Semi-globally Uniformly Ultimately Bounded Research Articles

Adaptive neural network dynamic surface optimal saturation control for single‐phase grid‐connected photovoltaic systems

AbstractAn adaptive neural network (NN) based optimal saturation control scheme is investigated for single‐phase grid‐connected photovoltaic (PV) systems by incorporating dynamic surface control (DSC) and adaptive dynamic programming (ADP) based on the backstepping control design framework. For each backstepping step, a critic‐actor architecture is constructed via reinforcement learning (RL), and the PV system is optimized according to the cost function in the architecture. Due to the nonlinearity, it is difficult to solve the Hamilton–Jacobi–Bellman (HJB) equation. The neural networks (NNs) are employed to approximate the solution of the HJB equation such that the optimal virtual control and the actual controller are obtained. By considering control input symmetric saturation nonlinearity link, constraints on pulse width modulation (PWM) are ensured. On this basis, the combination of backstepping control design and dynamic surface technique is used to overcome the shortcomings of “differential explosion” and simplify calculations. Based on the Lyapunov method, the stability analysis proves that all signals of the closed‐loop PV systems are semiglobally uniformly ultimately bounded (SGUUB). Simulation experiments and comparative results are given to verify the efficacy of the studied control strategy.

Decentralized adaptive tracking control for interconnected nonlinear systems with unmodeled dynamics and input delays

This paper focuses on the decentralised adaptive tracking control problem for nonstrict-feedback interconnected nonlinear systems with unmodeled dynamics and input delays. To identify the unstructured uncertainties, a novel broad learning system (BLS) approximation technique is introduced in this study to solve it. On this basis, a nonlinear state observer is designed to estimate the unmeasurable state variables. A dynamic signal is introduced to deal with the effect of unmodeled dynamics, and the appropriate error transformation is utilised to handle the effect of input delays. The decentralised adaptive tracking control strategy is proposed to the considered interconnected nonlinear systems using the design procedures of backstepping control with command filter. The semi-globally uniformly ultimately boundedness (SGUUB) stability and the tracking performance of the whole closed-loop systems could be guaranteed by using the Lyapunov approach. Finally, simulation results are provided to validate the present theoretical claims.

Performance-prescribed optimal neural control for hypersonic vehicles considering disturbances: An adaptive dynamic programming approach

The precise trajectory tracking control of hypersonic vehicles plays a crucial role in secure flight. To address this challenge, this article develops an optimal neural control framework with prescribed performance constraints for height-velocity control tasks with disturbances. To this end, the control-oriented error model is firstly established and transformed into an affine nonlinear form to provide a foundation for the design of controller. Then, in order to balance performance constraints and convergence speed, a performance-constraint function is introduced to convert the constrained tracking error into an unconstrained one. After that, an improved sliding mode compensation observer is proposed by combining low-fidelity approximation data with high-fidelity compensation model for eliminating disturbances. The developed control scheme is organized by an adaptive dynamic programming (ADP) algorithm based on the actor-critic policy structure to achieve the near-optimal control strategy. Meanwhile, the designed neural network (NN) weight updating laws are provided to obtain the solution of Hamiltonian-Jacobi-Bellman (HJB) equation rapidly without high calculation consumption. Finally, the stability conditions of the closed-loop system are performed and ensure the entire framework is semi-global uniformly ultimately bounded (SGUUB), two simulation cases verify the effectiveness and superiority of the proposed approach.

Command Filter-Based Adaptive Neural Control for Nonstrict-Feedback Nonlinear Systems with Prescribed Performance

In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new performance function, the fixed-time performance function, which does not depend on the accurate initial value of the error signal and has the ability of fixed-time convergence, is proposed for the first time. A radial basis function neural network is introduced to identify unknown nonlinear functions, and the characteristic of Gaussian basis functions is utilized to overcome the difficulties of the nonstrict-feedback structure. Moreover, in contrast to the traditional Backstepping technique, a command filter-based adaptive control algorithm is constructed, which solves the “explosion of complexity” problem and relaxes the assumption on the reference signal. Additionally, it is guaranteed that the tracking error falls within a prescribed small neighborhood by the designed performance functions in fixed time, and the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the proposed control scheme is verified by numerical simulation.

