Altitude Subsystem Research Articles

Minimal-learning-parameter based simplified adaptive neural back-stepping control of flexible air-breathing hypersonic vehicles without virtual controllers

In this paper, a novel adaptive neural control methodology is addressed for a flexible air-breathing hypersonic vehicle (FAHV) by a fusion of improved back-stepping and a minimal-learning-parameter (MLP) scheme. To facilitate the control design, the vehicle dynamics is decomposed into the altitude subsystem and the velocity subsystem. Different from the traditional back-stepping design, in this paper, the virtual control laws for the altitude dynamics are artificial intermediate variables required only for analytic purpose while only the final actual controller is needed to be implemented. For each subsystem, only one neural network is employed to approximate the lumped uncertainty. Moreover, by the merit of the MLP technique, only one learning parameter is required for neural approximation in each subsystem. The novel contribution with respect to the existing literatures is that the proposed control strategy is concise and the computational load is low. Finally, the effectiveness of the exploited control approach is verified by simulation results in the presence of uncertain parameters.

High-order tracking differentiator based adaptive neural control of a flexible air-breathing hypersonic vehicle subject to actuators constraints

In this paper, an adaptive neural controller is exploited for a constrained flexible air-breathing hypersonic vehicle (FAHV) based on high-order tracking differentiator (HTD). By utilizing functional decomposition methodology, the dynamic model is reasonably decomposed into the respective velocity subsystem and altitude subsystem. For the velocity subsystem, a dynamic inversion based neural controller is constructed. By introducing the HTD to adaptively estimate the newly defined states generated in the process of model transformation, a novel neural based altitude controller that is quite simpler than the ones derived from back-stepping is addressed based on the normal output-feedback form instead of the strict-feedback formulation. Based on minimal-learning parameter scheme, only two neural networks with two adaptive parameters are needed for neural approximation. Especially, a novel auxiliary system is explored to deal with the problem of control inputs constraints. Finally, simulation results are presented to test the effectiveness of the proposed control strategy in the presence of system uncertainties and actuators constraints.

Novel adaptive neural control of flexible air-breathing hypersonic vehicles based on sliding mode differentiator

A novel adaptive neural control strategy is exploited for the longitudinal dynamics of a generic flexible air-breathing hypersonic vehicle (FAHV). By utilizing functional decomposition method, the dynamics of FAHV is decomposed into the velocity subsystem and the altitude subsystem. For each subsystem, only one neural network is employed for the unknown function approximation. To further reduce the computational burden, minimal-learning parameter (MLP) technology is used to estimate the norm of ideal weight vectors rather than their elements. By introducing sliding mode differentiator (SMD) to estimate the newly defined variables, there is no need for the strict-feedback form and virtual controller. Hence the developed control law is considerably simpler than the ones derived from back-stepping scheme. Finally, simulation studies are made to illustrate the effectiveness of the proposed control approach in spite of the flexible effects, system uncertainties and varying disturbances.

Composite dynamic surface control of hypersonic flight dynamics using neural networks

This paper addresses the composite neural tracking control for the longitudinal dynamics of hy-personic flight dynamics. The dynamics is decoupled into velocity subsystem, altitude subsystem, and attitude subsystem. For the altitude subsystem, the reference command of flight path angle is derived for the attitude subsystem. To deal with the system uncertainty and provide efficient neural learning, the composite law for neural weights updating is studied with both tracking error and modeling error. The uniformly ultimate bound-edness stability is guaranteed via Lyapunov approach. Under the dynamic surface control with novel neural design, the neural system converges in a faster mode and better tracking performance is obtained. Simulation results are presented to show the effectiveness of the design.

Adaptive Neural Control Based on High Order Integral Chained Differentiator for Morphing Aircraft

This paper presents an adaptive neural control for the longitudinal dynamics of a morphing aircraft. Based on the functional decomposition, it is reasonable to decompose the longitudinal dynamics into velocity and altitude subsystems. As for the velocity subsystem, the adaptive control is proposed via dynamic inversion method using neural network. To deal with input constraints, the additional compensation system is employed to help engine recover from input saturation rapidly. The highlight is that high order integral chained differentiator is used to estimate the newly defined variables and an adaptive neural controller is designed for the altitude subsystem where only one neural network is employed to approximate the lumped uncertain nonlinearity. The altitude subsystem controller is considerably simpler than the ones based on backstepping. It is proved using Lyapunov stability theory that the proposed control law can ensure that all the tracking error converges to an arbitrarily small neighborhood around zero. Numerical simulation study demonstrates the effectiveness of the proposed strategy, during the morphing process, in spite of some uncertain system nonlinearity.

