A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input

Adaptive Tracking Control for Underactuated Double Pendulum Overhead Cranes With Variable Cable Length

Although the literature on control of overhead crane systems is extensive and relatively mature, there is still a need to develop strategies that can simultaneously handle factors such as the double pendulum effect, variable cable length, input saturation, input dead zones, and external disturbances. This article is concerned with adaptive tracking control for underactuated overhead cranes in the presence of the above-mentioned challenging effects. The proposed controller is composed of the following two components. First, a tracking signal vector that effectively reduces system swing magnitudes is constructed to improve the transient performance and guarantee smooth operation of the system. Second, an adaptive law is designed to estimate and compensate for the overall effects of the friction, the external disturbances, and certain nonlinearities. The system stability has been proved rigorously via the Lyapunov method and Barbalat's lemma. Extensions to the cases with input saturation and dead zones have also been discussed. Extensive numerical simulations have been conducted to verify the performance and robustness of the proposed controller, in comparison to some existing methods.

Review of the Flight Control Method of a Bird-like Flapping-Wing Air Vehicle

The Bird-like Flapping-wing Air Vehicle (BFAV) is a robotic innovation that emulates the flight patterns of birds. In comparison to fixed-wing and rotary-wing air vehicles, the BFAV offers superior attributes such as stealth, enhanced maneuverability, strong adaptability, and low noise, which render the BFAV a promising prospect for numerous applications. Consequently, it represents a crucial direction of research in the field of air vehicles for the foreseeable future. However, the flapping-wing vehicle is a nonlinear and unsteady system, posing significant challenges for BFAV to achieve autonomous flying since it is difficult to analyze and characterize using traditional methods and aerodynamics. Hence, flight control as a major key for flapping-wing air vehicles to achieve autonomous flight garners considerable attention from scholars. This paper presents an exposition of the flight principles of BFAV, followed by a comprehensive analysis of various significant factors that impact bird flight. Subsequently, a review of the existing literature on flight control in BFAV is conducted, and the flight control of BFAV is categorized into three distinct components: position control, trajectory tracking control, and formation control. Additionally, the latest advancements in control algorithms for each component are deliberated and analyzed. Ultimately, a projection on forthcoming directions of research is presented.

Indefinite Mean-Field Stochastic Cooperative Linear-Quadratic Dynamic Difference Game With Its Application to the Network Security Model

In this article, we show how to obtain all of the Pareto optimal decision vectors and solutions for the finite horizon indefinite mean-field stochastic cooperative linear-quadratic (LQ) difference game. First, the equivalence between the solvability of the introduced N coupled generalized difference Riccati equations (GDREs) and the solvability of the multiobjective optimization problem is established. However, it is difficult to obtain Pareto optimal decision vectors based on the N coupled GDREs because the optimal joint strategy adopted by all players to optimize the performance criterion of some players in the game is different from the strategies of other players, which rely on the weighted matrices of cost functionals that may be different among players. Second, a necessary and sufficient condition is developed to guarantee the convexity of the costs, which makes the weighting technique not only sufficient but also necessary for searching Pareto optimal decision vectors. It is then shown that the mean-field Pareto optimality algorithm (MF-POA) is presented to identify, in principle, all of the Pareto optimal decision vectors and solutions via the solutions to the weighted coupled GDREs and the weighted coupled generalized difference Lyapunov equations (GDLEs), respectively. Finally, a cooperative network security game is reported to illustrate the results presented. Simulation results validate the solvability, correctness, and efficiency of the proposed algorithm.

Adaptive Neural Dynamic Surface Control With Prespecified Tracking Accuracy of Uncertain Stochastic Nonstrict-Feedback Systems

This article addresses the adaptive neural tracking control problem for a class of uncertain stochastic nonlinear systems with nonstrict-feedback form and prespecified tracking accuracy. Some radial basis function neural networks (RBF NNs) are used to approximate the unknown continuous functions online, and the desired controller is designed via the adaptive dynamic surface control (DSC) method and the gain suppressing inequality technique. Different from the reported works on uncertain stochastic systems, by combining some non-negative switching functions and dynamic surface method with the nonlinear filter, the design difficulty is overcome, and the control performance is analyzed by employing stochastic Barbalat's lemma. Under the constructed controller, the tracking error converges to the accuracy defined a priori in probability. The simulation results are shown to verify the availability of the presented control scheme.

