Robust missile autopilot design based on dynamic surface control

Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control(DSC)technique in order to make the missile control system more robust despite the uncertainty of the dynamical parameters and the presence of disturbances. Firstly, the nonlinear mathematical model of the tail-controlled missile is decomposed into slow acceleration dynamics and fast pitch rate dynamics based on the naturally existing time scale separation. Secondly, the controller based on DSC is designed after obtaining the linear dynamics characteristics of the slow and fast subsystems. An extended state observer is used to detect the uncertainty of the system state variables and aerodynamic parameters to achieve the compensation of the control law. The closed-loop stability of the controller is derived and rigorously analyzed. Finally, the effectiveness and robustness of the design is verified by Monte Carlo simulation considering different initial conditions and parameter uptake. Simulation results illustrate that the missile autopilot based DSC controller achieves better performance and robustness than the other two well-known autopilots.The method proposed in this paper is applied to the design of a missile autopilot, and the results show that the acceleration tracking autopilot based on the DSC controller can ensure accurate tracking of the required commands and has better performance.

Adaptive Dynamic Surface Control for Integrated Missile Guidance and Autopilot

Integrated guidance and control for homing missiles utilizing adaptive dynamic surface control approach is considered based on the three channels independence design idea. A time-varying integrated guidance and control model with unmatched uncertainties is first formulated for the pitch channel, and an adaptive dynamic surface control algorithm is further developed to deal with these unmatched uncertainties. It is proved that the proposed feedback controller can ensure not only the accuracy of target interception, but also the stability of the missile dynamics. Then, the same control approach is further applied to the control design of the yaw and roll channels. The 6-degree-of-freedom （6-DOF） nonlinear missile simulation results demonstrate the feasibility and advantage of the proposed integrated guidance and control design scheme.

Adaptive dynamic surface control for air-breathing hypersonic vehicle

This paper describes an adaptive control approach for an air-breathing hypersonic vehicle. The control objective is to provide robust altitudes and velocity tracking in the presence of model uncertainties and varying disturbances. A fuzzy-neural disturbance observer is developed to estimate uncertainties and disturbances, and the adaptive controller is synthesized by the dynamic surface approach combing with the observer. The tracking error at the steady state can be guaranteed to converge to inside of a small residue set which the size of the set can be an arbitrary small value. Simulation results demonstrate the effectiveness of the presented approach.

Adaptive Fuzzy Dynamic Surface Control of Flexible-Joint Robot Systems With Input Saturation

In this paper, we propose an adaptive fuzzy dynamic surface control(DSC) scheme for single-link flexible-joint robotic systems with input saturation. A smooth function is utilized with the mean-value theorem to deal with the difficulties associated with input saturation. An adaptive DSC design with an auxiliary first-order filter is used to solve the "explosion of complexity"problem. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood around zero. The main advantage of the proposed method is that only one adaptation parameter needs to be updated,which reduces the computational burden significantly. Simulation results demonstrate the feasibility of the proposed scheme and the comparison results show that the improved DSC method can reduce the computational burden by almost two thirds in comparison with the standard DSC method.

Output-feedback Dynamic Surface Control for a Class of Nonlinear Non-minimum Phase Systems

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems.To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control(DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed outputfeedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.

Output Feedback Dynamic Surface Controller Design for Airbreathing Hypersonic Flight Vehicle

This paper addresses issues related to nonlinear robust output feedback controller design for a nonlinear model of airbreathing hypersonic vehicle. The control objective is to realize robust tracking of velocity and altitude in the presence of immeasurable states, uncertainties and varying flight conditions.A novel reduced order fuzzy observer is proposed to estimate the immeasurable states. Based on the information of observer and the measured states, a new robust output feedback controller combining dynamic surface theory and fuzzy logic system is proposed for airbreathing hypersonic vehicle. The closedloop system is proved to be semi-globally uniformly ultimately bounded(SUUB), and the tracking error can be made small enough by choosing proper gains of the controller, filter and observer. Simulation results from the full nonlinear vehicle model illustrate the effectiveness and good performance of the proposed control scheme.