Adaptive Optimal Tracking Control of an Underactuated Surface Vessel Using Actor-Critic Reinforcement Learning.

In this article, we present an adaptive reinforcement learning optimal tracking control (RLOTC) algorithm for an underactuated surface vessel subject to modeling uncertainties and time-varying external disturbances. By integrating backstepping technique with the optimized control design, we show that the desired optimal tracking performance of vessel control is guaranteed due to the fact that the virtual and actual control inputs are designed as optimized solutions of every subsystem. To enhance the robustness of vessel control systems, we employ neural network (NN) approximators to approximate uncertain vessel dynamics and present adaptive control technique to estimate the upper boundedness of external disturbances. Under the reinforcement learning framework, we construct actor-critic networks to solve the Hamilton-Jacobi-Bellman equations corresponding to subsystems of surface vessel to achieve the optimized control. The optimized control algorithm can synchronously train the adaptive parameters not only for actor-critic networks but also for NN approximators and adaptive control. By Lyapunov stability theorem, we show that the RLOTC algorithm can ensure the semiglobal uniform ultimate boundedness of the closed-loop systems. Compared with the existing reinforcement learning control results, the presented RLOTC algorithm can compensate for uncertain vessel dynamics and unknown disturbances, and obtain the optimized control performance by considering optimization in every backstepping design. Simulation studies on an underactuated surface vessel are given to illustrate the effectiveness of the RLOTC algorithm.

Event-Triggered Output-Feedback Adaptive Control of Interconnected Nonlinear Systems: A Cyclic-Small-Gain Approach.

This article proposes a novel output-feedback event-triggered control protocol for a class of interconnected parametric nonlinear systems. Different from most existing works where event-triggering mechanisms are considered for only the controller-to-actuator channel or the sensor-to-controller channel, this work adopts event-triggering mechanisms for both channels as well as adaptive laws. An adaptive states observer is designed to estimate the unavailable system state and then a novel adaptive event-triggered controller is proposed based on the celebrated backstepping technique. By utilizing the cyclic small-gain theorem and Lyapunov theory, it is shown that the proposed control scheme ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the Zeno behavior is successfully excluded. Finally, a practical example is provided to illustrate the effectiveness and advantages of the proposed approach.

Adaptive neural event‐triggered near‐optimal control for affined uncertain nonlinear discrete‐time system

AbstractA novel event‐triggered heuristic dynamic programming (HDP) algorithm is proposed for the near‐optimal control of uncertain discrete‐time nonlinear input‐affine systems. Based on input‐to‐state stability (ISS) analysis, a new event‐triggered mechanism (ETM) is designed. Under constant coefficients, a Lipschitz‐like assumption that forms the basis of the event‐triggering condition is considered to be conservative. To further reduce the conservativeness of the triggering condition and enlarge the average interevent time, an adaptive threshold parameter is utilized in the proposed ETM. In the HDP algorithm framework, model, critic, and action network are adopted to achieve state estimation, approximation to the optimal cost function, and solution to Hamilton–Jacobian–Bellman (HJB) equation. Under the proposed event‐triggered HDP algorithm, the closed system is proved to possess semiglobal uniform ultimate boundedness (SGUUB). Finally, by conducting simulation, it shows that on the premise of satisfying control performance, the event‐triggered strategy can realize reduction on the updating frequency of the controller.

Adaptive output-feedback control for switched nonlinear systems with measurement sensitivity based on double-side event-triggering mechanisms

This article concentrates on the problem of adaptive event-triggered control with double-side event-triggering mechanisms for a family of switched nonlinear systems with measurement sensitivity. In order to circumvent the negative effect of intermittent transmission and sensor measurement sensitivity on the output, an extended system is constructed by introducing a first-order output filter. Then, an input-driven neural switched observer is designed to estimate unmeasurable system states. To deal with the mutual interaction between the triggering and the switching mechanisms and their negative effect on the positive lower bound of inter-execution intervals, an incremental compensation is incorporated in the event-triggering mechanism (ETM) at the output sensor side. At last, a novel event-triggered control scheme built on both sides of the controller and output is proposed, which exhibits superior efficacy compared to the one-side event-triggered control scheme. By using the methods of the average dwell time (ADT) and the backstepping design, it is guaranteed that all signals of the switched closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the Zeno phenomenon is excluded. The efficacy of the proposed methodology is validated by using a numerical simulation and a one-link robot system.