Actuators Coupled Design Based Adaptive Backstepping Control of Air-breathing Hypersonic Vehicle

In this paper, we study the robust design of the flight control system for the longitudinal dynamics of air-breathing hypersonic vehicles. First, the longitudinal dynamics model is divided into the velocity subsystem and the altitude subsystem. An adaptive controller is developed based on dynamic inversion method for the former subsystem, and an adaptive backstepping controller is proposed with coupled elevator and canard actuators for the latter, where the coupled design idea makes the control efficiency optimization. Then, the stability analysis shows that the closed system is asymptotically stable under certain conditions, and all the states of the closed-loop system are within a given flight envelope, which means that we realize the restriction control of the states of the vehicles. Finally, simulation illustrates the proposed method. Our designs differ with the published results in 4 aspects. Besides the couples actuators design, we give the specific controller solvers and control parameters selection approaches, and the controller designed doesn't contain the uncertain parameters which are cancelled adaptively.

Adaptive Neural Back-Stepping Control with Constrains for a Flexible Air-Breathing Hypersonic Vehicle

The design of an adaptive neural back-stepping control for a flexible air-breathing hypersonic vehicle (AHV) in the presence of input constraint and aerodynamic uncertainty is discussed. Based on functional decomposition, the dynamics can be decomposed into the velocity subsystem and the altitude subsystem. To guarantee the exploited controller’s robustness with respect to parametric uncertainties, neural network (NN) is applied to approximate the lumped uncertainty of each subsystem of AHV model. The exceptional contribution is that novel auxiliary systems are introduced to compensate both the tracking errors and desired control laws, based on which the explored controller can still provide effective tracking of velocity and altitude commands when the actuators are saturated. Finally, simulation studies are made to illustrate the effectiveness of the proposed control approach in spite of the flexible effects, system uncertainties, and varying disturbances.

Nonlinear Constrained Adaptive Backstepping Tracking Control for a Hypersonic Vehicle with Uncertainty

The control problem of a flexible hypersonic vehicle is presented, where input saturation and aerodynamic uncertainty are considered. A control-oriented model including aerodynamic uncertainty is derived for simple controller design due to the nonlinearity and complexity of hypersonic vehicle model. Then it is separated into velocity subsystem and altitude subsystem. On the basis of the integration of robust adaptive control and backstepping technique, respective controller is designed for each subsystem, where an auxiliary signal provided by an additional dynamic system is used to compensate for the control saturation effect. Then to deal with the “explosion of terms” problem inherent in backstepping control, a novel first-order filter is proposed. Simulation results are included to demonstrate the effectiveness of the adaptive backstepping control scheme.

Multivariable Super Twisting Based Robust Trajectory Tracking Control for Small Unmanned Helicopter

This paper presents a highly robust trajectory tracking controller for small unmanned helicopter with model uncertainties and external disturbances. First, a simplified dynamic model is developed, where the model uncertainties and external disturbances are treated as compounded disturbances. Then the system is divided into three interconnected subsystems: altitude subsystem, yaw subsystem, and horizontal subsystem. Second, a disturbance observer based controller (DOBC) is designed based upon backstepping and multivariable super twisting control algorithm to obtain robust trajectory tracking property. A sliding mode observer works as an estimator of the compounded disturbances. In order to lessen calculative burden, a first-order exact differentiator is employed to estimate the time derivative of the virtual control. Moreover, proof of the stability of the closed-loop system based on Lyapunov method is given. Finally, simulation results are presented to illustrate the effectiveness and robustness of the proposed flight control scheme.

Neural discrete back-stepping control of hypersonic flight vehicle with equivalent prediction model

This paper describes the back-stepping controller design in discrete time for the longitudinal dynamics of a generic hypersonic flight vehicle with neural networks. For the altitude subsystem, to avoid the causality contradiction, the original system is formulated into a new equivalent prediction model with strict-feedback form from which the virtual control is designed with error feedback and neural approximation via back-stepping. For stability analysis, Lyapunov function is chosen with regard to the novel formulation of new strict-feedback system. Under the proposed controller, the semiglobal uniform ultimate boundedness stability is guaranteed. The step response is presented in the simulation studies to show the effectiveness of the proposed control approach.

