Class Of Strict-feedback Nonlinear Systems Research Articles

Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the “explosion of complexity”, the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

Finite-Time Tracking Control for a Class of Uncertain Strict-Feedback Nonlinear Systems With State Constraints: A Smooth Control Approach.

This article is concerned with the finite-time tracking control problem for a class of strict-feedback nonlinear systems involving state constraints, unknown nonlinearities, and nonvanishing disturbances. Unlike the literature that mainly focuses on a C0 finite-time controller, in this article, a novel C1 smooth finite-time adaptive neural network (NN) controller is proposed by employing a smooth switch between the fractional and cubic form state feedback. The proposed controller not only avoids the singularity but also makes it possible to implement the dynamic surface control (DSC) technique. By applying the adaptive NN control technique, together with barrier Lyapunov functions (BLFs) and a generalized first-order filter including both linear and fractional terms, the desired fast finite-time control performance of the closed-loop nonlinear systems can be guaranteed, and meanwhile, the state constraints are never violated. Under the proposed control scheme, the tracking control problems of nonlinear systems with output constraint and full-state constraints are, respectively, discussed. It is explicitly shown that all the internal error signals are driven to converge into small regions in a finite time. Finally, the effectiveness of the control scheme is also confirmed by the applications to the control of a second-order nonlinear system and an uncertain ship autopilot.

Observer-Based Adaptive Fuzzy Tracking Control for a Class of Strict-Feedback Systems with Event-Triggered Strategy and Tan-type Barrier Lyapunov Function

In this paper, an observer-based adaptive fuzzy tracking control is considered for a class of strict-feedback nonlinear systems. The nonlinear functions and unmeasured states in the system are estimated by means of fuzzy logic systems and fuzzy state observers, respectively. In addition, the tan-type barrier Lyapunov specifies that the tracking error is limited to a given area. An improved event-triggered technique is introduced in the controller design to save the network resources and avoid the Zeno-behavior. It is proven that the proposed controller can ensure that all the signals of the closed-loop system are uniformly and ultimately bounded. Finally, the simulation results verify the feasibility of the design scheme.

Adaptive control of a class of strict feedback nonlinear systems under replay attacks

The adaptive control of a class of strict-feedback nonlinear system under replay attack is investigated in this paper. Durations of each attack and the resting time after each attack are analyzed and their explicit bounds are presented to ensure closed-loop stability. Two scenarios are considered. In the first scenario, it is shown that if the duration of each attack is less than a given constant, asymptotical convergence of system output is still preserved. The second scenario shows that if the resting time of each attack meets certain condition after each arbitrarily long duration of attack, closed-loop boundedness is still preserved. This shows that the system controlled under our proposed adaptive controller will not be broken down even in the presence of replay attacks. Simulation results are given to illustrate the effectiveness of the control schemes.

Simplified Optimized Backstepping Control for a Class of Nonlinear Strict-Feedback Systems With Unknown Dynamic Functions.

In this article, a control scheme based on optimized backstepping (OB) technique is developed for a class of nonlinear strict-feedback systems with unknown dynamic functions. Reinforcement learning (RL) is employed for achieving the optimized control, and it is designed on the basis of the neural-network (NN) approximations under identifier-critic-actor architecture, where the identifier, critic, and actor are utilized for estimating the unknown dynamic, evaluating the system performance, and implementing the control action, respectively. OB control is to design all virtual controls and the actual control of backstepping to be the optimized solutions of corresponding subsystems. If the control is developed by employing the existing RL-based optimal control methods, it will become very intricate because their critic and actor updating laws are derived by carrying out gradient descent algorithm to the square of Bellman residual error, which is equal to the approximation of the Hamilton-Jacobi-Bellman (HJB) equation that contains multiple nonlinear terms. In order to effectively accomplish the optimized control, a simplified RL algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function, which is generated from the partial derivative of the HJB equation. Meanwhile, the design can also release the condition of persistence excitation, which is required in most existing optimal controls. Finally, effectiveness is demonstrated by both theory and simulation.

Adaptive Control of Second-Order Nonlinear Systems With Injection and Deception Attacks

In this article, the adaptive control for a class of strict-feedback nonlinear systems with uncertainties under injection and deception attacks is considered. An adaptive control scheme is proposed to deal with the injection and deception attacks meanwhile guarantee that regulation errors could be made arbitrarily small by adjusting control parameters. Compared with existing works whose models are linear or relatively simple, the model we consider in this article is nonlinear with parametric uncertainties. A new type of feedback control scheme is introduced to solve this problem. A simulation example is given to verify the effectiveness of our proposed control scheme.