Event‐triggered adaptive fuzzy bipartite containment control for switched nonlinear multi‐agent systems with actuator attacks

AbstractThis paper considers the event‐triggered adaptive fuzzy bipartite containment control problem for switched nonlinear multi‐agent systems (MASs) with actuator attacks. To handle the completely unknown nonlinear functions in the considered system, fuzzy logic systems (FLSs) are applied to approximate the unknown nonlinear functions. In addition, an adaptive bipartite containment control approach is designed to deal with the actuator attacks, which can reduce the burden of communication. According to the designed adaptive bipartite containment control scheme, it is shown that all the signals are semi‐globally uniformly ultimately bounded (SGUUB), and all the outputs of the followers achieve the bipartite consensus and finally enter the convex set spanned by leaders' in the presence of actuator attacks. Eventually, a simulation example is presented to illustrate the availability of the developed strategy.

Funnel-Based Adaptive Neural Fault-Tolerant Control for Nonlinear Systems with Dead-Zone and Actuator Faults: Application to Rigid Robot Manipulator and Inverted Pendulum Systems

This study addresses an adaptive neural funnel fault-tolerant control problem for a class of strict-feedback nonlinear systems with actuator faults and input dead zone. To guarantee the boundedness of the tracking error, a modified transformation for funnel error is devised and incorporated into the control design process. To manage unknown nonlinear functions, radial basis function neural networks (RBFNN) are employed in designing an adaptive neural funnel fault-tolerant controller through the backstepping technique. The proposed controller guarantees the output tracking error stays within a predefined funnel, and all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, simulations of a rigid robot manipulator system and an inverted pendulum system are conducted to validate the practicality and effectiveness of the proposed control method.

Self-tuning iterative learning control for an USV: Application to an autonomous berthing operation with an avoidance obstacle mechanism

This note focuses on the path planning and path-following control in the task of berthing for the underactuated surface vessel (USV), aiming to realize these functions that the accuracy of path-following can be preset and the smoother path planning based on the task of berthing. The proposed scheme is formulated as two components, i.e., the potential field virtual ship (PFVS) guidance part and the self-tuning iterative learning control (STILC) part. By utilizing one novel repulsive field applied around the obstacle and one corrected potential field, the PFVS guidance law is developed in the scheme to plan the reference path and program the real-time heading angle for the USV. The main superiorities of this design are that the guidance signal buffeting and target unreachable problem have been evaded in obstacle avoidance. In addition, the reference speed has been ingenious combined with the artificial potential field (APF). Furthermore, to improve the suitability of the closed-loop control system with ocean engineering, the iterative learning control (ILC) has been improved by introducing the input event-triggered mechanism. An STILC algorithm is designed for preset accuracy can achieve and reduce computing burden. In this algorithm, the number of iterations would self-turning based on the preset accurate. The computation burden of the proposed controller is reduce with the decreasing number of iterations. Through the Lyapunov analysis, we have exerted sufficient effort to ensure that all signals of the closed-loop control system are semi-globally uniformly ultimately bounded (SGUUB). The simulation experiments have been presented to verify the obstacle avoidance effectiveness and the burden-some superiority of the algorithm.

Optimized backstepping consensus control using adaptive observer-critic–actor reinforcement learning for strict-feedback multi-agent systems

In this paper, we present a novel control method, combining observer-based optimized backstepping (OB) control, reinforcement learning (RL) strategy, and adaptive neural networks (NN), for strict-feedback multi-agent systems with unmeasurable states. The primary objective is to enhance the overall system backstepping controller by optimizing both virtual and actual controllers for corresponding subsystems. To achieve this, we develop an observer-critic–actor RL approach based on NN approximation in all backstepping steps. The observers are utilized to estimate the unmeasurable system states, while the critic–actor algorithm assesses the control performance and executes control actions. Our optimized control method offers advantages such as not requiring the state observer to satisfy the Hurwitz equation. Additionally, our designed RL algorithm is simple due to the critic–actor adaptive laws obtained by means of the negative gradient of a simple positive function associated with the partial derivative of Hamilton–Jacobi–Bellman (HJB) equation. Consequently, our proposed control method ensures that all error states of the multi-agent systems are semi-globally uniformly ultimately bounded (SGUUB), and that all outputs can synchronously follow the reference signal with desired accuracy. Finally, we demonstrate the efficacy of our control strategy by means of theoretical analysis and simulation results.

