Input Saturation Nonlinearity Research Articles

Event-triggered adaptive output-feedback neural-networks control for saturated strict-feedback nonlinear systems in the presence of external disturbance

An event-triggered (ET) neural-networks (NNs) adaptive output-feedback control approach is proposed for a class of input-saturated strict-feedback nonlinear systems with external disturbance. Compared with overall existing event-triggered control strategies, which are free from control input nonlinearities and suffer from the explosion of complexity, the proposed event-triggered-based NNs controller is able to handle system input saturation along with completely avoiding the complexity explosion problem. First, by introducing alternative state variables, and by implementing a low-pass filter, the difficulty arising from the cascading of the input-saturated strict-feedback system has been avoided. Thus, the system is converted to the normal canonical system, for which the controller synthesis is much simpler without resort to traditional back-stepping approach. Then, an observer is adopted to estimate the unknown states of the newly derived canonical system based on strictly positive real theory. In the design procedure, the unknown nonlinear functions are approximated by NNs to design a baseline controller, for which an additional robust term is embedded to deal with the input saturation nonlinearity, unknown disturbances and approximation errors using only two adaptive parameters. The proposed ET adaptive NNs control scheme is shown to guarantee the convergence of the output of the system to a small neighborhood of the origin along with the boundedness of all signals in the closed loop. Finally, simulation examples are presented to show the effectiveness of the proposed controller.

Event-Triggered Fuzzy Adaptive Leader-Following Tracking Control of Nonaffine Multiagent Systems With Finite-Time Output Constraint and Input Saturation

This article considers the problem of distributed adaptive fuzzy event-based finite-time prescribed performance leader-following tracking control for heterogeneous nonlinear multiagent systems (NMASs) over a directed topology. Each agent is considered in a nonaffine nonstrict-feedback form under input saturation and output constraint which contains unknown dynamics and external disturbances. Fuzzy logic systems (FLSs) are exploited as an effective online approximation tool to tackle system uncertainties. By employing the unique property of FLS, the algebraic loop problem is overcome and by designing novel adaptive laws of the FLS weights, the computation burden is decreased significantly. The threshold of the event-triggered condition is improved compared to the conventional relative-threshold mechanism. A modified performance function called finite-time performance function is introduced to constrain the synchronization errors within the prescribed performance bounds in finite time. The dynamic surface control technique is then developed to avoid the issue of the “explosion of complexity.” Moreover, by developing a new decomposition for the controller gain function resulting from the mean-value theorem and introducing an auxiliary system, the input saturation nonlinearity that affects the nonaffine form stability is handled. Through the Lyapunov stability analyses, it is shown that the developed control algorithm ensures the closed-loop NMAS trajectory to be cooperatively semi-globally uniformly ultimately bounded. Additionally, the tracking errors are driven to a predefined region around zero in finite time. Finally, the efficiency of the established theoretical results is validated by the simulation studies.

Saturated Output-Feedback Hybrid Reinforcement Learning Controller for Submersible Vehicles Guaranteeing Output Constraints

In this brief, we propose a new neuro-fuzzy reinforcement learning-based control (NFRLC) structure that allows autonomous underwater vehicles (AUVs) to follow a desired trajectory in large-scale complex environments precisely. The accurate tracking control problem is solved by a unique online NFRLC method designed based on actor-critic (AC) structure. Integrating the NFRLC framework including an adaptive multilayer neural network (MNN) and interval type-2 fuzzy neural network (IT2FNN) with a high-gain observer (HGO), a robust smart observer-based system is set up to estimate the velocities of the AUVs, unknown dynamic parameters containing unmodeled dynamics, nonlinearities, uncertainties and external disturbances. By employing a saturation function in the design procedure and transforming the input limitations into input saturation nonlinearities, the risk of the actuator saturation is effectively reduced together with nonlinear input saturation compensation by the NFRLC strategy. A predefined funnel-shaped performance function is designed to attain certain prescribed output performance. Finally, stability study reveals that the entire closed-loop system signals are semi-globally uniformly ultimately bounded (SGUUB) and can provide prescribed convergence rate for the tracking errors so that the tracking errors approach to the origin evolving inside the funnel-shaped performance bound at the prescribed time.

Single-parameter-learning-based finite-time tracking control of underactuated MSVs under input saturation

This paper investigates the adaptive finite-time (FT) tracking control problem of underactuated marine surface vehicles (MSVs) subject to parameter uncertainties and external disturbances under input saturation. The input saturation nonlinearity is approximated employing Gaussian error function. Definition of hand position is extended to transform the original motion mathematical model of underactuated MSVs into the standard integral cascade form. The compounded uncertain vector synthesizing the uncertain parameters and unknown external disturbances is transformed into a linear parameterized form with a single parameter. Then, by employing the adaptive vector-backstepping design framework, a novel adaptive FT tracking control law is designed, and the estimation of the single unknown parameter is provided by an adaptive law online. Theoretical analysis shows that under the proposed tracking control scheme, FT convergence of position tracking errors of underactuated MSVs into a small set around the origin is ensured, while all signals in the closed-loop tracking control system are bounded. Simulation and comparison verify the effectiveness of the proposed novel adaptive tracking control scheme.

