Development and application of a lyapunov synthesis based neural adaptive controller

Presented herein are the results of an adaptive control simulation study using metrics and pilot handling qualities on a generic commercial aviation aircraft. For this study, seven model reference adaptive control (MRAC) technologies were identified for investigation. Each technology was tuned using a consistent methodology based on metrics and specific design requirements. Additionally, each adaptive control technology was integrated with a preexisting dynamic-inversion baseline control architecture. Scenarios for evaluation were then designed using Cooper-Harper design criteria. This paper presents the development, execution, and results from the study; additional background material is provided in the references. I. Introduction HE Integrated Resilient Aircraft Control (IRAC) project is part of the Aviation Safety Program under the Aeronautics Research Mission Directorate (ARMD) at NASA. A key focus of this project is to research the use of adaptive control technologies as a risk-mitigating tool for damaged and off-nominal aircraft. In a traditional gain-scheduled design approach, the flight controller is designed by treating the aircraft’s flight envelope as a discrete space. Controls engineers then use traditional linear control techniques to shape the handling qualities of the aircraft at each of these discrete locations. In an off-nominal or damage scenario, this design approach can break down if large model uncertainties are introduced. Even in the case of a relatively robust baseline, gain-scheduled controller, aircraft performance can be severely impacted. The goal of an adaptive flight controller is to then augment the baseline controller such that larger uncertainties can be compensated for instantaneously and without a reduction in the aircraft handling qualities. If successful, these technologies then mitigate overall risk by reducing pilot workload and providing the aircraft with improved handling qualities. The use of adaptive control technologies in manned flight has at its core a component of handling qualities and pilot controller interaction. This is evidenced by the fact that the verification and validation process (VV extremely remote combinations of occurrences are not considered. In the realm of military procurement vehicles, MIL-HDBK-1797A outlines handling qualities specifications for military aircraft. Thus, irrespective of the application, pilot based evaluations of the aircraft are an integral part of maturing any control technology to a real-world platform. Given the above, this paper presents a study to evaluate the strengths and weaknesses of several adaptive control technologies through the design and execution of a handling qualities experiment. The experiment was performed at the NASA Ames Research Center using a full-motion flight simulator and NASA test pilots. In terms of format, Section II of this paper outlines the study design. Section III then presents the simulation environment and the relevant aircraft models. Section IV very briefly reviews adaptive control, the baseline control architecture, and the adaptive control technologies considered for this study; the interested reader will find significantly greater detail on

This paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed 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 simulation examples are provided to further illustrate the effectiveness of the proposed approach.

In the braking control of single rope winding hoisting systems (SRWHS), reasonable braking torque is of great significance in reducing the probability of significant hidden dangers such as overwinding, overspeeding, rope breaking, vibration, conveyance crash and so on. However, dynamic nonlinearity, time-varying disturbances, mechanical dynamic uncertainties and measurement noise severely affect the practical braking control performance. To address those problems, a neural adaptive braking torque controller with disturbance compensation is developed to enhance the braking performance for a single rope winding hoisting system in this paper. Firstly, considering the elastic of steel wire rope, the nonlinear braking model of the SRWHS is established using Lagrange equations and an extended state observer (ESO) is introduced to estimate the system’s unmeasured states and modelling error. Next, a neural adaptive controller is developed to estimate and compensate the mechanical dynamical disturbances resulted from friction forces and random external disturbances. Then, a neural adaptive network controller combined with the ESO (ESONAC) is designed to solve the modelling nonlinearity, time-varying disturbances and system’s unmeasurable states. Finally, the advantages of the ESONAC in improving the braking control performance of winding hoisting systems is verified by comparative experiments.

This paper presents a neural adaptive flight controller for ducted fan UAVs which are capable of vertical takeoff and landing(VTOL). These ducted fan propulsion systems pose great challenges in aerodynamics and control and we propose a backstepping neural adaptive control law to track its nonlinear dynamics. This controller can handle unmodeled dynamics and external disturbances as well, providing stability to the vehicle. A single layer radial basis neural network is used to approximate the unmodeled dynamics and vehicle stability is guaranteed through Lyapunov synthesis. For simulation study six degree of freedom model (6-DOF) is implemented in MATLAB along with the proposed control approach. The performance of the controller is evaluated using nonlinear bop-up maneuver and the necessary stability and tracking performance of the UAV have been investigated.

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.

In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.

This paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict-feedback form with unknown backlash-like hysteresis nonlinearities. To overcome the design difficulty of nonstrict-feedback structure, variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic. By combining radial basis function neural networks' universal approximation capability with an adaptive backstepping technique, an adaptive neural control algorithm is proposed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are four-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results further show the effectiveness of the presented control scheme.

