Actuator Saturation Nonlinearities Research Articles

Periodic event-triggered adaptive neural control of USVs under replay attacks

This work aims to address the control issue of unmanned surface vehicles (USVs) under replay attacks, where the influence of internal/external uncertainties and actuator’s physical constraints are taken into account. In the control design, a hyperbolic tangent function is used to replace the actuator saturation nonlinearity. To solve the design problem of mismatched unknown time-varying control gain caused by replay attacks, the single-parameter-learning technique is introduced, which avoids the operation of estimating for the unknown gain directly. To compensate for the effect of lumped uncertainties including attacks, unknown dynamics and external disturbances, the adaptive neural network with the finite covering principle is involved in the kinematic and dynamic channels, respectively. Furthermore, to reduce the update rate of actuator and alleviate the actuator wear, a periodic event-triggering mechanism (PETM) is established in the controller-actuator (C-A) channel. Finally, a periodic event-triggered (PET) adaptive neural tracking control solution for USVs under replay attacks is proposed, and it is verified that the control solution can force the trajectory of USVs to follow the reference trajectory even if there exists the effect of replay attacks. In addition, all signals in the closed-loop control system of USVs under replay attacks are bounded, and simulation and comparison results demonstrate the effectiveness of the control strategy.

Adaptive neural bounded formation tracking control of multiple autonomous surface vessels subject to actuator saturation and faults

This paper introduces an adaptive neural bounded formation tracking control strategy for a fleet of autonomous surface vessels with actuator saturation nonlinearity and faults. To begin with, by using the error transformation technique, the proposed algorithm derives the controller only based on the relative distance and angles measured by local sensor, which can avoid the requirement for supplementary leader-related information. Secondly, by employing neural networks (NNs) and auxiliary dynamic system, the system uncertainty and actuator saturation nonlinearity are handled, and a NNs-based bounded control law is derived. In addition, in order to solve actuator faults such as loss of validity, hard over faults and bias faults, the fault-tolerant adaptive law is introduced to compensate the weight matrix of the neural network and the upper bound of the fault parameters, instead of dealing with each individual matrix element. This can significantly decrease the computational workload of the algorithm, facilitating its practical implementation in engineering applications. Finally, it is demonstrated that all signals of the closed-loop system are semi-globally ultimately uniformly bounded. The performance and superiority of this control strategy are validated through numerical examples in various scenarios.

Reinforcement learning-based saturated adaptive robust output-feedback funnel control of surface vessels in different weather conditions

This article tackles the problem of saturated adaptive robust actor–critic learning PID tracking control design guaranteeing a prescribed funnel performance for ships with multiple dead bands in which the ship’s velocities/accelerations and dynamic parameters are unknown and time-variant subject to the availability of external disturbances. The controller is proposed by integrating an observer, adaptive actor–critic multi-layer neural networks, generalized saturation functions, the prescribed performance funnel control, an adaptive robust controller and multiple dead bands. The observer calculates the estimation of ship’s velocities/accelerations, in which the peaking phenomenon is prevented by limiting the observer signals. Within the structure of adaptive actor–critic design, adaptive multi-layer neural networks are exerted, which counteracts against ship’s time-variant uncertainties and the actuator saturation nonlinearity. In order to reduce the likelihood of actuator saturation well, generalized saturation functions are taken into account. To realize prespecified transient and steady-state performance of the tracking errors, the prescribed performance control is applied. With the purpose of avoiding the corner cutting to increase the trajectory tracking accuracy, curvature of the circular trajectories is calculated and the angle of arc is compensated. An adaptive robust controller is utilized to resist against external disturbances, and a scheme of multiple dead bands is devised in this paper to protect the actuator system in heavy seas.