Adaptive Neural Network Dynamic Surface Control for Perturbed Nonlinear Time-delay Systems

This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of ＂explosion of complexity＂ in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of ＂curse of dimensionality＂ and ＂explosion of complexity＂ are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach.

Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.

Dynamic Surface Control with Nonlinear Disturbance Observer for Uncertain Flight Dynamic System

A new robust control method of a nonlinear flight dynamic system with aerodynamic coefficients and external disturbance has been proposed.The proposed control system is a combination of the dynamic surface control(DSC)and the nonlinear disturbance observer(NDO).DSC technique provides the ability to overcome the″explosion of complexity″problem in backstepping control.NDO is adopted to observe the uncertainties in nonlinear flight dynamic system.It has been proved that the proposed design method can guarantee uniformly ultimately boundedness of all the signals in the closed-loop system by Lyapunov stability theorem.Finally,simulation results show that the proposed controller provides better performance than the traditional nonlinear controller.

Adaptive integral dynamic surface control based on fully tuned radial basis function neural network

An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.

Adaptive Synchronization of Rssler System Based on Dynamic Surface Control

A synchronization scheme for R6ssler system based on Dynamic Surface Control （DSC） is proposed in this paper. The DSC method is a recursive design procedure like conventional backstepping methods. Different from the backstepping design, a first-order fdter is introduced in every DSC design step. For this introduced fdter, the derivative of the selected virtual control is avoided and then the drawback of ＂explosion of complexity＂ existing in backstepping design is overcome. Moreover, adaptive method is used for controller design when the system parameters are unknown. Finally, a numerical example is given to illustrate the effectiveness and performance of the proposed method.

Adaptive dynamic surface control for quadrotor-slung load transportation system with uncertainties

Quadrotors play a significant role in our lives and are transforming our lives.Transporting cable-suspended loads is an unavoidable quadrotor application trend and a hot research topic in the control field.Nonetheless,the load swing and unpredictability pose significant challenges to the quadrotor's stability.In this paper,an anti-swing controller with an inner-outer control strategy for the quadrotor-slung load transportation system is presented.To facilitate the controller design,the outer position dynamics are restructured in the form of cascades.Then,a virtual controller is created to force the underactuated states to the dynamic surface to ensure the position subsystem's stability.To improve robustness,an adaptive law is used to eliminate the effects of uncertain cable length.Lastly,a dynamic surface controller for the inner attitude subsystem is presented to drive the actual force to the virtual force.It is demonstrated that the control strategy can stabilize the quadrotor despite mass and cable length uncertainties.Comparative results are provided to demonstrate the efficacy and durability of the proposed method.

Adaptive block dynamic surface control for integrated missile guidance and autopilot

A novel integrated guidance and autopilot design method is proposed for homing missiles based on the adaptive block dynamic surface control approach. The fully integrated guidance and autopilot model is established by combining the nonlinear missile dynamics with the nonlinear dynamics describing the pursuit situation of a missile and a target in the three-dimensional space. The integrated guidance and autopilot design problem is further converted to a state regulation problem of a time-varying nonlinear system with matched and unmatched uncertainties. A new and simple adaptive block dynamic surface control algorithm is proposed to address such a state regulation problem. The stability of the closed-loop system is proven based on the Lyapunov theory. The six degrees of freedom （6DOF） nonlinear numerical simulation results show that the proposed integrated guidance and autopilot algorithm can ensure the accuracy of target interception and the robust stability of the closed-loop system with respect to the uncertainties in the missile dynamics.

Robust dynamic surface control of flexible joint robots using recurrent neural networks

A robust neuro-adaptive controller for uncertain flexible joint robots is presented. This control scheme integrates H^infinity disturbance attenuation design and recurrent neural network adaptive control technique into the dy- namic surface control framework. Two recurrent neural networks are used to adaptively learn the uncertain functions in a flexible joint robot. Then, the effects of approximation error and filter error on the tracking performance are attenuated to a prescribed level by the embedded H-infinity controller, so that the desired H-infinity tracking performance can be achieved. Finally. simulation results verifv the effectiveness of the nronosed control scheme.