Command filter‐based adaptive robust prescribed performance formation control for nonlinear multi‐agent systems

SummaryThis paper investigates an observer‐based adaptive robust fuzzy formation tracking control method for nonlinear multi‐agent systems (MAS) with input delay. The considered nonlinear MAS contains the unknown nonlinear functions, that is, unmeasured states. The fuzzy logic systems (FLS) are used to approximate the unknown nonlinear functions, and then a fuzzy adaptive state observer is designed to estimate the unmeasured states. The Pade approximation approach is introduced to solve the input delay issue. By combining command filtering and backstepping recursive control techniques, a robust adaptive prescribed performance formation output feedback tracking controller is designed. Moreover, the proposed controller can avoid the “explosion of complexity” and “singularity” problems in the backstepping design framework. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (SGUUB), and the formation tracking errors do not exceed the prescribed performance bounds. Finally, the feasibility of the proposed control approach can be further verified through numerical and practical examples.

Adaptive robust control of nonaffine nonlinear systems via an improved event‐triggered mechanism

AbstractThis paper aims to address the problem of event‐based adaptive robust control for a class of nonaffine nonlinear systems against actuator faults and unknown deception attacks. Firstly, different from the widely used relative threshold triggering mechanism, an improved event‐triggered mechanism with the time‐varying function threshold is devised for effectively saving more communication costs between controller and actuator. Then, based on a class of modified filter‐based coordinate transformations and the improved event‐triggered mechanism, the intermediate virtual control laws are devised to construct actual controllers, which not only guarantees robust stabilization of the system but also relaxes the universal assumptions on control coefficients and attack weights. Besides, the design challenges resulting from the presence of coupling terms in the nonaffine nonlinear system are successfully overcome by virtue of mean value theorem and the property of fuzzy basis function. Theoretical analysis proves that all signals of the closed‐loop system are semiglobally uniformly ultimately bounded (SUUB) and the Zeno behavior can be averted. Finally, the effectiveness of the proposed strategy is verified via comprehensive simulation results.

Adaptive Neural Network Stochastic-Filter-Based Controller for Attitude Tracking With Disturbance Rejection.

This article proposes a real-time neural network (NN) stochastic filter-based controller on the Lie group of the special orthogonal group [Formula: see text] as a novel approach to the attitude tracking problem. The introduced solution consists of two parts: a filter and a controller. First, an adaptive NN-based stochastic filter is proposed, which estimates attitude components and dynamics using measurements supplied by onboard sensors directly. The filter design accounts for measurement uncertainties inherent to the attitude dynamics, namely, unknown bias and noise corrupting angular velocity measurements. The closed-loop signals of the proposed NN-based stochastic filter have been shown to be semiglobally uniformly ultimately bounded (SGUUB). Second, a novel control law on [Formula: see text] coupled with the proposed estimator is presented. The control law addresses unknown disturbances. In addition, the closed-loop signals of the proposed filter-based controller have been shown to be SGUUB. The proposed approach offers robust tracking performance by supplying the required control signal given data extracted from low-cost inertial measurement units. While the filter-based controller is presented in continuous form, the discrete implementation is also presented. In addition, the unit-quaternion form of the proposed approach is given. The effectiveness and robustness of the proposed filter-based controller are demonstrated using its discrete form and considering low sampling rate, high initialization error, high level of measurement uncertainties, and unknown disturbances.

Pinning-Based Neural Control for Multiagent Systems With Self-Regulation Intermediate Event-Triggered Method.