Disturbance observer-based control for a class of strict-feedback nonlinear systems with derivative-bounded disturbances

An anti-disturbance control problem is investigated in this paper. The disturbance observer plus back-stepping (DOPBS) control scheme is proposed for a class of strict-feedback nonlinear systems with derivative-bounded disturbances. A nonlinear disturbance observer is designed to estimate the derivative-bounded disturbances. By combining the disturbance observer with back-stepping method, the DOPBS controller is designed to reject and attenuate the disturbances. Stability analysis proves that all the signals in the the closed-loop system are uniformly ultimately bounded (UUB). Finally, simulation examples demonstrate the feasibility and effectiveness of the proposed approach compared with existing methods.

Distributed adaptive leader–follower and leaderless consensus control of a class of strict-feedback nonlinear systems: a unified approach

In this paper, distributed adaptive consensus for a class of strict-feedback nonlinear systems under directed topology condition is investigated. Both leader–follower and leaderless cases are considered in a unified framework. To design distributed controller for each subsystem, a local compensatory variable is generated based on the signals collected from its neighbors. Such a technique enables us to solve the leader–follower consensus and leaderless consensus problems in a unified framework. And it further allows us to treat the leaderless consensus as a special case of the leader–follower consensus. For leader–follower consensus, the assumption that the leader trajectory is linearly parameterized with some known functions as required in most recent relevant literatures is successfully relaxed. It is shown that global uniform boundedness of all closed-loop signals and asymptotically output consensus could be achieved for both cases. Simulation results are provided to verify the effectiveness of our schemes.

Finite-Time Stabilization-Based Adaptive Fuzzy Control Design

This article is aimed at developing a finite-time adaptive fuzzy control strategy for a class of nonlinear strict-feedback systems. For the first time, a fast finite-time practical stability criteria is set up, which provides an effective approach to address the finite-time adaptive fuzzy control design. Furthermore, a systematic finite-time adaptive fuzzy control design procedure is developed by embedding that practical stability criteria. The closed-loop stability analysis shows that the tracking error converges to a small region around the origin in finite time. Meanwhile, all the signals in the closed-loop system are bounded. At last, the presented results are tested by a numerical example.

Adaptive neural optimal control of uncertain nonlinear systems with output constraints

In this paper, adaptive optimal control is proposed for a class of strict-feedback nonlinear systems with unmodeled dynamics and output constraints. The controller design procedure contains two parts. In the first part, to satisfy output constraints, nonlinear mapping is used to transform constrained system into a novel one without output constraints. A dynamical signal is utilized to deal with unmodeled dynamics. A feedforward controller is designed using the dynamics surface control technique. In the second part, an auxiliary dynamical system is introduced to optimize cost function, and neural-network based adaptive dynamic programming(ADP) is employed to approximate the optimal cost function and the optimal control law. It is proved that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB) and the output constraints are not triggered by theoretical analysis. Two simulation examples are provided to illustrate the effectiveness of the proposed scheme.

Fuzzy Adaptive Finite-Time Fault-Tolerant Control for Strict-Feedback Nonlinear Systems

This article devotes to investigating the issue of fuzzy adaptive control for a class of strict-feedback nonlinear systems with nonaffine nonlinear faults. The computational complexity is reduced by adopting the dynamic surface control technique. Under the framework of finite-time stability, a novel fault-tolerant control strategy is designed so that the closed-loop system is semiglobally practically finite-time stable, and the tracking error converges to a small residual set in a finite time. Finally, simulation studies for an electromechanical system are shown to verify the feasibility of the presented approach.

Improved Adaptive Dynamic Surface Control for a Class of Uncertain Nonlinear Systems

An improved dynamic surface control (IDSC) approach is presented for a class of strict-feedback nonlinear systems with unknown functions. The proposed method makes the state errors get rid of the influence of first-order filters, which simplifies the design of control. By employing neural networks to account for system uncertainties, the virtual control signal of the IDSC is directly used to construct the state error instead of the signal generated by the first-order filter in the dynamic surface control (DSC) method. The stability of the method is proved by Lyapunov stability theory, and the semi-global uniform ultimate boundedness of all signals in the closed-loop system is guaranteed. Simulation results demonstrate the IDSC method has better tracking performance and stability than traditional DSC method.