Event-Triggered Adaptive PID Fault-Tolerant Control of Underactuated ASVs Under Saturation Constraint

This article discusses a control problem of underactuated autonomous surface vehicles (ASVs) subject to internal/external uncertainties, input saturations, and actuator faults, and proposes a novel event-triggered adaptive PID fault-tolerant (ETAPID-FT) control solution. To resolve the design difficulty caused by the underactuated feature, a standard multivariate integral cascade form regarding the mathematical model of underactuated ASVs is established. And then, to facilitate the implementation of PID-based design framework, the nonsmooth actuator saturation nonlinearity caused by the saturation constraint is represented by a smooth saturation model. In the control design, considering full features of the actuator fault and smooth function, an indirect neural approximation with single-parameter-leaning technique is developed, which endows the function of self-tuning control gain for the control solution. To relieve the mechanical wear of actuator, an improved event-triggered protocol by implanting a decreasing function of ASV’s position error is proposed. Moreover, the theoretical results show that the proposed ETAPID-FT control solution can guarantee the boundedness of all the signals in the closed-loop control system of underactuated ASVs. Finally, the validity of the developed control solution is confirmed by the simulation and comparative results

Composite event-triggered disturbance-observer-based control and passive control for semi-Markovian jump nonlinear systems with actuator saturation

In this paper, the composite control problem of continuous time semi-Markovian jump system with actuator saturation, multiple disturbances and unknown nonlinearity is investigated. A stochastic stability condition and a lower bound of the time between two consecutive events are derived to avoid Zeno behaviour, based on the combination of disturbance-observer-based control and event-triggered control. In addition, the passive control of the system based on the disturbance observer is studied. Finally, numerical simulation proves that the designed composite controller can effectively save communication resources, and can maintain the system to meet the passive performance indicators of the obtained closed-loop system under the influence of multiple disturbances and actuator saturation.

Reinforcement learning-based saturated adaptive robust neural-network control of underactuated autonomous underwater vehicles

This paper studies a high-performance intelligent online adaptive robust saturated dynamic surface control framework for underactuated autonomous underwater vehicles by engaging Actor–Critic neural networks in the presence of unmodeled dynamics, uncertainties, ocean disturbances and actuator saturation. The proposed controller is designed based on reinforcement learning method to compensate the effects of unmodeled dynamics and uncertainties more accurately that can lead to a better performance for the controller. The Actor–Critic neural networks are trained real-time by designing online training laws creatively and a new critic function is proposed to supervise the closed-loop performance with the aid of the Critic neural network. The proposed structure for the reinforcement learning method benefits from a model-free algorithm and only relies on the measurable variables of the closed-loop control system. This independency from system dynamics results in considerable low computational burden for the controller and, hence, the proposed control algorithm is efficient computationally. The hyperbolic tangent function is ingeniously used as a saturated stabilizer term to bound the control signals that results in low-amplitude control action and the probability of actuator saturation phenomenon is minimized by learning and compensating the actuator saturation nonlinearity as well. Finally, the stability of the proposed closed-loop system is investigated by the Lyapunov’s direct methodology and simulations along a comparative study with some quantitative assessments certify the contributions of this paper.

A novel model-free robust saturated reinforcement learning-based controller for quadrotors guaranteeing prescribed transient and steady state performance

For the purpose of improving the performance of trajectory tracking for quadrotors with the control input saturation, a novel model-free saturated prescribed performance reinforcement learning framework is proposed in the presence of the model uncertainties, nonlinearities and external disturbances. In this paper, saturation functions are employed to deal with input saturation, and the actuator's saturation nonlinearity is compensated by an intelligent method to decrease the saturation effects. Moreover, the prescribed performance control is utilized to ensure an adjustable transient and steady state response for the tracking errors. Besides, adaptive robust controllers are introduced to handle the effects of external disturbances online. A novel controller is proposed in collaboration with a reinforcement learning method based on actor-critic neural networks. The actor neural network is employed to estimate nonlinearities, actuator saturation nonlinearity, and model uncertainties, and the critic neural network is applied to estimate the reinforcement signals, which regulates the control action of the actor neural network online. The proposed actor-critic-based control structure benefits from a model-free calculation and only depends on the measurable signals of the closed-loop system. This freedom from system dynamics leads to a significant low computational load for the controller and, therefore, the proposed control method is computationally cost-effective. The adaptive robust controllers and the proposed actor-critic structures are trained online, and the convergence behavior of their learning laws is investigated in the course of stability examination. For the proof of stability, Lyapunov's direct method is used to show that all error variables of the closed-loop nonlinear control system are uniformly ultimately bounded. Finally, simulations along with some quantitative comparisons verify the efficiency and usefulness of the proposed control scheme.