Consensus of One-Sided Lipschitz Multi-Agents Under Input Saturation

This brief investigates a new consensus control methodology for nonlinear one-sided Lipschitz (OSL) multi-agents by considering the input saturation nonlinearity for each agent. Local design approaches are followed for dealing with the constrained consensus control of nonlinear agents by using the OSL dynamics, saturation nonlinearity, and quadratic inner-boundedness property. A region of initial conditions based on the consensus error is revealed, for which the proposed control approach guarantees the consensus error’s convergence to the origin. A new design condition for computation of the consensus protocol gain is developed for the leader-following consensus. Then, simulation results on synchronization of mobile OSL are provided by considering input saturation.

Adaptive Neural Tracking Control of Full-state Constrained Nonstrict-feedback Time-delay Systems with Input Saturation

In this study, an adaptive neural backstepping control scheme is proposed for a class of nonstrict-feedback time-delay systems with input saturation, full-state constraints and unknown disturbances. A structural property of radial basis function neural network is presented to deal with the design from the nonstrict-feedback formation. This method does not require the parameter separation technique and its assumption. With the help of the Lyapunov-Krasovskii functionals and Young’s inequalities, the effects of time delays are compensated, and the unknown disturbances are eliminated in the design process. The barrier Lyapunov function (BLF) is applied to arrest the violation of the full-state constraints. To overcome the problem of input saturation nonlinearity, the smooth nonaffme function of the control input signal is adopted to approach the input saturation function. Moreover, an adaptive backstepping neural control strategy is proposed. The proposed adaptive neural controller ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Furthermore, the tracking error can converge to a small neighborhood of the origin. The simulation result shows the effectiveness of this method.

Adaptive Neural Path Following Control of Underactuated Surface Vessels With Input Saturation

In this paper, considering the input saturation, off-diagonal mass matrix, model uncertainties and time-varying environment disturbances, an adaptive neural path following control strategy, which is based on the surge-heading line-of-sight guidance law, is presented for underactuated surface vessels. In view of the practical situation, we consider that the mass and damping matrices are off-diagonal. For the sake of better path following performance, a surge-heading line-of-sight guidance law is established, where the surge-heading line-of-sight guidance law not only generates the desired heading angle, but also designs the desired surge speed for the control system. Then, adaptive neural path following controllers are designed to track the referenced signals, where the input saturation nonlinearity is handled by a hyperbolic tangent function, and the lumped disturbances including external environment disturbances, approximation errors and model uncertainties are approximated by adaptive radial basis function neural network. On the basis of the proposed control scheme, all error signals of the whole system are proven to be uniformly ultimately bounded, so that the target of path following problem is realized. At last, simulation results are applied to indicate that the presented approach is effective.

Robust Adaptive Finite-Time Tracking Control for Uncertain Euler-Lagrange Systems With Input Saturation

In this paper, a robust adaptive finite-time (FT) tracking control scheme is proposed for Euler-Lagrange systems (ELSs) subject to nonparametric uncertainties, unknown disturbances and input saturation. In the design procedure, a Gaussian error function is utilized to approximate the input saturation nonlinearity. Following that, by employing the natural property that the upper bound of model parameters uncertainties is linear-in-parameters, the lumped uncertain term caused by uncertain model parameters and external disturbances is formulated by a linear-parametric form with a single parameter. And then, a novel robust adaptive tracking control law is designed to resolve the tracking control problem of uncertain ELSs. The proposed control scheme is featured by FT convergence rate, and robustness against uncertainties and unknown disturbances. Furthermore, the robust adaptive FT tracking control scheme is insensitive to the character of the uncertainties, and is with low computational burden and easy to implement in engineering applications. And its rigorous stability is analyzed with the aid of the Lyapunov stability theory, and its effectiveness is verified by simulation results and comparison.