This paper focuses on the problem of the adaptive neural control for a class of a perturbed pure-feedback nonlinear system. Based on radial basis function (RBF) neural networks’ universal approximation capability, an adaptive neural controller is developed via the backstepping technique. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood around the origin. The main advantage of this note lies in that a control strategy is presented for a class of pure-feedback nonlinear systems with external disturbances being bounded by functions of all state variables. A numerical example is provided to illustrate the effectiveness of the suggested approach.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

Chaotic systems are known to be extremely sensitive to initial conditions, meaning small changes can have a significant impact on the outcomes. By analyzing the average profit margin in relation to chaotic dynamics, companies can conduct sensitivity analysis to assess the potential impact of various factors on their profitability. This analysis can help identify critical variables or scenarios that may significantly affect profit margins. In this article, we have proposed a hyperchaotic financial system with sinusoidal hyperbolic non-linear variables applied to the average profit margin. Furthermore, we have investigated the stability of the hyperchaotic financial dynamics model to provide information to companies to assess the consistency and reliability of their profitability. In addition, fundamental dynamic behavior like Lyapunov exponents, bifurcation analysis, coexisting attractors have been reported. Finally, a nonlinear feedback control approach is developed to train an adaptive neural fuzzy controller. The application of Lyapunov theory confirms that this nonlinear feedback controller can effectively minimize the synchronization error within a finite duration. The results from simulations establish the effectiveness of the proposed neural fuzzy controller architecture in controlling the synchronization of two hyperchaotic financial models. Additionally, the simulation includes a comparison between the performance of the nonlinear controller and the adaptive neural fuzzy controller.

A robust adaptive neural dynamic surface control (DSC) approach is presented for the longitudinal dynamics of a morphing aircraft in the presence of unknown dynamics and input constraints. For the altitude subsystem, neural systems are utilized to approximate the unknown nonlinear functions with smooth robust compensations to counteract the lumped approximation errors. By combining dynamic surface control and minimal learning parameter techniques, a robust adaptive neural control scheme is proposed and a simple adaptive algorithm is constructed. Meanwhile, an auxiliary system is incorporated into the control scheme to overcome the problem of input saturation. The highlight is that the proposed neural controller not only owns less updated neural parameters, but also has the ability of handling input constraints. It is proved that all the signals in the closed-loop system are bounded. Simulation results demonstrate the effectiveness of the proposed control scheme.

This work devises a neural adaptive backstepping control of the chaotic permanent magnet synchronous motor system with output constraint. In the specific backstepping steps, to resolve the restraint of output tracking error, the Lyapunov function of the tangent barrier is introduced. Chebyshev neural networks and Nussbaum-type function are utilized to deal with uncertain nonlinearities and uncertain gain. The tracking differentiator is exploited to eliminate the "explosion of complexity" of virtual controller. Then, the boundedness of all the closed-loop signals is proved without bypassing the output constraint by Lyapunov synthesis. Eventually, simulation results verify the validities of the presented scheme.

Adaptive neural dynamic surface control for servo systems with unknown dead-zone

The resurgence of interest in flexible computational methods loosely inspired by biological signal processing mechanisms has produced a variety of possible new algorithms for adaptively controlling partially known nonlinear systems. However, for such methods to be useful in practice, the exact factors which govern successful applications must be identified and quantified; ad hoc, trial and error approaches must be supplanted by rigorous theoretical foundations and practical, constructive algorithms. Recent developments in this direction have provided just such a framework, by combining into a single methodology elements of constructive approximation theory, nonlinear stability theory, and robust nonlinear adaptation and control techniques. This paper presents an overview of this methodology and illustrates it by reviewing the structure of neural adaptive robot controllers with guaranteed stability and convergence properties. >

Due to the complexities existing in the electric load simulator, this article develops a high-performance nonlinear adaptive controller to improve the torque tracking performance of the electric load simulator, which mainly consists of an adaptive fuzzy self-recurrent wavelet neural network controller with variable structure (VSFSWC) and a complementary controller. The VSFSWC is clearly and easily used for real-time systems and greatly improves the convergence rate and control precision. The complementary controller is designed to eliminate the effect of the approximation error between the proposed neural network controller and the ideal feedback controller without chattering phenomena. Moreover, adaptive learning laws are derived to guarantee the system stability in the sense of the Lyapunov theory. Finally, the hardware-in-the-loop simulations are carried out to verify the feasibility and effectiveness of the proposed algorithms in different working styles.