Nonsingular direct neural control of air-breathing hypersonic vehicle via back-stepping

This paper investigates the design of nonsingular direct neural control systems for the longitudinal dynamics of a generic air-breathing hypersonic vehicle (AHV). The control objective is to steer the velocity and altitude to track the given commands in the presence of unmatched disturbances. For the velocity subsystem, a neural network (NN) is employed to approximate the developed control law directly where a direct neural controller is designed. For the altitude subsystem that is transformed into strict feedback form, two NNs are used to estimate the virtual and actual control laws derived from back-stepping design. Hence the problem of possible control singularity and “explosion of terms” are avoided. More specially, a nonlinear tracking differentiator is introduced to reconstruct the flight-path angle and angle of attack that are difficult and costly to measure in practice. Numerical simulations are presented to verify the feasibility of the proposed control approach.

Nonlinear Control for a Model-scaled Helicopter with Constraints on Rotor Thrust and Fuselage Attitude

A nonlinear control is proposed for trajectory tracking of a 6-DOF model-scaled helicopter with constraints on main rotor thrust and fuselage attitude. In the procedure of control design, the mathematical model of helicopter is simplified into three subsystems: altitude subsystem, longitudinal-lateral subsystem and attitude subsystem. The proposed control is developed by combining the sub-controls for the corresponding subsystems. The sub-controls for altitude subsystem and longitudinal-lateral subsystem are designed with hyperbolic tangent functions to satisfy the constraints; the sub-control for attitude subsystem is based on backstepping technique such that fuselage attitude tracks the virtual control for longitudinal-lateral subsystem. It is proved theoretically that tracking errors are ultimately bounded, and control constraints are satisfied. Performances of the proposed controller are demonstrated by simulation results.

Robust Adaptive Approximate Backstepping Control Design for a Flexible Air-Breathing Hypersonic Vehicle

AbstractThis paper presents a tracking control problem of a flexible air-breathing hypersonic vehicle with aerodynamic uncertainty. The flight control design is challenging because of heavily coupled propulsive, aerodynamic forces and flexibility effects. A control-oriented model is derived where the flexible dynamics are regarded as perturbations and the aerodynamic uncertainty is included. It does not need to be transformed into a linear parameterization formulation. Based on an analysis of it, it is decomposed into a velocity subsystem and an altitude subsystem. Then dynamic inversion and a sliding mode control are combined to design the controller of the velocity subsystem. In addition, the sliding mode control and adaptive control are incorporated into a backstepping control architecture to develop the controller for the altitude subsystem after it is transformed into approximately strict-feedback form. The upper bounds of the uncertain terms do not need to be known in advance. They are estimated onl...

Multiple-time scale smooth second order sliding mode controller design for flexible hypersonic vehicles

A nonlinear robust control strategy is proposed for flexible hypersonic vehicles with aerodynamic parameters uncertainties. Firstly, the longitude dynamics of this vehicle are divided into velocity subsystem, altitude and flight path angle subsystem, angle of attack, and pitch rate subsystem. Then the smooth second order sliding mode controller and disturbance observer are designed to ensure the finite time stability for each subsystem. Furthermore, the stability of the whole system is guaranteed via the assumption of multiple-time scale characteristic. Moreover, the effect of flexible modes on rigid-body states can be estimated exactly using the disturbance observer. In addition, two representative simulations are carried out to analyze the effect of elevator deflection and canard on the dynamics of velocity, flight path angle, and angle of attack. Finally, the Monte Carlo simulations are provided to verify the effectiveness of the proposed control strategy.

Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty

The flight control problem of a flexible air-breathing hypersonic vehicle is presented in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, where aerodynamic uncertainty and the strong couplings between the engine and flight dynamics are included, is derived to reduce the complexity of controller design. The flexible dynamics are viewed as perturbations of the model. They are not taken into consideration at the level of control design, the influence of which is evaluated through simulation. The control-oriented model is decomposed into velocity subsystem and altitude subsystem, which are controlled separately. Then robust adaptive controller is developed for the velocity subsystem, while the controller which combines dynamic surface control and radial basis function neural network is designed for the altitude subsystem. The unknown nonlinear function is approximated by the radial basis function neural network. Minimal-learning parameter technique is utilized to estimate the maximum norm of ideal weight vectors instead of their elements to reduce the computational burden. To handle input constraints, additional systems are constructed to analyze their impact, and the states of the additional systems are employed at the level of control design and stability analysis. Besides, “explosion of terms” problem in the traditional backstepping control is circumvented using a first-order filter at each step. By means of Lyapunov stability theory, it is proved theoretically that the designed control law can assure that tracking error converges to an arbitrarily small neighborhood around zero. Simulations are performed to demonstrate the effectiveness of the presented control scheme in coping with input constraint and aerodynamic uncertainty.

