate virtual reference signal and to extract the derivative of virtual control law. Referring to the effects of the kinematics subsystem on the kinetics subsystem caused by the error of tracking differentiator, and the effects of the input saturation on the control accuracy and the dynamic quality of the trajectory tracking control system, we propose an error-driven-based nonlinear feedback recursive design technique to design trajectory tracking control law, and employ a new non-quadratic Lyapunov functions to analyze the trajectory tracking control system stability. The proposed control scheme fully embodies the characteristics of the lowgain and high-gain control, and overcomes the effect of tracking differentiator error on closed-loop system by recursive design method. Simulation results verify the effectiveness of our proposed control scheme.

Finite-time predictor line-of-sight–based adaptive neural network path following for unmanned surface vessels with unknown dynamics and input saturation

In the presence of unknown dynamics and input saturation, a finite-time predictor line-of-sight–based adaptive neural network scheme is presented for the path following of unmanned surface vessels. The proposed scheme merges with the guidance and the control subsystem of unmanned surface vessels together. A finite-time predictor–based line-of-sight guidance law is developed to ensure unmanned surface vessels effectively converging to and following the referenced path. Then, the path-following control laws are designed by combining neural network-based minimal learning parameter technique with backstepping method, where minimal learning parameter is applied to account for system nonparametric uncertainties. The key features of this scheme, first, the finite-time predictor errors are guaranteed; second, designed controllers are independent of the system model; and third, only required two parameters update online for each control law. The rigorous theory analysis verifies that all signals in the path-following guidance-control system are semi-globally uniformly ultimately bounded via Lyapunov stability theory. Simulation results illustrate the effectiveness and performance of the presented scheme.

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.

The neural correlates of case and inflection in the processing of morphologically complex words: An fMRI study of Russian nouns

Chapter 14 introduces a non-singular terminal sliding mode funnel control for servo systems with unknown input saturation. A smooth and affine function is used to approximate the input saturation dynamics. A funnel constraint variable is utilized in constructing the non-singular terminal sliding mode control (NTSMC) to make the tracking error fall within a prescribed bound. Neural network (NN) is also used to cope with other unknown system dynamics. The effectiveness is demonstrated by simulation results.

Adaptive fuzzy decentralized control for a class of MIMO large-scale nonlinear state delay systems with unmodeled dynamics subject to unknown input saturation and infinite number of actuator failures

This paper addresses design of an adaptive fuzzy decentralized fault-tolerant controller for a class of uncertain multi-input multi-output (MIMO) large-scale nonlinear systems with unmodeled dynamics subject to unknown state time-varying delay, external disturbances, unknown input saturation and actuator faults. It is shown that the proposed fault-tolerant control (FTC) scheme can handle infinite number of actuator failures including partial and total loss of effectiveness. System uncertainties have been approximated by the fuzzy logic systems (FLSs). To cope with the unknown state time-varying delay, the Razumikhin lemma has been utilized and unmodeled dynamics has been tackled by introducing a dynamical signal. To avoid high computational burden, the dynamic surface control (DSC) technique has been used and the number of adaption laws has been reduced by updating the maximum norm of fuzzy weight vectors of each subsystem. It has been shown that all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation results demonstrate the effectiveness of the proposed control scheme.

Dead-Zone Model-Based Adaptive Fuzzy Wavelet Control for Nonlinear Systems Including Input Saturation and Dynamic Uncertainties

In this study, the problem of adaptive fuzzy wavelet network (FWN) control is investigated for nonlinear strict-feedback systems with unknown functions, unknown virtual control gains and unknown input saturation. An adaptive FWN as an adaptive nonlinear-in-parameter approximator is proposed to represent the model of the unknown functions. Saturation nonlinearity is described by the dead-zone operator-based model which does not require the bound of the saturated input to be known. Then, a novel control scheme is designed based on the adaptive FWN, the saturation model and the dynamic surface control approach. The proposed control scheme does not require any prior knowledge about input saturation, unknown dynamics and unknown virtual control gains. It simultaneously eliminates the “explosion of complexity” and “curse of dimensionality” problems; also, the design approach avoids the controller singularity problem completely without using projection algorithm. The stability analysis is studied using Lyapunov theorem; it shows that all signals of the resulting closed-loop system are uniformly ultimately bounded and the tracking error can be made small by proper selection of the design parameters. Comparing the simulation results of the proposed scheme with other control methods demonstrates the effectiveness and superior performance of the proposed scheme.