A Novel Supertwisting Zeroing Neural Network With Application to Mobile Robot Manipulators

Various zeroing neural network (ZNN) models have been investigated to address the tracking control of robot manipulators for the capacity of parallel processing and nonlinearity handling. However, two limitations occur in the existing ZNN models. The first one is the convergence time that tends to be infinitely large. The second one is the research of robustness that remains in the analyses of stability and asymptotic convergence. To simultaneously enhance the convergence performance and robustness, this article proposes a new ZNN model by using a supertwisting (ST) algorithm, termed STZNN model, for the tracking control of mobile robot manipulators. The proposed STZNN model inherently possesses the advantages of finite-time convergence and robustness making the control process fast and robust. The bridge from the sliding mode control to the ZNN is built, and the essential connection between the ST algorithm and ZNN is explored by constructing a unified design process. Theorems and proofs about global stability, finite-time convergence, and robustness are provided. Finally, path-tracking applications, comparisons, and tests substantiate the effectiveness and superiority of the STZNN model for the tracking control handling of mobile robot manipulators.

Adaptive Neural Event-Triggered Control for Discrete-Time Strict-Feedback Nonlinear Systems

This paper proposes a novel event-triggered (ET) adaptive neural control scheme for a class of discrete-time nonlinear systems in a strict-feedback form. In the proposed scheme, the ideal control input is derived in a recursive design process, which relies on system states only and is unrelated to virtual control laws. In this case, the high-order neural networks (NNs) are used to approximate the ideal control input (but not the virtual control laws), and then the corresponding adaptive neural controller is developed under the ET mechanism. A modified NN weight updating law, nonperiodically tuned at triggering instants, is designed to guarantee the uniformly ultimate boundedness (UUB) of NN weight estimates for all sampling times. In virtue of the bounded NN weight estimates and a dead-zone operator, the ET condition together with an adaptive ET threshold coefficient is constructed to guarantee the UUB of the closed-loop networked control system through the Lyapunov stability theory, thereby largely easing the network communication load. The proposed ET condition is easy to implement because of the avoidance of: 1) the use of the intermediate ET conditions in the backstepping procedure; 2) the computation of virtual control laws; and 3) the redundant triggering of events when the system states converge to a desired region. The validity of the presented scheme is demonstrated by simulation results.

Event-Based Adaptive Neural Tracking Control for Discrete-Time Stochastic Nonlinear Systems: A Triggering Threshold Compensation Strategy

This paper investigates the event-triggered (ET) tracking control problem for a class of discrete-time strict-feedback nonlinear systems subject to both stochastic noises and limited controller-to-actuator communication capacities. The ET mechanism with fixed triggering threshold is designed to decide whether the current control signal should be transmitted to the actuator. A systematic framework is developed to construct a novel adaptive neural controller by directly applying the backstepping procedure to the underlying system. The proposed framework overcomes the noncausality problem, avoids the possible controller-related singularity problem, and gets rid of the neural approximation of the virtual control laws. Under the ET mechanism, the corresponding ET-based actuator is put forward by introducing an ET threshold compensation operator. Such a compensation operator (with an adjustable design parameter) is subtly designed based on a hyperbolic tangent function and a sign function. The threshold compensation error is analytically characterized in terms of a time-varying parameter, and the error bound is shown to be relatively small that is dependent on the adjustable design parameter. Compared with the traditional ET-based actuator without the compensation operator, the proposed ET-based actuator exhibits several distinguished features including: 1) improvement of the tracking accuracy (especially at the triggering instants); 2) further mitigation of the communication load; and 3) enlargement of the allowable range of the ET threshold. These features are illustrated by numerical and practical examples.

Neural-Network-Based Adaptive Funnel Control for Servo Mechanisms With Unknown Dead-Zone

This paper proposes an adaptive funnel control (FC) scheme for servo mechanisms with an unknown dead-zone. To improve the transient and steady-state performance, a modified funnel variable, which relaxes the limitation of the original FC (e.g., systems with relative degree 1 or 2), is developed using the tracking error to replace the scaling factor. Then, by applying the error transformation method, the original error is transformed into a new error variable which is used in the controller design. By using an improved funnel function in a dynamic surface control procedure, an adaptive funnel controller is proposed to guarantee that the output error remains within a predefined funnel boundary. A novel command filter technique is introduced by using the Levant differentiator to eliminate the "explosion of complexity" problem in the conventional backstepping procedure. Neural networks are used to approximate the unknown dead-zone and unknown nonlinear functions. Comparative experiments on a turntable servo mechanism confirm the effectiveness of the devised control method.

