Control For Strict-feedback Nonlinear Systems Research Articles

Adaptive robust fault-tolerant control for nonlinear systems with prescribed performance

Based on prescribed performance, backstepping, and $$H_{\infty }$$ techniques, adaptive robust fault-tolerant control for strict-feedback nonlinear systems with prescribed performance is investigated in the paper. A prescribed performance function, which is characterized by the maximum overshoot, convergence rate, and steady-state error, is utilized for the output error transformation. Based on the error transformation model, an adaptive robust fault-tolerant controller is designed, which guarantees that the output tracking error is bounded by the prescribed performance function and the effect of external disturbances and approximation errors is attenuated by $$H_{\infty }$$ tracking performance. The compensation control strategy is adopted in the fault-tolerant control system, where the fault functions are approximated by neural networks. It is shown by Lyapunov stability theory that the state trajectories of the closed-loop system are bounded, the prescribed dynamic performance for the output tracking error is achieved, and the $$H_{\infty }$$ tracking performance is guaranteed whether the faults occur or not. Finally, comparative simulation results show the effectiveness of the proposed approach.

Simplified adaptive neural control of strict-feedback nonlinear systems

This paper presents a simplified adaptive backstepping neural network control (ABNNC) strategy for a general class of uncertain strict-feedback nonlinear systems. In the backstepping design, all unknown functions at intermediate steps are passed down such that only a single neural network is needed to approximate a lumped uncertainty at the last step. The closed-loop system achieves practical asymptotic stability in the sense that all involved signals are bounded and the tracking error converges to a small neighborhood of zero. The contribution of this study is that the complexity growing problem of the traditional ABNNC design is substantially eliminated for a general class of uncertain strict-feedback nonlinear systems, where the constraints of control parameters that guarantee closed-loop stability is clearly demonstrated. An illustrative example has verified effectiveness of our approach.

Fuzzy-Approximation-Based Adaptive Control of Strict-Feedback Nonlinear Systems With Time Delays

This paper focuses on the problem of adaptive control for a class of nonlinear time-delay systems with unknown nonlinearities and strict-feedback structure. Based on the Lyapunov-Krasovskii functional approach, a state-feedback adaptive controller is constructed by backstepping. The proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal, and all the signals of the closed-loop system remain bounded. Compared with the results that exist, the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy-membership functions; therefore, a priori knowledge of fuzzy approximators is not necessary for control design, and the proposed approach requires only one adaptive law for an nth-order system. Two numerical examples are used to illustrate the effectiveness of the proposed approach.

Observer-based fuzzy adaptive control for strict-feedback nonlinear systems

In this paper, a new fuzzy adaptive control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is introduced for state estimation as well as system identification. Under the framework of the backstepping design, fuzzy adaptive output feedback control is constructed recursively. It is proven that the proposed fuzzy adaptive control approach guarantees the semi-global boundedness property for all the signals and the tracking error to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.

DSC-backstepping based robust adaptive NN control for strict-feedback nonlinear systems via small gain theorem

The adaptive tracking control problem is discussed for a class of strict-feedback uncertain systems. RBF Neural Networks are used to approximate the uncertainties. A unified and systematic procedure is developed to derive a robust adaptive tracking controller with the fusion of dynamic surface control technique and small gain approach. The proposed algorithm can avoid both problems of 'explosion of complexity' and 'curse of dimension' synchronously, thus is convenient to implement in applications. The stability of the closed-loop system is proved. Finally, simulation results via two application examples validate the effectiveness and performance of the proposed scheme.

A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach.