Search Results (22)

In this paper, the problem of pitching attitude finite-horizon optimization for aircraft is posed with system uncertainties, external disturbances, and input constraints. First, a neural network (NN) and a nonlinear disturbance observer (NDO) are employed to estimate the value of system uncertainties and external disturbances. Taking input constraints into account, an auxiliary system is designed to compensate for the constrained input. Subsequently, the backstepping control containing NN and NDO is used to ensure the stability of systems and suppress the adverse effects caused by the system uncertainties and external disturbances. In order to avoid the derivation operation in the process of backstepping, a dynamic surface control (DSC) technique is utilized. Simultaneously, the estimations of the NN and NDO are applied to derive the backstepping control law. For the purpose of achieving finite-horizon optimization for pitching attitude control, an adaptive method termed adaptive dynamic programming (ADP) with a single NN-termed critic is applied to obtain the optimal control. Time-varying feature functions are applied to construct the critic NN in order to approximate the value function in the Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, a supplementary term is added to the weight update law to minimize the terminal constraint. Lyapunov stability theory is used to prove that the signals in the control system are uniformly ultimately bounded (UUB). Finally, simulation results illustrate the effectiveness of the proposed finite-horizon optimal attitude control method. Full article

In this paper, the theoretical stability of batch offline action-dependent heuristic dynamic programming (BOADHDP) is analyzed for deep neural network (NN) approximators for both the action value function and controller which are iteratively improved using collected experiences from the environment. Our findings extend previous research on the stability of online adaptive ADHDP learning with single-hidden-layer NNs by addressing the case of deep neural networks with an arbitrary number of hidden layers, updated offline using batched gradient descend updates. Specifically, our work shows that the learning process of the action value function and controller under BOADHDP is uniformly ultimately bounded (UUB), contingent on certain conditions related to NN learning rates. The developed theory demonstrates an inverse relationship between the number of hidden layers and the learning rate magnitude. We present a practical implementation involving a twin rotor aerodynamical system to emphasize the impact difference between the usage of single-hidden-layer and multiple-hidden-layer NN architectures in BOADHDP learning settings. The validation case study shows that BOADHDP with multiple hidden layer NN architecture implementation obtains $0.0034$ on the control benchmark, while the single-hidden-layer NN architectures obtain $0.0049$, outperforming the former by 1.58% by using the same collected dataset and learning conditions. Also, BOADHDP is compared with online adaptive ADHDP, proving the superiority of the former over the latter, both in terms of controller performance and data efficiency. Full article

Mixed zero-sum games consider both zero-sum and non-zero-sum differential game problems simultaneously. In this paper, multiplayer mixed zero-sum games (MZSGs) are studied by the means of an integral reinforcement learning (IRL) algorithm under the dynamic event-triggered control (DETC) mechanism for completely unknown nonlinear systems. Firstly, the adaptive dynamic programming (ADP)-based on-policy approach is proposed for solving the MZSG problem for the nonlinear system with multiple players. Secondly, to avoid using dynamic information of the system, a model-free control strategy is developed by utilizing actor–critic neural networks (NNs) for addressing the MZSG problem of unknown systems. On this basis, for the purpose of avoiding wasted communication and computing resources, the dynamic event-triggered mechanism is integrated into the integral reinforcement learning algorithm, in which a dynamic triggering condition is designed to further reduce triggering times. With the help of the Lyapunov stability theorem, the system states and weight values of NNs are proven to be uniformly ultimately bounded (UUB) stable. Finally, two examples are demonstrated to show the effectiveness and feasibility of the developed control method. Compared with static event-triggering mode, the simulation results show that the number of actuator updates in the DETC mechanism has been reduced by 55% and 69%, respectively. Full article

This paper introduces a stable adaptive PID-like control scheme for quadrotor Unmanned Aerial Vehicle (UAV) systems. The PID-like controller is designed to closely estimate an ideal controller to meet specific control objectives, with its gains being dynamically adjusted through a stable adaptation process. The adaptation process aims to reduce the discrepancy between the ideal controller and the PID-like controller in use. This method is considered model-free, as it does not require knowledge of the system’s mathematical model. The stability analysis performed using a Lyapunov method demonstrates that every signal in the closed-loop system is Uniformly Ultimately Bounded (UUB). The effectiveness of the proposed PID-like controller is validated through simulations on a quadrotor for path following, ensuring accurate monitoring of the target positions and yaw angle. Simulation results highlight the performance of this control scheme. Full article

As a substitute for human arms, underwater vehicle dual-manipulator systems (UVDMSs) have attracted the interest of global researchers. Visual servoing is an important tool for the positioning and tracking control of UVDMSs. In this paper, a reinforcement-learning-based adaptive control strategy for the UVDMS visual servo, considering the model uncertainties, is proposed. Initially, the kinematic control is designed by developing a hybrid visual servo approach using the information from multi-cameras. The command velocity of the whole system is produced through a task priority method. Then, the reinforcement-learning-based velocity tracking control is developed with a dynamic inversion approach. The hybrid visual servoing uses sensors equipped with UVDMSs while requiring fewer image features. Model uncertainties of the coupled nonlinear system are compensated by the actor–critic neural network for better control performances. Moreover, the stability analysis using the Lyapunov theory proves that the system error is ultimately uniformly bounded (UUB). At last, the simulation shows that the proposed control strategy performs well in the task of dynamical positioning. Full article

This paper focuses on a distributed cooperative time-varying formation maneuvering issue of under-actuated unmanned surface vehicles (USVs). A fleet of USVs is guided by a parameterized path with a time-varying formation while avoiding collisions and preserving the connectivity in the environment with multiple obstacles. In some surface missions, due to the obstacles in the external environment, the bandwidth limitations of the communication channel, and the hardware components/performance constraints of the USVs themselves, each vehicle is considered to be subject to model uncertainty, actuator quantization, sensor dead zone, and velocity constraints. During the control design process, the radial basis function (RBF) neural networks (NNs) are utilized to deal with nonlinear terms. Based on a nonlinear decomposition method, the relationship between the control signal and the quantization one is established, which overcomes the difficulty arising from actuator quantization. A Nussbaum function is introduced to handle the unknown output dead zone problem caused by reduced sensor sensitivity. Moreover, a universal-constrained function is employed to satisfy both the constrained and unconstrained requirements during formation keeping and obstacle avoidance. The Lyapunov stability theory confirmed that the error signals are uniformly ultimately bounded (UUB). The simulation results demonstrate the effectiveness of the proposed distributed formation control of multiple USVs. Full article

This study presents the development of an adaptive fuzzy control strategy for double-star PMSM-PWM inverters used in ship electrical propulsion. The approach addresses the current and speed tracking challenges of double-star permanent magnet synchronous motors (DSPMSMs) in the presence of parametric uncertainties. Initially, a modeling technique employing a matrix transformation method is introduced, generating decoupled and independent star windings to eliminate inductive couplings, while maintaining model consistency and torque control. The precise DSPMSM model serves as the foundation for an unknown nonlinear backstepping controller, approximated directly using an adaptive fuzzy controller. Through the Lyapunov direct method, system stability is demonstrated. All signals in the closed-loop system are ensured to be uniformly ultimately bounded (UUB). The proposed control system aims for low tracking errors, while also mitigating the impact of parametric uncertainties. The effectiveness of the adaptive fuzzy nonlinear control system is validated through tests conducted in hardware-in-the-loop (HIL) simulations, utilizing the OPAL-RT platform, OP4510. Full article

As technology evolves, more complex non-affine systems are created. These complex systems are hard to model, whereas most controllers require information on systems to be designed. This information is hard to obtain for systems with varying control directions. Therefore, this study introduces a novel data-driven estimator and controller tailored for single-input single-output non-affine discrete-time systems. This approach focuses on cases when the control direction varies over time and the mathematical model of the system is completely unknown. The estimator and controller are constructed using a Multiple-input Fuzzy Rules Emulated Network framework. The weight vectors are updated through the gradient descent optimization method, which employs a unique cost function that multiplies the error by a hyperbolic tangent. The stability analyses demonstrate that both the estimator and controller converge to uniformly ultimately bounded (UUB) functions of Lyapunov. To validate the results, we show experimental tests of force control that were executed on the z-axis of a drive-controlled 3D scanning robot. This system has a varying control direction, and we also provide comparison results with a state-of-the-art controller. The results show a mean absolute percentage tracking error smaller than one percent on the steady state and the expected variation in the system’s control direction. Full article

This study describes a circular curve path-following controller for an underactuated unmanned surface vessel (USV) experiencing unmodeled dynamics and external disturbances. Initially, a three degrees of freedom kinematic model of the USV is proposed for marine environmental disturbances and internal model parameter deterrence. Then, the circular path guidance law and controller are designed to ensure that the USV can move along the desired path. During the design process, a proportional derivative (PD)-based sigmoid fuzzy function is applied to adjust the guidance law. To accommodate unknown system dynamics and perturbations, a radial basis function neural network and adaptive updating laws are adopted to design the surge motion and yaw motion controllers, estimating the unmodeled hydrodynamic coefficients and external disturbances. Theoretical analysis shows that tracking errors are uniformly ultimately bounded (UUB), and the closed-loop system is asymptotically stable. Finally, the simulation results show that the proposed controller can achieve good control effects while ensuring tracking accuracy and demonstrating satisfactory disturbance rejection capability. Full article

