Fixed-Time Command Filtered Adaptive Backstepping Control for Uncertain Nonlinear Systems With Zero-Error Tracking.

In this paper, an adaptive control scheme based on command-filtered backstepping technique is developed for a class of uncertain multiple-input-multiple-output (MIMO) strict-feedback nonlinear systems. Within this scheme, extreme learning machine (ELM) with random hidden nodes is used in the controller to approximate unknown functions, and a smooth projection algorithm is adopted to adjust online estimated parameters in the controller such that the boundedness of the parameter estimates can be ensured. Furthermore, some stale command filters are designed to produce virtual control signals and their derivations such that the analytic calculation of the partial derivatives of virtual control signals is removed. Also, some other stable filters are proposed to generate compensating signals of above-mentioned filtered errors to compute compensated tracking errors. It is proved that the proposed control scheme can guarantee the boundedness of all signals in the closed-loop system. Finally, the proposed control scheme is applied to control wind turbine and the simulation studies illustrate the theoretic results obtained.

This article proposes a robust adaptive controller design method for strict feedback nonlinear systems with unmodeled dynamics and input saturation. By using command filters, the explosion of complexity is obviated. The influence of filter errors bought in by command filters is eliminated by introducing compensating signals. Moreover, by skillfully constructing annth‐order auxiliary dynamic system, the effect of input saturation is avoided, where the disadvantages of conventional methods based on the hyperbolic tangent function are overcome. To tackle the effect of unmodeled dynamics which can destroy the performance and even destabilize the system, based on input‐to‐state stability theory, a dynamic signal is designed. Finally, the Lyapunov theory‐based stability analysis proves that all the closed‐loop signals are uniformly ultimately bounded. The effectiveness of the proposed controller design scheme is verified in simulation experiments.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application

Event-triggered adaptive optimal tracking control for nonlinear stochastic systems with dynamic state constraints

In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients.

Most optimal control method aim at finding a control law to minimize the corresponding cost function, and the key problem is to solve the Hamilton–Jacobi–Bellman equation (HJBE). However, the solution of HJBE is hard and even unavailable to obtain for nonlinear system and, thus, the optimal control method can not be developed. To address this problem, an adaptive neural inverse optimal control method is proposed for nonlinear systems with external disturbances and actuator failures in this article. The cost function in this article is defined based on the controller and, therefore, once the controller is obtained, the corresponding cost function is minimized. Accordingly, the directly solution of HJBE is avoided. In more detail, the auxiliary system is constructed to develop the auxiliary controller, based on which the actual optimal fault-tolerant controller can be further obtained. The uncertainties in system dynamics are compensated by neural networks, and the unknown actuator failures are handled by adaptive control gain. It is proved that nonlinear system is input-to-state stabilizable (ISS) and the proposed controller can minimize the cost function that puts penalty on tracking error and system input. Two simulation examples are provided to demonstrate the effectiveness of the proposed control method.

This article settles the issue of adaptive fixed-time control of uncertain nonlinear quantized systems. Different from the traditional study about fixed-time control for uncertain nonlinear systems, quantitative control issue is considered in this paper, and the nonlinear term can be unknown. The new adaptive control tactic of fixed-time tracking control is proposed via fuzzy logic systems approaching unknown nonlinearity, which overcomes the existing limitation of the upper boundary of system settling time relies on the initial condition. The closed-loop system stability is guaranteed in a fixed time. At the end of this paper, the availability of the strategy is proved by a numerical simulation.

In this work, the tracking control problem of nonlinear system which contains unknown parameters, multiple state delays, external disturbances and the dead-zone input is studied. By introducing a dynamic gain-based adaptive control strategy and employing a new Lyapunov–Krasovskii (L–K) functional, we construct an adaptive tracking controller to ensure the boundedness of all the states and guarantee the tracking error small enough. Two examples are given to verify the correctness of the control theory.

This paper addresses the problem of state estimation and the tracking control scheme combining fuzzy control technique for a class of MIMO nonlinear systems, in which some variables are not measurable, with plant uncertainties and external disturbances First, the nonlinearities are approximated using neural networks, and then are modeled based on linear difference inclusions(LDI), which makes the structure of the desired filter simpler and parameter turning easier. A unified framework is established to solve the addressed H ∞ filtering problem by exploiting linear matrix inequality (LMI) approach. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion to resolve system uncertainties and external disturbances. This is done in such a way that all states of the system are bounded and the H ∞ tracking performance is achieved. Finally, A numerical example is investigated to demonstrate the feasibility and the effectiveness of the proposed methodology.

Event-triggered low-computation adaptive output-feedback fuzzy tracking control of uncertain nonlinear systems

Event-triggered adaptive tracking control of uncertain nonlinear systems with prescribed performance and actuator failures

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults based on dynamic surface technique

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

Command-filter-based adaptive tracking control for nonlinear systems with unknown input quantization and mismatching disturbances