Observer-based robust platoon formation control of electrically driven car-like mobile robots under collision avoidance and connectivity maintenance with a prescribed performance

This study intends to address the platoon formation control problem of a team of N electrically driven underactuated autonomous car-like mobile robots. A platoon controller is proposed by using the relative distance and angle between each two successive robots in the platoon. A high-gain observer is also used to leave out velocity sensors to reduce the cost of the implementation/maintenance and the weight of the robots. Then, the dynamic surface control method is used to prevent complexity of the controller design. Next, by utilizing the prescribed performance bound method, predetermined desired transient and steady-state behavior of the tracking formation errors, robots connectivity preservation, and their collision avoidance are guaranteed as well as singularity avoidance. Adaptive neural networks and adaptive robust controllers are used to improve the tracking performance in the presence of parametric and nonparametric uncertainties, unmodeled dynamics, actuator saturation nonlinearity, and unwanted external disturbances including exogenous forces and torques, friction, and vibration. The Lyapunov direct method proves that all signals of the closed-loop control system are uniformly ultimately bounded. Finally, simulation results are demonstrated to show the superiority of the proposed convoy tracking system.

Event-Triggered Adaptive Neural Fault-Tolerant Control of Underactuated MSVs With Input Saturation

This paper investigates the tracking control problem of marine surface vessels (MSVs) in the presence of uncertain dynamics and external disturbances. The facts that actuators are subject to undesirable faults and input saturation are taken into account. Benefiting from the smoothness of the Gaussian error function, a novel saturation function is introduced to replace each nonsmooth actuator saturation nonlinearity. Applying the hand position approach, the original motion dynamics of underactuated MSVs are transformed into a standard integral cascade form so that the vector design method can be used to solve the control problem for underactuated MSVs. By combining the neural network technique and virtual parameter learning algorithm with the vector design method, and introducing an event triggering mechanism, a novel event-triggered indirect neuroadaptive fault-tolerant control scheme is proposed, which has several notable characteristics compared with most existing strategies: 1) it is not only robust and adaptive to uncertain dynamics and external disturbances but is also tolerant to undesirable actuator faults and saturation; 2) it reduces the acting frequency of actuators, thereby decreasing the mechanical wear of the MSV actuators, via the event-triggered control (ETC) technique; 3) it guarantees stable tracking without the a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> knowledge of the dynamics of the MSVs, external disturbances or actuator faults; and 4) it only involves two parameter adaptations—a virtual parameter and a lower bound on the uncertain gains of the actuators—and is thus more affordable to implement. On the basis of the Lyapunov theorem, it is verified that all signals in the tracking control system of the underactuated MSVs are bounded. Finally, the effectiveness of the proposed control scheme is demonstrated by simulations and comparative results.

Finite-time sampled-data control of switched stochastic model with non-deterministic actuator faults and saturation nonlinearity

This work addresses the problem of extended-dissipative finite-time reliable control of switched stochastic model with non-deterministic actuator faults, time-delay, sampled-data scheme, saturation nonlinearity and stochastic uncertainties, where the actuator faults obey certain probabilistic distribution. The important of this article is to develop a stochastic fault-tolerant sampled-data controller under actuator saturation nonlinearity such that the considered stochastic switched model is stochastically stable and obeys a dissipative pursuance ratio in the finite-time interval. A novel finite-time criteria are proposed to guaranteeing the stochastically stable in finite time for switched stochastic system based on the finite-time stability theory and suitable Lyapunov–Krasovskii functional (LKF) along with convex integral inequality method. Then, the derived criteria are presented in terms of linear matrix inequalities (LMIs) and it can be solved efficiently by standard Matlab software. Finally, numerical simulations are given to illustrate the efficiency of the proposed method.