Adaptive sliding-mode control of automotive electronic throttle in the presence of input saturation constraint

In modern vehicles, electronic throttle &#x0028 ET &#x0029 has been widely utilized to control the airflow into gasoline engine. To solve the control difficulties with an ET, such as strong nonlinearity, unknown model parameters and input saturation constraints, an adaptive sliding-mode tracking control strategy for an ET is presented. Compared with the existing control strategies for an ET, input saturation constraints and parameter uncertainties are adequately considered in the proposed control strategy. At first, the nonlinear dynamic model for control of an ET is described. According to the dynamical model, the nonlinear adaptive sliding-mode tracking control method is presented, where parameter adaptive laws and auxiliary design system are employed. Parameter adaptive law is given to estimate the unknown parameter with an ET. An auxiliary system is designed, and its state is utilized in the tracking control method to handle the input saturation. Stability proof and analysis of the adaptive sliding-mode control method is performed by using Lyapunov stability theory. Finally, the reliability and feasibility of the proposed control strategy are evaluated by computer simulation. Simulation research shows that the proposed sliding-mode control strategy can provide good control performance for an ET.

Distributed zero-sum differential game for multi-agent systems in strict-feedback form with input saturation and output constraint

This paper investigates the distributed differential game tracking problem for nonlinear multi-agent systems with output constraint under a fixed directed graph. Each follower can be taken as strict-feedback structure with uncertain nonlinearities and input saturation. Firstly, by utilizing the command filtered backstepping technique, the distributed tracking control problem of multi-agent systems in strict-feedback form can be transformed into an equivalent distributed differential game problem of tracking error dynamics in affine form by designing a distributed feedforward tracking controller, in which neural networks (NNs) and the auxiliary system are introduced to deal with the unknown nonlinearities and input saturation, respectively. Especially, a novel barrier Lyapunov function (BLF) is firstly introduced to tackle with the output constraint. Subsequently, by using adaptive dynamic programming (ADP) technique, the distributed zero-sum differential game strategy is derived, in which a critic network is constructed to approximate the cooperative cost function online with a novel updating law. Therefore, the whole distributed control scheme not only guarantees the closed-loop signals to be cooperatively uniformly ultimately bounded (CUUB), but also ensures the cooperative cost function to be minimized. Meanwhile, the output constraint and input saturation are not violated. Finally, simulation results demonstrate the effectiveness of the proposed method.

Terminal sliding mode control with non-symmetric input saturation for vibration suppression of electrostatically actuated nanobeams in the presence of Casimir force

• The nonlinear ordinary differential equation is derived for an electrostatically actuated functionally graded nanobeam. • A robust sliding mode controller is designed for the uncertain nanobeam. • A disturbance-observer-based terminal sliding mode control is presented to suppress the nonlinear vibration of the nanobeam. • Stability of the closed-loop system is proved in the presence of unknown disturbance and non-symmetric input saturation. In the present article, a robust sliding mode controller and a disturbance-observer-based terminal sliding mode tracking controller with finite time convergence are proposed for stabilization of a functionally graded and homogeneous nanobeam. The considered nanobeam is modeled based on the nonlocal strain gradient theory and Euler–Bernoulli beam theory and subjected to Casimir force. Electrostatic actuation is considered in the governing equations of the system as the control input modeling. The Galerkin approach is employed to reduce the governing nonlinear partial differential equation of motion to a nonlinear ordinary differential equation with quadratic and cubic nonlinearities. The robust sliding mode controller is designed for stabilization of the nanobeam with the uncertain parameters which eliminates chattering. Furthermore, a disturbance-observer-based terminal sliding mode controller is used for stabilization of the nanobeam in the presence of an external load disturbance and unknown non-symmetric input saturation which is useful for when a constraint exists in the system control input due to the electrostatic actuation. Simulation results are presented and comparisons of the suggested control techniques are accomplished for the mentioned system and also for an atomic force microscope as the second case study in order to show the performance of the proposed controllers. Finally, experimental verification has been done by using the suggested terminal sliding mode controller to prove the high precision positioning.