Robust adaptive approximate backstepping control of a flexible air-breathing hypersonic vehicle with input constraint and uncertainty

This article shows the controller design problem of a flexible air-breathing hypersonic vehicle in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, derived from curve-fitted model, is reasonably decomposed into subsystems that include velocity subsystem, altitude and flight path angle subsystem and angle of attack and pitch rate subsystem. Then, dynamic inversion and robust adaptive control are integrated with approximate backstepping control philosophy to design the control scheme, in which the upper bounds of uncertainties are not to be known in advance and estimated by adaptive law. To tackle input constraints, auxiliary systems are constructed and the states of them are used for controller design and stability analysis. Moreover, a detailed stability analysis of the resulting rigid body system is carried out within the framework of Lyapunov theory. Finally, simulation results illustrate the property of the designed control strategy in handling input constraint and aerodynamic uncertainty.

Adaptive Neural Control of a Hypersonic Vehicle in Discrete Time

The article investigates the discrete-time controller for the longitudinal dynamics of the hypersonic flight vehicle with throttle setting constraint. Based on functional decomposition, the dynamics can be decomposed into the altitude subsystem and the velocity subsystem. Furthermore, the discrete model could be derived using the Euler expansion. For the velocity subsystem, the controller is proposed by estimating the system uncertainty and unknown control gain separately with neural networks. The auxiliary error signal is designed to compensate the effect of throttle setting constraint. For the altitude subsystem, the desired control input is approximated by neural network while the error feedback is synthesized for the design. The singularity problem is avoided. Stability analysis proves that the errors of all the signals in the system are uniformly ultimately bounded. Simulation results show the effectiveness of the proposed controller.

Universal Kriging control of hypersonic aircraft model using predictor model without back‐stepping

This study describes the design of adaptive universal Kriging (UK) controller for the longitudinal dynamics of a generic hypersonic flight vehicle (HFV). The altitude subsystem is transformed into the explicit four-step ahead state predictor model, which provides the relationship between states and future outputs. Furthermore, the input--output predictor model is derived to obtain the input information for the UK estimator. The UK takes advantages of the parametric regression model and simple Kriging model to describe the systematic aspects and local fluctuations of unknown functions simultaneously. With the state prediction feedback and input--output UK estimation, the controller is synthesised. The control scheme is considerably simpler than the ones based on back-stepping since only one Kriging system is employed to approximate the lumped system uncertainty. Owing to the prediction function and the UK structure, the novel stochastic Lyapunov function-based stability analysis is conducted. The closed-loop system achieves almost surely boundedness. The effectiveness of the proposed control approach is verified by step tracking.

Direct neural control of hypersonic flight vehicles with prediction model in discrete time

In this paper, the direct adaptive neural controller is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle (HFV). The objective of the controller is to make the altitude and velocity to follow a given desired trajectory in the presence of aerodynamic uncertainties. Based on the functional decomposition, the adaptive discrete-time nonlinear controllers are developed using feedback linearization and neural approximation for the two subsystems. Different from the back-stepping design, the altitude subsystem is transformed into the explicit four-step ahead prediction model. With the prediction model, the controller is proposed without virtual controller design. Furthermore, only one direct neural network (NN) is employed for the lumped system uncertainty approximation. The controller is considerably simpler than the ones based on back-stepping scheme and the algorithm needs less NN parameters to be adjusted online. The semiglobal uniform ultimate boundedness (SGUUB) stability is investigated by the discrete-time Lyapunov analysis and the output tracking error is made within a neighborhood of zero. Accordingly, the NN controller is designed for velocity subsystem. The simulation is presented to show the effectiveness of the proposed control approach.

Composite controller design for an airbreathing hypersonic vehicle

In this paper, a tracking control problem for the longitudinal model of an airbreathing hypersonic vehicle subject to external disturbances is investigated. Based on the characteristics of the longitudinal model, the model is divided into two subsystems, including an altitude subsystem and a velocity subsystem. A novel ideal is that, for each subsystem, some nonlinear coupling terms are considered to be parts of lumped disturbances, which are estimated by a nonlinear disturbance observer, and a corresponding feedforward design is then implemented to compensate the lumped disturbances. Meanwhile, by using a finite time control technique, a continuous finite time control law is introduced in the feedback control design. Then, a composite control scheme is obtained, which consists of a feedback control law based on the finite time control technique and a feedforward compensator based on the nonlinear disturbance observer technique. This scheme can guarantee stable tracking of the reference trajectories of velocity and altitude. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method. The results show that the control performance of the proposed method in terms of both tracking and disturbance rejection are considerably better than the traditional method.