Robust Constraint Satisfaction for Continuous-Time Nonlinear Systems in Strict Feedback Form

A global state feedback output regulating control for uncertain systems in strict feedback form

In this paper, by incorporating this dynamic structure control technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of explosion of complexity inherent in the existing method. Taking the neural network as a model of the system, control signals are directly obtained by minimizing the cumulative differences between a setpoint and output of the model. The applicability in nonlinear system is demonstrated by simulation experiments.

In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

Finite-time stabilization of stochastic nonlinear systems in strict-feedback form

Cascade control for a class of uncertain nonlinear systems: a backstepping approach

In this paper, output feedback direct adaptive robust NN control is investigated for a class of nonlinear discrete-time systems in strict-feedback form. To construct output feedback control, the original strict-feedback system is transformed into a cascade form, which the output feedback of the nonlinear discrete-time system can be carried out. Then with employment of the inputs and outputs, the output feedback direct adaptive robust NN control is developed. The HONNs is exploited to approximate unknown function, and a stable adaptive NN controller is synthesized. The proposed algorithm improves the rubostness of the discrete-time nonlinear systems. It is proven that all the signals in closed-loop system are uniformly ultimately bounded (UUB). A simulation example is presented to illustrate the effectiveness of the proposed algorithm.Keywordsoutput feedbackrubostnessdirect adaptive NN controldiscrete-time nonlinear system

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Online lifelong optimal tracking control of uncertain nonlinear continuous-time strict-feedback systems using deep neural networks.

This paper investigates adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems in strict feedback form. The considered nonlinear systems contain unknown nonaffine nonlinear faults and unmeasured states. Fuzzy logic systems are used to approximate cost function and unknown nonlinear functions, respectively. It is assumed that the states of the systems to be controlled are unmeasurable, thus an adaptive state observer is developed. To solve the nonaffine nonlinear fault control design problem, filtered signals are introduced into the adaptive backstepping control design procedures, and in the framework of adaptive critic technique and fault-tolerant control technique, a novel adaptive fuzzy fault-tolerant optimal control scheme is developed. The stability of the closed-loop system is proved by using Lyapunov stability theory. The simulation results verify the effectiveness of the proposed control strategy.

Reduced-order observer-based control design for nonlinear stochastic systems

This paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.

This paper addresses the event-triggered feedback optimization problem for a class of nonlinear systems in strict-feedback form with dynamic uncertainties. The system has access to real-time gradients of the objective function along its output trajectory, which is a milder requirement than having access to the objective function’s analytical form. By employing backstepping and gain assignment techniques, two event-triggered mechanisms and a feedback optimization protocol are developed that construct the closed-loop system as a feedback interconnection of multiple Input-to-State Stable (ISS) subsystems. The small-gain theorem is applied to guarantee closed-loop stability, ensuring that the proposed protocol drives the system output to the optimal solution while excluding Zeno behavior. We further relax the uncertain system dynamics to allow nonvanishing terms at the equilibrium point and bounds given by nonlinear functions involving unknown parameters. Unlike existing small-gain methods for event-triggered control, the proposed approach avoids constructing set-valued maps and incorporates the optimization objective into the small-gain analysis. The effectiveness of the approach is demonstrated through its application to a source-seeking problem.

In this paper, a novel robust adaptive tracking control approach is presented for a class of strict-feedback single-input single-output nonlinear systems. By employing radial basis function neural network to account for system uncertainties, the proposed scheme is developed by combining “command filter” and “minimal learning parameter” techniques. The main advantages of the proposed controller are that: (1) the problem of “explosion of complexity” inherent in the conventional backstepping method is avoided; (2) the problem of “dimensionality curse” is solved, and only one adaptive parameter needs to be updated online. These advantages result in a much simpler adaptive control algorithm, which is convenient to implement in applications. In addition, stability analysis shows that uniform ultimate boundedness of the solution of the closed-loop system can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.

Adaptive fuzzy tracking controller design is addressed for a class of uncertain nonlinear system in strict-feedback form. The system dynamics are unknown, and external disturbances satisfy triangular bounds. We utilize Tagaki-Sugeno (T-S) fuzzy logic system to approximate the unknown system functions. The proposed scheme can guarantee the ultimate uniform boundedness of all the signals in the closed-loop system. Compensated tracking errors are employed to construct Lyapunov candidate function. The proposed design circumvents the repeated differential of virtual control law, which renders the controller structures simple and easy to implement. Simulation researches are carried out. The simulation results demonstrate the effectiveness and usage of the proposed design.

This paper presents a finite-time fault-tolerant fuzzy adaptive controller for uncertain interconnected nonlinear systems in strict-feedback form. The controller addresses input saturation, state-dependent actuator faults, external disturbances, and unavailable states for measurement. To avoid any unexpected alteration due to failures, the proposed control scheme design addresses all types of actuator faults that are bias, drift, and loss of accuracy as additive faults, as well as a multiplicative fault that results in loss of effectiveness with nonaffine state-dependency. Restrictions on control gains and unmatched interconnections are eliminated, and the explosion complexity caused by recursive back-stepping designs is avoided. Fuzzy Systems approximate the unknown ideal control laws along side the acutator faults and disturbances. The stability analysis guarantees that tracking errors converge to a small compact set around the origin in finite time. Simulation results on a quad-rotor UAV and a mathematical system confirm the effectiveness of the proposed approach.