Adaptive Neural Network Dynamic Surface Control for a Class of Nonlinear Systems with Uncertain Time Delays

This paper presents a solution to tracking control problem for a class of nonlinear systems with unknown parameters ana uncertain time-varying delays. A new adaptive neural network （NN） dynamic surface controller （DSC） is developed. Some assumptions on uncertain time delays, which were required to be satisfied in previous works, are removed by introducing a novel indirect neural network algorithm into dynamic surface control framework. Also, the designed controller is independent of the time delays. Moreover, the dynamic compensation terms are introduced to facilitate the controller design. It is shown that the closed-loop tracking error converges to a small neighborhood of zero. Finally, a chaotic circuit system is initially bench tested to show the effectiveness of the proposed method.

A robust output-feedback adaptive dynamic surface control for linear systems with input disturbance

In this paper, a robust output-feedback adaptive control is proposed for linear time-invariant （LTI） single- input single-output （SISO） plants with unmeasurable input disturbance. Using dynamic surface control （DSC） technique, it is shown that the explosion of complexity problem in backstepping control can be eliminated. Furthermore, the proposed adaptive DSC scheme has the following merits： 1） by introducing an initialization technique, the L~ performance of system tracking error can be guaranteed even if the plant high-frequency gain is unknown and the input disturbance exists, and 2） the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. It is proved that with the proposed scheme, all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.

Adaptive NN Dynamic Surface Control for a Class of Uncertain Non-affine Pure-feedback Systems with Unknown Time-delay

Adaptive neural network （NN） dynamic surface control （DSC） is developed for a class of non-affine pure-feedback systems with unknown time-delay. The problems of ＂explosion of complexity＂ and circular construction of the practical controller in the traditional backstepping algorithm are avoided by using this controller design method. For removing the requirements on the sign of the derivative of function f~, Nussbaum control gain technique is used in control design procedure. The effects of unknown time-delays are eliminated by using appropriate Lyapunov-Krasovskii functionals. Proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Two simulation examples are presented to demonstrate the method.

Adaptive Fuzzy Dynamic Surface Control for a Class of Perturbed Nonlinear Time-varying Delay Systems with Unknown Dead-zone

In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approximate the unknown nonlinear functions.Then,by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach,the adaptive fuzzy tracking controller is designed.Our development is able to eliminate the problem of 'explosion of complexity' inherent in the existing backstepping-based methods.The main advantages of our approach include:1) for the n-th-order nonlinear systems,only one parameter needs to be adjusted online in the controller design procedure,which reduces the computation burden greatly.Moreover,the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results;2) the proposed control scheme does not need to know the time delays and their upper bounds.It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound,Finally,simulation results demonstrate the effectiveness of the proposed approach.

Dynamic surface control and active disturbance rejection control-based integrated guidance and control design and simulation for hypersonic reentry missile

This paper proposes a novel integrated guidance and control(IGC)method combining dynamic surface control(DSC)and active disturbance rejection control(ADRC)for the guidance and control system of hypersonic reentry missile(HRM)with bounded uncertainties.First,the model of HRM is established.Second,the proposed IGC method based on DSC and ADRC is designed.The stability of closed-loop system is proved strictly.It is worth mentioning that the ADRC technique is used to estimate and compensate the disturbance in the proposed IGC system.This makes the closed-loop system a better performance and reduces the chattering caused by lumped disturbances.Finally,a series of simulations and comparisons with a 6-DOF non-linear missile that includes all aerodynamic effects are demonstrated to illustrate the effectiveness and advantage of the proposed IGC method.

Disturbance Observer-Based Safe Tracking Control for Unmanned Helicopters With Partial State Constraints and Disturbances

In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown external disturbances. A safety protection algorithm is proposed to keep the constrained states within the given safe-set. A second-order disturbance observer technique is utilized to estimate the external disturbances. It is shown that the desired tracking performance of the controlled unmanned helicopter can be achieved with the application of the backstepping approach, dynamic surface control technique, and Lyapunov method. Finally, the availability of the proposed control scheme has been shown by simulation results.