Adaptive Fuzzy Tracking Control for a Class of Strict-Feedback Nonlinear Systems With Time-Varying Input Delay and Full State Constraints

This article investigates the adaptive fuzzy tracking control problem for a class of strict-feedback nonlinear systems with time-varying input delay and full state constraints. By using state vector transformation and barrier Lyapunov function techniques, the effect of time-varying input delay and full state constraints are compensated. The unknown nonlinear functions are approximated by utilizing fuzzy logic systems, and then a novel adaptive fuzzy backstepping control strategy is proposed to guarantee that the closed-loop nonlinear system is semiglobally ultimately uniformly bounded. Finally, two simulation examples of an inverted pendulum system and three-degrees-of-freedom helicopter nonlinear system are studied to verify the effectiveness of the proposed control strategy.

Adaptive neural fault-tolerant control for a class of strict-feedback nonlinear systems with actuator and sensor faults

This paper investigates the adaptive neural fault-tolerant control problem for a class of strict-feedback nonlinear systems with simultaneous actuator and sensor faults. The faults considered in this paper are bias (lock-in-place), drift, loss of accuracy, and loss of effectiveness faults. Only one parameter law is updated at each step to reduce the computational burden. By utilizing the adaptive neural network backstepping control strategy, the closed-loop nonlinear system is guaranteed to be semi-globally uniform ultimate bounded, and all the signals are bounded. Finally, a simulation example is given to show the effectiveness of the proposed control strategy.

TABLF-based adaptive control for uncertain nonlinear systems with time-varying asymmetric full-state constraints

ABSTRACT In this paper, we investigate the tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and time-varying asymmetric full-state constraints. By introducing novel tan-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design, the boundedness of the fictitious state tracking errors are ensured. A novel adaptive backstepping control design based on tuning function is given, which successfully eliminates the effect of uncertainties. In addition, only one parameter needs to be adjusted online in the control design, which greatly alleviates the computation burden. Based on the proposed control scheme the asymptotic convergence of system output tracking error is realised and the time-varying full-state constraints are not violated for all the time. A numerical example is given to illustrate the effectiveness of the proposed control scheme.

Finite-Time Adaptive Fuzzy Control for Nonlinear Systems With Full State Constraints

In this paper, an adaptive fuzzy controller is constructed to address the finite-time tracking control problem for a class of strict-feedback nonlinear systems, where the full state constraints are strictly required in the systems. Backstepping design with a tan-type barrier Lyapunov function is proposed. Meanwhile, fuzzy logic systems are used to approximate the unknown nonlinear functions. The addressed control scheme guarantees that the output is followed the reference signals within a bounded error, and all the signals in the closed-loop system are bounded. The simulation results demonstrate the validity of the proposed method.

Direct Adaptive Preassigned Finite-Time Control With Time-Delay and Quantized Input Using Neural Network.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.

Observer-based adaptive fuzzy funnel control for strict-feedback nonlinear systems with unknown control coefficients

This paper proposes an adaptive fuzzy funnel controller for a class of strict-feedback nonlinear systems with unknown control coefficients. A fuzzy state observer is designed to estimate the unmeasurable system states. An improved funnel error is given and embedded in the procedure of control design. Furthermore, based on the backstepping method, an observer-based adaptive fuzzy funnel controller is constructed, which can guarantee that the output tracking error remains in a pre-set funnel and converges to a prescribed interval in finite time as long as the initial error is in the funnel. All the signals in the closed-loop system are also semi-globally uniformly and ultimately bounded. Simulation results demonstrate the effectiveness of the developed controller.

Online Performance-Based Adaptive Fuzzy Dynamic Surface Control for Nonlinear Uncertain Systems Under Input Saturation

As an extension of the conventional prescribed tracking performance constraint problem, this paper proposes a novel online tracking performance constrained control combined with the dynamic surface control (DSC) technique for a class of strict-feedback nonlinear systems with unmeasurable states and input saturation. Using fuzzy logic systems to approximate the unknown nonlinear functions, a high-gain fuzzy observer is designed for state estimation. In the development of DSC control, a serial-parallel estimation model is introduced to analyze the effect of input saturation, and a compensation term is added. To deal with the singularity problem of the prescribed performance constrained method, a novel online performance function is investigated to obtain a satisfactory tracking performance. Under the proposed control scheme, the stability and boundedness of all closed-loop signals are confirmed via Lyapunov synthesis. Finally, numerical simulation results illustrate the effectiveness of the proposed scheme.