Sliding mode control for an aerodynamic missile based on backstepping design

In order to solve the mismatched uncertainties of a class of nonlinearsystems, a control method of sliding mode control (SMC) based on the backstepping design isproposed. It introduces SMC in to the last step of backstepping design to modify the backsteppingalgorithm. This combination not only enables the generalization of the backstepping design to beapplied to more general nonlinear systems, but also makes the SMC method become effective in solvingthe mismatched uncertainties. The SMC based on the backstepping design is applied to the flightcontrol system design of an aerodynamic missile. The control system is researched throughsimulation. The simulation results show the effectiveness of the proposed control method.

CHAOS SYNCHRONIZATION OF MORSE OSCILLATOR VIA BACKSTEPPING DESIGN

Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function with the design of controller. The proposed approaches offers a syetematic design procedure for synchronization and adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approaches.

Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper,an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system.The considered system contains unknown nonlinearfunction and actuator saturation.Fuzzy logic systems(FLSs)and a smooth function are used to approximate the unknownnonlinearities and the actuator saturation,respectively.By com-bining the command-filter technique with the backsteppingdesign algorithm,a novel adaptive fuuzy tracking backsteppingcontrol method is developed.It is proved that the adaptive fuuzycontrol scheme can guarantee that all the variables in the closed-loop system are bounded,and the system output can track thegiven reference signal as close as possible.Simulation results areprovided to illustrate the effectiveness of the proposed approach.

Adaptive Backstepping Slide Mode Control of Pneumatic Position Servo System

With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental performance, as compared with some existing methods. results show that the designed controller can achieve better tracking

Output-Feedback Based Simplified Optimized Backstepping Control for Strict-Feedback Systems with Input and State Constraints

In this paper,an adaptive neural-network(NN)output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics,input saturation and state constraints.Neural networks are used to approximate unknown internal dynamics and an adaptive NN state observer is developed to estimate immeasurable states.Under the framework of the backstepping design,by employing the actor-critic architecture and constructing the tan-type Barrier Lyapunov function(BLF),the virtual and actual optimal controllers are developed.In order to accomplish optimal control effectively,a simplified reinforcement learning(RL)algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function,instead of employing existing optimal control methods.In addition,to ensure that all the signals in the closed-loop system are bounded and the output can follow the reference signal within a bounded error,all state variables are confined within their compact sets all times.Finally,a simulation example is given to illustrate the effectiveness of the proposed control strategy.

Adaptive robust dissipative designs on straight path control for underactuated ships

An adaptive robust control algorithm for ship straight path control system in the presence of both modeling uncertainties and the bounded disturbances is proposed. Motivated by the backstepping approach, the algorithm is developed by using the dissipation theory, such that the resulting dosed-loop system is both strictly dissipative and asymptotically adaptively stable for all admissible uncertainties. Also, it is able to steer an underactuated ship along a prescribed straight path with ultimate bounds under external disturbances induced by wave, wind and ocean current. When there are no disturbances, the straight path control can be implemented in a locally asymptotically stable manner. Simulation results on an ocean-going training ship ‘YULONG＇ are presented to validate the effectiveness of the algorithm.

Function Projective Synchronization of Discrete-Time Chaotic and Hyperchaotic Systems Using Backstepping Method

In this paper, a function projective synchronization scheme is developed to investigate the function projective synchronization between the discrete-time driven chaotic system and the discrete-time response chaotic system. With the aid of symbolic-numeric computation, we use the scheme to study the function projective synchronization between 2D Lorenz discrete-time system and Hdnon discrete-time system, as well as that between 3D discrete-time hyperchaotic system and Henon-like map via three scalar controllers, respectively. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme.

Synchronization of spatiotemporal chaos in complex networks via backstepping

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures. The synchronization of multi-spatiotemporal chaotic systems is imple- merited by adding the control only to a terminal node, and the controller is designed via a corresponding update law. The control law is applied to spatiotemporal Gray-Scott systems. Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.

Direct Adaptive Fuzzy Based Backstepping Control of Semi Strict Feedback Nonlinear Systems

In this paper, a direct adaptive fuzzy tracking control is proposed for a class of uncertain single-input single-output nonlinear semi-strict feedback systems. Based on Takagi-Sugeno type fuzzy systems, a direct adaptive fuzzy tracking controller is developed by using the backstepping approach. The main advantage of the developed method is that for an n-th order system, only one parameter is needed to be adjusted online. It is proven that, under the appropriate assumptions, the developed scheme can achieve that the output system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. The efficacy of the proposed algorithm is investigated by an illustrative simulation example of one link robot.

ROBUST CONTROL OF A CLASS OF NONLINEAR SYSTEM WITH TIME-VARYING PAR AMETRIC UNCERTAINTIES

A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

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.

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization （FPS） of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme.

Adaptive L_2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L 2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set. Moreover, the generalized matching conditions are also relaxed in the proposed L 2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.

Robust Adaptive Actuator Failure Compensation for a Class of Uncertain Nonlinear Systems

This paper presents a robust adaptive state feedback control scheme for a class of parametric-strict-feedback nonlinear systems in the presence of time varying actuator failures. The designed adaptive controller compensates a general class of actuator failures without any need for explicit fault detection. The parameters, times, and patterns of the considered failures are completely unknown. The proposed controller is constructed based on a backstepping design method. The global boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighborhood of the origin. The proposed approach is employed for a two-axis positioning stage system as well as an aircraft wing system. The simulation results show the correctness and effectiveness of the proposed robust adaptive actuator failure compensation approach.