Adaptive finite time controller design for switched systems with unknown parameters, mismatched uncertain terms, external disturbances and input perturbations

The main objective of this study concerns with the problem of control and stabilization design schemes for a class of nonlinear switching systems whose dynamics are excited with an undetermined switching logic. Several conditions are taken into account for the subsystems of the whole structure to mimic the natural properties of the real-world nonlinear physical systems. The first is to assume that there is no prior information about the values of the system parameters. The second is to add matched and mismatched uncertain terms to the system dynamics. Furthermore, the effects of the input fluctuations in the actuator model are reflected via gain variations. We assume that the dynamic of a part of the system is uncertain and fully unknown with no control inputs to be relaxed as mismatching uncertainties. And, it is supposed that there is no previous knowledge about the bounds of the lumped uncertainties. To cope the mentioned issues, a robust adaptive control methodology is proposed in this paper. One of the main attributes of the designed control approach is that it guarantees the fast convergence of the system responses to zero with a (practical) finite settling time. A Lyapunov function tactic is then constructed to confirm the theoretic findings of the study. It is also demonstrated that the same controller is applicable for the switched systems perturbed by unknown input saturation nonlinearities. As a result, the chief contributions of this article involve: (1) handling the effects of the system unknown dynamics, external perturbations, unmatched uncertainties, control input variations, unknown parameters and input saturation limiter with no prior information about them and (2) providing a simple effective adaptive algorithm which ensures the fast finite time stability of the entire system under any arbitrary switch schemes. The provided computer simulations highlight the effective performance of the introduced adaptive control technology.

Robust Guaranteed Cost Control for a Class of Nonlinear 2-D Systems with Input Saturation

In this paper, a robust guaranteed cost controller is designed for a class of two-dimensional(2-D) discrete-time systems described by Roesser model, where the system simultaneously contains input saturation, parametric uncertainty and sector nonlinearity. Firstly, a convex hull representation is used to describe saturated input of the system. Secondly, a sufficient condition for ensuring the asymptotic stability of the closed-loop system and the existence of the robust guaranteed cost controller is given according to the Lyapunov stability theory. Then, this sufficient condition is transformed into a linear matrix inequality form by using Schur complement lemma and the design of robust guaranteed cost controller is realized by the solution of LMI. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Observed-based adaptive finite-time tracking control for a class of nonstrict-feedback nonlinear systems with input saturation

This paper concentrates upon the problem of adaptive neural finite-time tracking control for uncertain nonstrict-feedback nonlinear systems with input saturation. The design difficulty of non-smooth input saturation nonlinearity is solved by applying a smooth non-affine function to approximate the saturation signal. Neural networks, as a kind of specialized function estimators, are used to estimate the uncertain function. Meanwhile, a neural network-based observer is constructed to observe the unavailable states, and thus an observer-based adaptive finite-time tracking control strategy is developed by combining dynamic surface control (DSC) technique and backstepping approach. Furthermore, the stability of the considered system is analyzed via semi-global practical finite-time stability theory. Under the proposed control method, all the signals in the closed-loop system are bounded, and the system output can almost surely track the desired trajectory within a specified bounded error in a finite time. In the end, two examples are adopted to illustrate the validity of our results.

Robust adaptive NN tracking control for MIMO uncertain nonlinear systems with completely unknown control gains under input saturations

This paper focuses on the study of tracking control problem for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems with completely unknown control gains under input saturations. A hyperbolic tangent function is introduced to approximate the input saturation nonlinearity. Based on the above, a novel robust adaptive neural network (NN) tracking control scheme is proposed combining finite-time nonlinear tracking differentiator (FTNTD), Nussbaum-type function and adaptive NN with backstepping design tool. Within our scheme, a constructed novel nonlinear function featured by “small-error large-gain and large-error small-gain” is inset into virtual and actual control laws to achieve a balance between the feedback control gain and the system control performance and prevent the over-learning of parameter adaptive laws caused by the input saturation. By means of a newly constructed non-quadratic Lyapunov function, it is theoretically shown that all the signals in the closed-loop control system are semi-globally uniformly ultimately bounded. Finally, the effectiveness of our proposed scheme is verified by the simulations of two simulation examples.

Boundary robust adaptive anti-saturation control of vibrating flexible riser systems

In this paper, we address the vibration abatement problem of a flexible riser system preceded by nonlinear input saturation characteristic and uncertainties of the system. By virtue of Lyapunov theory, auxiliary system and robust control strategy, a boundary robust adaptive anti-saturation control is developed to restrain the vibration, remove the nonlinear input saturation effects and compensate for the uncertainties of system parameters and boundary disturbance. Applying the rigorous analysis without simplifying or discretizing the partial differential equation dynamics, the controlled system is ensured to be uniformly bounded stable with the designed control law. In the end, simulation results are presented for control performance verification.