Enhanced Composite Nonlinear Control Technique using Adaptive Control for Nonlinear Delayed Systems

Background and Introduction: The proposed control law is designed to provide fast reference tracking with minimal overshoot and to minimize the effect of unknown nonlinearities and external disturbances. Methods: In this work, an enhanced composite nonlinear feedback technique using adaptive control is developed for a nonlinear delayed system subjected to input saturation and exogenous disturbances. It ensures that the plant response is not affected by adverse effect of actuator saturation, unknown time delay and unknown nonlinearities/ disturbances. The analysis of stability is done by Lyapunov-Krasovskii functional that guarantees asymptotical stability. Results: The proposed control law is validated by its implementation on exothermic chemical reactor. MATLAB figures are provided to compare the results. Conclusion: The simulation results of the proposed controller are compared with the conventional composite nonlinear feedback control which illustrates the efficiency of the proposed controller.

Adaptive Event-Triggered H∞ Control for Networked Control Systems With Actuator Saturation and Random Nonlinearities

This paper investigates the problem of the adaptive event-triggered control for networked nonlinear systems with actuator saturation using dynamic output feedback controller (DOFC). In view of adaptive event-triggered mechanism (AETM), a model of networked control systems (NCSs) with actuator saturation and random nonlinearities is first established. Then, by constructing the Lyapunov–Krasovskii functional (LKF), sufficient condition for asymptotically stable with an $H_\infty $ performance index is derived in terms of linear matrix inequalities (LMIs). In the process, through combining the Wirtinger-based integral inequality and the extended reciprocally convex matrix inequality (ERCMI), the delay-dependent integral terms obtained by the derivative of the constructed LKF are estimated. Based on the above results, the DOFC gains and corresponding AETM parameter are co-designed. Finally, two numerical examples are demonstrated to illustrate the effectiveness of the proposed method.

Adaptive Sliding Mode Control of Vehicular Platoons With Prescribed Tracking Performance

This paper investigates a vehicular platoon control problem with prescribed tracking performance in the presence of actuator saturation, uncertain parameters, and unknown disturbances. Two adaptive sliding mode control schemes based on leader–predecessor and leader–bidirectional information flows are presented to ensure string stability and strong string stability, respectively, with a prescribed tracking performance. The actuator saturation nonlinearity is addressed by approximating it with a smooth hyperbolic tangent function. The effects of uncertain parameters and exogenous disturbances are dealt with by introducing a set of adaptation laws. The effectiveness of the proposed control schemes is demonstrated via numerical simulation results.

A New Anti-Windup Compensator Based on Quantitative Feedback Theory for an Uncertain Linear System with Input Saturation

This paper devotes to the robust stability problem for an uncertain linear time invariant (LTI) feedback system with actuator saturation nonlinearity. Based on a three degree of freedom (DOF) non-interfering control structure, the robust stability is enforced with the describing function (DF) approach for an uncertain LTI system to avoid the limit cycle. A new type of anti-windup (AW) compensator is designed using the quantitative feedback theory (QFT) graphical method, which results in a simple design procedure and low-order AW control system. One of the most significant benefits of the proposed method is free of the non-convexity (intractable) drawback of the linear matrix inequality (LMI)-based approach. The analysis conducted on the benchmark problem clearly reveals that the proposed QFT-based anti-windup design is able to handle both saturation and uncertainty in a very effective manner.

Fault-tolerant control for commercial aircraft with actuator faults and constraints

In this paper, a constrained control scheme based on model reference adaptive control is investigated for the longitudinal motion of a commercial aircraft with actuator faults and saturation nonlinearities. Actuator faults and constraints are both important factors adversely affecting the stability and performance of flight control systems. An adaptive adjustment law based on Lyapunov function is utilized to adjust the fault-tolerant control law. Both additive and multiplicative faults are considered in the designed controller to deal with the three types of actuator faults: locked in place, loss of effectiveness, and bias. Moreover, different techniques are implemented in the basic and fault-tolerant controller to anti-windup. Proofs for the stability of the two modified controllers which improve the performance of control system operating in the presence of actuator faults and saturations are proposed. Finally, a numerical example of the anti-windup fault-tolerant controller for a commercial aircraft is demonstrated. The stability and performance improvements can be accrued with the presented fault-tolerant control scheme.