A pinning-based self-regulation intermediate event-triggered (ET) funnel tracking control strategy is proposed for uncertain nonlinear multiagent systems (MASs). Based on the backstepping framework, a pinning control strategy is designed to achieve the tracking control objective, which only uses the communication weight between the agents without additional feedback parameters. Moreover, by designing a self-regulation triggered condition based on the tracking error, the intermediate triggered signal is calculated to replace the continuous signal in the controller, so as to achieve the goal of discontinuous update of the controller signal, and this mechanism does not need to add additional compensation function to the controller signal. At the same time, the funnel method is adopted to restrict the error of step n and avoid the possible negative impact caused by control signal. Furthermore, the nonlinear noncontinuous faults are compensated by the disturbance observer. Then, the Lyapunov stability theorem is used to prove that all signals of the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, some simulation results confirm the effectiveness of the proposed control scheme.

Adaptive neural output-feedback control for nonstrict-feedback stochastic nonlinear time-delay systems with hysteresis

This paper proposes an adaptive neural outputfeedback controller for a class of nonstrict-feedback stochastic nonlinear time-delay systems with unknown backlash-like hysteresis. First, a state observer is established for estimating the unmeasured states. Second, an appropriate Lyapunov-Krasovskii functional is used to compensate the unknown time-delay terms, and the neural network is employed to approximate the unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are presented to further show the effectiveness of the proposed approach.

Echo state network-based adaptive control for nonstrict-feedback nonlinear systems with input dead-zone and external disturbance

This paper addressed the adaptive control problem for non-strict-feedback nonlinear systems with dead-zone and external disturbances. The design methodology integrated the backstepping technique with the approximation of unknown functions using an echo state network (ESN), enabling real-time adjustments. A comprehensive Lyapunov stability study was conducted to confirm the semi-globally uniformly ultimately boundedness (SGUUB) of all signals in the closed-loop system, ensuring that the tracking error converged to a small neighborhood of the origin. The effectiveness of the proposed method was further demonstrated through two examples, and error assessment criteria were utilized for comparisons with existing controllers.

Barrier Lyapunov function-based dual event-triggered prescribed performance path following control for marine surface vessel under input saturation

Concentrated on the marine surface vessel (MSV) with input saturation, model uncertainties and unknown disturbances, this paper proposes the error-constrained line-of-sight guidance-based prescribed performance dual event-triggered path following control (ECLOS-PPDETPFC) strategy which applies the dual relative threshold event-triggered mechanism (ETM) to both guidance and controller of the MSV path following. We apply the prescribed performance function (PPF) as the bounds of asymmetric modified barrier Lyapunov function (AMBLF) to construct the prescribed performance asymmetric modified barrier Lyapunov function (PPAMBLF). In guidance, event-triggered error-constrained line-of-sight (ETECLOS) is constructed by relative threshold ETM and AMBLF to reduce the calculation pressure and keep position errors within the constraint range; In controller, prescribed performance event-triggered path following control (PPETPFC) is based on the relative threshold ETM and PPAMBLF, which makes the heading error meet the prescribed performance requirements, while reducing the loss of actuator. At the same time, the adaptive auxiliary systems are used to compensate the influence of input saturation, radial basis function neural networks (RBFNNs) and adaptive laws are used to approximate the model uncertainties and composite disturbances. According to the Lyapunov stability theory, all signals are semi-globally uniformly ultimately bounded (SGUUB) and the Zeno phenomenon is avoided. Finally, the comparative experiment shows the effectiveness and superiority of the designed control strategy.

Command filter and high gain observer based adaptive output feedback control for stochastic nonlinear systems with prescribed performance and input quantization

SummaryIn this paper, an adaptive output feedback dynamic surface control (DSC) strategy is proposed for strict‐feedback stochastic nonlinear systems with input quantization, prescribed performance and dynamic uncertainties. A new quantizer is used to process the input signal, which can avoid the chattering of the quantization signal and keep the upper bound of the quantization error constant. Radial basis functions are used to approximate unknown smooth functions, unmodeled dynamics are processed by dynamic signals, and unmeasurable states are estimated by high gain observer. Hyperbolic tangent functions are employed to handle prescribed performance. The second order command filter is used to replace the first order filter used in general DSC, and the compensation term is added in each step of DSC. By the Lyapunov stability analysis, all signals in the controlled system are semi‐globally uniformly ultimately bounded (SGUUB) in probability. Two examples further prove that the control scheme designed in this paper is reasonable and effective.