Observer-based adaptive prescribed performance tracking control for nonlinear systems with unknown control direction and input saturation

Abstract In this paper, the problem of observer-based adaptive tracking control is investigated for a class of nonlinear systems with unknown control direction, input saturation and tracking error constraint. The Nussbaum function is employed to address the unknown control direction and a state observer is constructed by neural networks (NNs) to estimate the unmeasurable states. A new error constraint transformation is proposed to guarantee that the tracking error satisfies the prescribed performance. Then, a novel adaptive prescribed performance neural network (NN) output feedback tracking control method is designed. It is proved that the designed controller can guarantee the boundedness of all the signals in the closed-loop system and the prescribed time-varying tracking performance. Finally, simulations on two examples are performed to illustrate the efficiency of the proposed control method.

Formula omitted] control for Markovian jump fuzzy systems with partly unknown transition rates and input saturation

This paper considers less conservative conditions of H∞ control for Markovian jump fuzzy systems (MJFSs) with partly unknown transition rates and input saturation. To find H∞ control for level γ, a set invariance condition and the stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) by considering the properties of transition rates. Then, to derive the less conservative stabilization conditions, all possible slack variables are incorporated into the relaxation process with fully considering the property of the fuzzy weights. Two numerical examples are provided to illustrate the effectiveness of the proposed method.

Adaptive Neural Dynamic Surface Control for Nonstrict-Feedback Systems With Output Dead Zone.

This paper focuses on the problem of adaptive output-constrained neural tracking control for uncertain nonstrict-feedback systems in the presence of unknown symmetric output dead zone and input saturation. A Nussbaum-type function-based dead-zone model is introduced such that the dynamic surface control approach can be used for controller design. The variable separation technique is employed to decompose the unknown function of entire states in each subsystem into a series of smooth functions. Radial basis function neural networks are utilized to approximate the unknown black-box functions derived from Young's inequality. With the help of auxiliary first-order filters, the dimensions of neural network input are reduced in each recursive design. A main advantage of the proposed method is that for an -order nonlinear system, only one adaptation parameter needs to be tuned online. It is rigorously shown that the proposed output-constrained controller guarantees that all the closed-loop signals are semiglobal uniformly ultimately bounded and the tracking error never violates the output constraint.

Reliability-based robust dynamic positioning for a turret-moored floating production storage and offloading vessel with unknown time-varying disturbances and input saturation

In this paper, we derived a mathematical model for a floating production storage and offloading (FPSO) vessel and its buoy mooring system and developed a new robust positioning controller to keep vessels in a desired region in the presence of unknown time-varying disturbances with uncertainties and input saturation. Different materials (chain and polyester) and buoys are considered in the model of mooring system to make the developed model more realistic. We employed a disturbance observer to estimate the disturbances and designed an auxiliary dynamic system integrated with the structural reliability's derivative to quantify the input saturation's influence, and its states are used to the control design. Our proposed controller can keep the structural reliability and heading at desired values with arbitrarily small errors while guaranteeing the uniform ultimate boundedness of all signals in the closed-loop control system. It is easier for the control design because disturbances and input saturation are handled simultaneously and so is the stability analysis because only one Lyapunov function is needed. Simulations are conducted to demonstrate our proposed controller's effectiveness and a comparison with a robust controller based on hyperbolic tangent functions shows our proposed controller can avoid steady errors with desired control goals.

Stable Backstepping Control of Marine Vehicles with Actuator Rate Limits and Saturation

A six degree of freedom nonlinear control law for the trajectory tracking of marine vehicles that operate in the presence of unknown time-varying disturbances, input saturation and actuator rate limits is developed using a disturbance observer and nonlinear backstepping. The disturbance observer provides estimates of the unknown time-varying disturbances and a continuously differentiable function is employed to model input saturation. The uniform ultimate boundedness of all signals in the closed-loop control system is proved. Trajectory-tracking simulations of an autonomous underwater vehicle demonstrate the performance of the proposed controller.

Distributed Fuzzy Adaptive Backstepping Optimal Control for Nonlinear Multi-missile Guidance Systems with Input Saturation

This paper investigates the distributed optimal tracking control problem for nonlinear multiagent systems with a fixed directed graph. The dynamics of followers are in strict-feedback form with unknown nonlinearities and input saturation. Fuzzy logic systems and auxiliary system are introduced to identify the unknown nonlinearities and compensate the effect of input saturation, respectively. Then, by using the command-filtered backstepping technique, the distributed optimal tracking control problem is transformed into a distributed optimal regulation problem of tracking error dynamics in affine form. Subsequently, the distributed optimal feedback controller is derived via adaptive dynamic programming technique, in which a critic network is constructed to approximate the associated cost function online with a designed weight update law. Therefore, the whole controller, consisting of distributed adaptive feedforward tracking controller and distributed optimal feedback controller, not only guarantees that all signals in the closed-loop system are uniformly ultimately bounded, but also guarantees that the cooperative cost function is minimized. The effectiveness of the proposed method is demonstrated by simulation on the cooperative guidance problem of multimissile systems.