This paper develops a novel output feedback control scheme for the motion-tracking problem of an electro-hydrostatic actuator (EHA) in the presence of model uncertainties and external disturbances. Firstly, a simplified third-order system model of the studied EHA is established using theoretical methods. For the first time, an extended sliding mode observer (ESMO) is introduced to simultaneously account for the shortage of unknown system states and modeling imperfections. Based on this, a robust nonlinear controller is developed using the backstepping control framework to stabilize the closed-loop system. This controller integrates estimates of immeasurable system states and lumped disturbances to deal with their adverse impacts. Moreover, the dynamic surface control (DSC) technique is employed to effectively mitigate the computational burden of the traditional backstepping framework. An ultimately uniformly bounded (UUB) performance is assured by using the recommended method. Furthermore, the stability of not only the observer but also the closed-loop system is concretely analyzed by using the Lyapunov theory. Finally, experiment results under various working scenarios are given to convincingly demonstrate the advantage of the suggested method in comparison with some reference control approaches. Full article

This paper addresses the problem of decentralized safety control (DSC) of constrained interconnected nonlinear safety-critical systems under reinforcement learning strategies, where asymmetric input constraints and security constraints are considered. To begin with, improved performance functions associated with the actuator estimates for each auxiliary subsystem are constructed. Then, the decentralized control problem with security constraints and asymmetric input constraints is transformed into an equivalent decentralized control problem with asymmetric input constraints using the barrier function. This approach ensures that safety-critical systems operate and learn optimal DSC policies within their safe global domains. Then, the optimal control strategy is shown to ensure that the entire system is uniformly ultimately bounded (UUB). In addition, all signals in the closed-loop auxiliary subsystem, based on Lyapunov theory, are uniformly ultimately bounded, and the effectiveness of the designed method is verified by practical simulation. Full article

In this paper, the safe optimal control method for continuous-time (CT) nonlinear safety-critical systems with asymmetric input constraints and unmatched disturbances based on the adaptive dynamic programming (ADP) is investigated. Initially, a new non-quadratic form function is implemented to effectively handle the asymmetric input constraints. Subsequently, the safe optimal control problem is transformed into a two-player zero-sum game (ZSG) problem to suppress the influence of unmatched disturbances, and a new Hamilton–Jacobi–Isaacs (HJI) equation is introduced by integrating the control barrier function (CBF) with the cost function to penalize unsafe behavior. Moreover, a damping factor is embedded in the CBF to balance safety and optimality. To obtain a safe optimal controller, only one critic neural network (CNN) is utilized to tackle the complex HJI equation, leading to a decreased computational load in contrast to the utilization of the conventional actor–critic network. Then, the system state and the parameters of the CNN are uniformly ultimately bounded (UUB) through the application of the Lyapunov stability method. Lastly, two examples are presented to confirm the efficacy of the presented approach. Full article

This paper presents the design of two predefined-time active fault-tolerant controllers for the trajectory tracking of autonomous underwater vehicles (AUVs) which can address actuator faults without causing actuator saturation. The first controller offers improved steady-state trajectory tracking precision, while the second ensures a nonsingular property. Firstly, a predefined-time sliding mode controller is formulated based on a predefined-time disturbance observer by integrating a novel predefined-time auxiliary system to prevent the control input from exceeding the actuator’s physical limitations. Subsequently, a non-singular backstepping controller is introduced to circumvent potential singularities in the sliding mode controller, guaranteeing that the trajectory tracking error is uniformly ultimately bounded (UUB) within the predefined time. Additionally, theoretical analysis and simulation results are presented to illustrate the advantages of the proposed method. Full article

Aiming at robotic manipulators subject to system uncertainty and external disturbance, this paper presents a novel adaptive control scheme that uses the time delay estimation (TED) technique and reinforcement learning (RL) technique to achieve a good tracking performance for each joint of a manipulator. Compared to conventional controllers, the proposed control scheme can not only handle the system parametric uncertainty and external disturbance but also guarantee both the angular positions and angular velocities of each joint without exceeding their preset constraints. Moreover, it has been proved by using Lyapunov theory that the tracking errors are uniformly ultimately bounded (UUB) with a small bound related to the parameters of the controller. Additionally, an innovative RL-based auxiliary term in the proposed controller further minimizes the steady state tracking errors, and thereby the tracking accuracy is not compromised by the lack of asymptotic convergence of tracking errors. Finally, the simulation results validate the effectiveness of the proposed control scheme. Full article

In this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety boundary function, a nominal system-dependent multi-input barrier transformation architecture is developed to deal with the time-varying safety constraints and uncertain disturbances. Based on the obtained transformation system, the coupled Hamilton–Jacobi–Bellman (HJB) function is established to obtain the constrained Nash equilibrium solution. In addition, due to the fact that it is difficult to solve the HJB function directly, the single critic neural network (NN) is constructed to approximate the optimal performance index function of different control inputs, respectively. It is proved theoretically that, under the influence of uncertain disturbances and time-varying safety constraints, the system states and neural network parameters can be uniformly ultimately bounded (UUB) by the proposed neural network approximation method. Finally, the effectiveness of the proposed method is verified by two nonlinear simulation examples. Full article