Anti‐windup compensator design for power system subjected to time‐delay and actuator saturation

In this study, a delay-dependent anti-windup compensator (AWC) is designed for supplementary damping control (SDC) of flexible AC transmission system (FACTS) device to enhance the damping of inter-area oscillations of the power system subjected to time-delay and actuator saturation. By employing global signal measurements, an SDC of FACTS device is designed without considering the effect of time-delay and actuator saturation to stabilise the power system using a robust output feedback controller with pole placement approach. Then, based on the generalised sector condition and Lyapunov–Krasovskii functional, an add-on delay-dependent AWC is designed to mitigate the adverse effect of time-delay and actuator saturation non-linearity. For the design of delay-dependent AWC, sufficient conditions guarantee the asymptotic stability of the closed-loop power system are formulated in the form of linear matrix inequalities (LMIs). These conditions are cast into the LMI-based convex optimisation problem to compute the AWC gains. To evaluate the effectiveness of the proposed controller, non-linear simulations were performed first using MATLAB/Simulink. Then, the authors implemented the proposed controller in real-time using the Opal-RT digital simulator. From the obtained results, it is observed that the proposed controller enhances the damping of inter-area oscillations by compensating the effect of time delay and actuator saturation.

Nonlinear optimized adaptive trajectory control of helicopter

This paper attempts to develop an optimized adaptive trajectory control system for helicopters based on the dynamic inversion method. This control algorithm is implemented by three time-scale separation architectures. Pseudo control hedging (PCH) is used to protect the adaptive element from actuator saturation nonlinearities and also from the inner-outer-loop interaction. In addition, to augment the attitude control system, two online adaptive architectures that employ a neural network are used. By tuning the neural network based on the system model, a better and faster learning will be achieved, but this is a frustrating and time consuming process. Due to complexity in accurate tuning of neural network, this paper introduces a non-dominated sorting genetic algorithm II (NSGA-II) for off-line optimization of the neural network. Thus, in the proposed method, the neural network can compensate model inversion error caused by the deficiency of full knowledge of helicopter dynamics more accurately. The effectiveness of proposed method is demonstrated by numerical simulations.

Neural Network Adaptive Control of Free Floating Space Robot with Actuator Saturation

This paper proposes an adaptive neural network law for trajectory tracking of a class of free-floating space robot with actuator saturation. Using neural network with global approximation, the control strategy design an on-line real time adaptive learning law to approach the uncertain model and the actuator saturation nonlinearity. The neural network approach errors and outside disturbance can be eliminated by a robust controller.The control strategy need not depend on the model, and can be used under actuator saturation.The control strategy can guarantee the stability of system and the asymptotic convergence of tracking errors based on the Lyapunov’s theory. The simulation results indicate that the proposed strategy can effectively work with actuator saturation.

An Improved Antiwindup Design Using an Anticipatory Loop and an Immediate Loop

We present an improved antiwindup design for linear invariant continuous-time systems with actuator saturation nonlinearities. In the improved approach, two antiwindup compensators are simultaneously designed: one activated immediately at the occurrence of actuator saturation and the other activated in anticipatory of actuator saturation. Both the static and dynamic antiwindup compensators are considered. Sufficient conditions for global stability and minimizing the inducedL2gain are established, in terms of linear matrix inequalities (LMIs). We also show that the feasibility of the improved antiwindup is similar to the traditional antiwindup. Benefits of the proposed approach over the traditional antiwindup and a recent innovative antiwindup are illustrated with well-known examples.

Approximation-Based Robust Adaptive Automatic Train Control: An Approach for Actuator Saturation

This paper addresses an on-line approximation-based robust adaptive control problem for the automatic train operation (ATO) system under actuator saturation caused by constraints from serving motors. A robust adaptive control law is proposed, which is proved capable of on-line estimating of the unknown system parameters and stabilizing the closed-loop system. To cope with actuator saturation, another robust adaptive control is proposed for the ATO system, by explicitly considering the actuator saturation nonlinearity other than unknown system parameters, which is also proved capable of stabilizing the closed-loop system. Simulation results are presented to verify the effectiveness of the two proposed control laws.