Distributed adaptive sliding mode control for attitudes synchronization of multiple autonomous underwater vehicles

This article is concerned with attitudes synchronization of networked autonomous underwater vehicles, which aims to enable all the autonomous underwater vehicles tracking the desired attitude coordinately, when the desired attitude information can only be achieved by one or one subset autonomous underwater vehicles. A Lyapunov technique is presented for designing an adaptive synchronization control protocol using sliding mode and consensus theory. The uncertainty of the autonomous underwater vehicle dynamics, and the unknown external disturbance and input saturation were both considered in our controller proposed; moreover, only the neighbors’ information were used by the controller, so it is totally distributed. Simulations were performed to validate the theoretical results.

Mathematical modelling and control of a nonholonomic spherical robot on a variable-slope inclined plane using terminal sliding mode control

Motion analysis and control of a pendulum-driven spherical robot (PDSR) on an inclined plane with a variable slope is investigated. Firstly, the mathematical model of a PDSR on a variable-slope inclined plane is deduced applying a Lagrangian formulation. Afterwards, in the presence of an unknown external disturbance, the terminal sliding mode control (TSMC) technique is employed to stabilize the robot on the inclined plane, while the plane is still moving. In other words, the terminal sliding mode disturbance observer is used to estimate the unknown disturbance. Based on the disturbance estimation, the TSMC scheme is established to control the single-input and single-output nonlinear system with control singularity and an unknown nonsymmetric control input saturation. In fact, a compound disturbance is defined and estimated, which includes the external disturbance, the control singularity and the unknown input saturation. Simulations are then conducted to validate the proposed approach for motion control of a PDSR on a variable-slope inclined plane with an unknown external disturbance and nonsymmetric input limits.

Finite-Time Tracking Control for a Class of MIMO Nonlinear Systems with Unknown Asymmetric Saturations

This paper addresses the problem of finite-time tracking control for multiple-input and multiple-output (MIMO) nonlinear systems with asymmetric saturations. A systematic approach is proposed to eliminate the effects of unmeasured external disturbances and unknown asymmetric saturations. In the proposed control strategy, a terminal sliding mode disturbance observer is provided to estimate the augmented disturbance (which contains the unknown asymmetric input saturation and external disturbance). The approximation error of the augmented disturbance can converge to zero in a fixed finite-time interval. Furthermore, a novel finite-time tracking control algorithm is developed to guarantee fast convergence of the tracking error. Compared with the existing results on finite-time tracking control, the chattering problem and the input saturation problem can be solved in a unified framework. Several simulations are given to demonstrate the effectiveness of the proposed approach.

Adaptive fault tolerant control for hypersonic vehicle with external disturbance

In this article, an adaptive fault tolerant control strategy is proposed to solve the trajectory tracking problem of a generic hypersonic vehicle subjected to actuator fault, external disturbance, and input saturation. The longitudinal model of generic hypersonic vehicle is divided into velocity subsystem and altitude subsystem, in which dynamic inversion and backstepping are applied, respectively, to track the desired trajectories. For the unknown maximum disturbance upper bound, actuator fault, and input saturation constraint, adaptive laws are proposed to estimate these information online. Finally, numeric simulation is conducted in the cruise phase for generic hypersonic vehicle. Simulation results show that the controllers designed in this article can make generic hypersonic vehicle track the desired trajectories in the presence of actuator fault, external disturbance, and input saturation.

Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation

This paper studies the problem of adaptive output tracking control for a class of nonlinear systems subject to unknown time delay and input saturation. To address the delay and the input saturation, some reasonable assumptions and an auxiliary system are introduced. The fuzzy logic approach is employed to approximate the unknown functions in the system. An observer is designed to estimate the unavailable system states. The dynamic surface control (DSC) technique is utilized to avoid the problem of “explosion of complexity”. By combining the backstepping and DSC methods, a bounded control input is designed to ensure that all signals of the closed-loop system are bounded and the tracking error can fluctuate around the origin within a small neighborhood. Finally, two examples are presented to demonstrate the effectiveness and potential of the proposed new design techniques.