Semi-global robust tracking consensus for multi-agent uncertain systems with input saturation via metamorphic low-gain feedback

This paper proposes a metamorphic adaptive low-gain feedback approach to investigate the semi-global robust tracking consensus problem of multi-agent uncertain systems with input saturation under a directed communication topology. The main contribution is to develop a new robust tracking consensus low-gain feedback algorithm, in which the feedback gain design does not rely on eigenstructure assignment algorithm and the solution of a parametric Algebraic Riccati Equation (ARE). By introducing appropriate assumptions, a class of metamorphic adaptive low-gain feedback protocols is designed based on the limited states information among neighbors. It is proved, in the sense of Lyapunov, that the robust tracking consensus problem for closed-loop multi-agent uncertain systems with input saturation and directed communication topology can be solved. Furthermore, the results are extended to the semi-global robust tracking consensus problem of nonlinear multi-agent uncertain systems with nonlinear input saturation under a jointly connected directed communication topology. Finally, two examples are presented to demonstrate the effectiveness of the proposed theories. ,

Fuzzy Adaptive DSC Design for an Extended Class of MIMO Pure-Feedback Non-Affine Nonlinear Systems in the Presence of Input Constraints

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

Vibration Control of an Axially Moving System with Restricted Input

In this study, we consider the global stabilization of an axially moving system under the condition of input saturation nonlinearity and external perturbation. Based on Lyapunov redesign method, observer backstepping, and high‐gain observers, an output feedback control strategy with an auxiliary system is constructed to eliminate the input saturation constraint effect and suppress the string system vibration, and a boundary disturbance observer is exploited to cope with the external disturbance. The stability of the controlled system is analyzed and proven based on Lyapunov stability without simplifying or discretizing the infinite dimensional dynamics. The presented simulation results show the effectiveness of the derived control.

Low-Complexity Adaptive Tracking Control for Unknown Pure Feedback Nonlinear Systems With Multiple Constraints

A low-complexity adaptive tracking control strategy for a class of pure feedback nonlinear systems is developed in the presence of completely unknown non-affine nonlinearities, prescribed tracking performance constraints, full states constraints, and input saturation constraint. To handle the input saturation nonlinearity and the constrained states without pre-calculating the bound of virtual controllers, a new coordinate transformation approach is presented with an arc-tangent function and an auxiliary first-order dynamics. Subsequently, to deal with the completely unknown non-affine nonlinearities and the problem of prescribed performance, an inverse hyperbolic tangent function and a Nussbaum function are introduced at each step of back-stepping design, which can guarantee the control errors to vary with prescribed performance functions in time and avoid the “explosion of complexity” issue simultaneously. Then, an adaptive controller is derived from the recursive design procedure without the use of any approximators. The semi-globally uniformly ultimate boundedness of all signals in the closed-loop system and the satisfaction of all constraints are rigorously proved through Lyapunov stability analysis. Finally, the simulation studies on a hypersonic flight vehicle system are worked out to demonstrate the effectiveness and the applicability of the investigated approach.

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.

Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation

In this paper, a novel technique for synthesizing static anti-windup compensator (AWC) is explored for dynamic nonlinear plants with state interval time-delays, exogenous input disturbance, and input saturation nonlinearity, by means of reformulated Lipschitz continuity property. A delay-range-dependent approach, based on Wirtinger-based inequality, is employed to derive a condition for finding the static AWC gain. By using the Lyapunov–Krasovskii functional, reformulated Lipschitz continuity property, Wirtinger-based inequality, sector conditions, bounds on delay, range of time-varying delay, and $$\mathcal {L}_2$$ gain reduction, several conditions are derived to guarantee the global and local stabilization of the overall closed-loop system. Further, when the lower time-delay bound is zero, the delay-dependent stabilization condition is derived for saturated nonlinear time-delay systems as a particular scenario of the suggested static AWC design approach. Furthermore, a static AWC design strategy is also provided when a delay-derivative bound is not known. An application to the nonlinear dynamical system is employed to demonstrate the usefulness of the proposed methodologies. A comparative numerical analysis with the existing literature is provided to show the superiority of the proposed AWC results.

Controlling Fluctuated Chaotic Power Systems With Compensation of Input Saturation: Application to Electric Direct Current Machines

It is shown that brushless direct current (DC) motors (BLDCMs), which have found many useful applications in motion control areas, display chaotic behaviors. To avoid undesirable inherent oscillations of such DC motors, a control strategy should be adopted in the applications. So, the control problem of applied chaotic power systems is taken into account in this paper. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. In this regard, it is assumed that the system is fluctuated by unknown uncertainties and environmental noises. Additionally, a part of the system dynamics is supposed to be unknown in advance and the effects of nonlinear input saturation are fully taken into account. Then, a one input nonsmooth adaptive sliding mode controller is realized to handle the aforementioned issues. The proposed controller does not require any knowledge about the bounds of the system uncertainties and external fluctuations as well as about the parameters of the input saturation. The finite time convergence and robustness of the driven control scheme are mathematically proved and numerically illustrated using matlab simulations for DC motors.