Event-Triggered Adaptive Control of Saturated Nonlinear Systems With Time-Varying Partial State Constraints

This paper investigates the problem of event-triggered adaptive control for a class of nonlinear systems subject to asymmetric input saturation and time-varying partial state constraints. To facilitate analyzing the influence of asymmetric input saturation, the saturation function is converted into a linear form with respect to control input. To achieve the objective that partial states do not exceed the constraints, a more general form of Lyapunov function is offered. Different from some existing results about output/full state constraints, the proposed scheme only requires that the partial states satisfy the time-varying constraints. Moreover, an event-triggered scheme with a varying threshold is designed to reduce the communication burden. With the time-varying asymmetric barrier Lyapunov functions, a novel event-triggered control scheme is developed, which ensures that partial states are without violation of required constraints and the tracking error converges to a small neighborhood of the origin despite appearing as saturated phenomenon. Eventually, the theoretic results are confirmed by two examples.

Neural Networks-Based Adaptive Control for Nonlinear State Constrained Systems With Input Delay

This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.

Event-Based Adaptive NN Tracking Control of Nonlinear Discrete-Time Systems

This paper is concerned with the simultaneous design of a neural network (NN)-based adaptive control law and an event-triggering condition for a class of strict feedback nonlinear discrete-time systems. The stability and tracking performance of the closed-loop network control system under the event-triggering strategy is formally proven based on the Lyapunov theory in a hybrid framework. The proposed Lyapunov formulation yields an event-triggered algorithm to update the control input and NN weights based on conditions involving the closed-loop state. Different from the existing traditional NN control schemes where the feedback signals are transmitted and executed periodically, the feedback signals are transmitted and executed only when the event-trigger error exceeds the specified threshold, which can largely reduce the communication load. The effectiveness of the approach is evaluated through a simulation example.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Adaptive Neural Network Control of a Flapping Wing Micro Aerial Vehicle With Disturbance Observer

The research of this paper works out the attitude and position control of the flapping wing micro aerial vehicle (FWMAV). Neural network control with full state and output feedback are designed to deal with uncertainties in this complex nonlinear FWMAV dynamic system and enhance the system robustness. Meanwhile, we design disturbance observers which are exerted into the FWMAV system via feedforward loops to counteract the bad influence of disturbances. Then, a Lyapunov function is proposed to prove the closed-loop system stability and the semi-global uniform ultimate boundedness of all state variables. Finally, a series of simulation results indicate that proposed controllers can track desired trajectories well via selecting appropriate control gains. And the designed controllers possess potential applications in FWMAVs.

Adaptive Neural Network Control of a Robotic Manipulator With Time-Varying Output Constraints

The control problem of an uncertain n -degrees of freedom robotic manipulator subjected to time-varying output constraints is investigated in this paper. We describe the rigid robotic manipulator system as a multi-input and multi-output nonlinear system. We devise a disturbance observer to estimate the unknown disturbance from humans and environment. To solve the uncertain problem, a neural network which utilizes a radial basis function is used to estimate the unknown dynamics of the robotic manipulator. An asymmetric barrier Lyapunov function is employed in the process of control design to avert the contravention of the time-varying output constraints. Simulation results validate the validity of the presented control scheme.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Discrete-Time Deterministic $Q$ -Learning: A Novel Convergence Analysis

In this paper, a novel discrete-time deterministic Q -learning algorithm is developed. In each iteration of the developed Q -learning algorithm, the iterative Q function is updated for all the state and control spaces, instead of updating for a single state and a single control in traditional Q -learning algorithm. A new convergence criterion is established to guarantee that the iterative Q function converges to the optimum, where the convergence criterion of the learning rates for traditional Q -learning algorithms is simplified. During the convergence analysis, the upper and lower bounds of the iterative Q function are analyzed to obtain the convergence criterion, instead of analyzing the iterative Q function itself. For convenience of analysis, the convergence properties for undiscounted case of the deterministic Q -learning algorithm are first developed. Then, considering the discounted factor, the convergence criterion for the discounted case is established. Neural networks are used to approximate the iterative Q function and compute the iterative control law, respectively, for facilitating the implementation of the deterministic Q -learning algorithm. Finally, simulation results and comparisons are given to illustrate the performance of the developed algorithm.

Fuzzy Adaptive Tracking Control of Constrained Nonlinear Switched Stochastic Pure-Feedback Systems

In this paper, the fuzzy adaptive control problem for a class of switched stochastic nonlinear systems in pure feedback form with output constraint is addressed. By proposing a nonlinear mapping, the constrained system is transformed into an unconstrained one, with equivalent control objective. All signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded. Meanwhile, the output constraint is satisfied and the output tracking error converges to an arbitrarily small neighborhood of zero. Finally, the applicability of the proposed controller is verified by a simulation example.