Output-feedback dynamic surface control for a class of nonlinear non-minimum phase systems

The problem of output feedback stabilization of a class of under-actuated benchmark nonlinear systems is discussed. The proposed method utilizes an extended high gain observer (EHGO)-based sliding mode control (SMC) technique to control a class of nonlinear systems which may have unstable zero dynamics. Starting with Lagrangian model of the system and using a suitable coordinate transformation, a generalized normal form representation is derived which decouples the system into an internal and external dynamics. The internal dynamics is utilized to derive an auxiliary system and the full-order EHGO thus obtained is used for estimation of derivative(s) of the system output that are further used in design of an output feedback control law. It is shown that the proposed output feedback controller stabilizes the system and convergence of estimated states is demonstrated with suitable selection of observer parameters. The proposed control scheme is applied to a benchmark nonlinear system, namely inertia wheel pendulum (IWP), in order to demonstrate the efficacy of the technique by simulation.

Fuzzy stable inversion-based output tracking for nonlinear non-minimum phase system and application to FAHVs

This paper proposes a global tracking control method for underactuated ships with input and velocity constraints using the dynamic surface control (DSC) method, where the control structure is formed in a modular way that cascaded kinematic and dynamic linearizations can be achieved similarly as in the backstepping method. First, the first step linearization of the kinematics determines the pseudo (or auxiliary) surge velocity and yaw angle, which are used as the commands for the second-step linearization. Then, in the second-step linearization of dynamics, the actual torque inputs are designed to make the actual surge velocity and yaw angle follow these pseudo commands to achieve the position and yaw angle tracking. By employing the dynamic surface control method in the design of each kinematic and dynamic linearization law, we can obtain a control structure that is much simpler than the previous backstepping-based controllers such that it is beneficial from the practical application viewpoint. In addition, it is possible to track general reference trajectories, i.e., the reference yaw velocity need not be persistently exciting and there is no restriction on the initial yaw tracking error. In particular, global tracking control is achieved even in the presence of input and velocity constraints, unlike the DSC method which introduces the several filters in the backstepping design procedure to avoid the model differentiation and make it easier to be implemented and usually has semiglobal tracking performance. Finally, the stability analysis and numerical simulations are performed to confirm the effectiveness of the proposed scheme.

Switched-observer-based adaptive DSC design of nonstrict-feedback switched stochastic nonlinear time-delay systems

This article focuses on an adaptive dynamic surface tracking control issue of nonlinear multiagent systems (MASs) with unmodeled dynamics and input quantization under predefined accuracy. Radial basis function neural networks (RBFNNs) are employed to estimate unknown nonlinear items. A dynamic signal is established to handle the trouble introduced by the unmodeled dynamics. Moreover, the predefined precision control is realized with the aid of two key functions. Unlike the existing works on nonlinear MASs with unmodeled dynamics, to avoid the issue of "explosion of complexity," the dynamic surface control (DSC) method is applied with the nonlinear filter. By using the designed controller, the consensus errors can gather to a precision assigned a priori. Finally, the simulation results are given to demonstrate the effectiveness of the proposed strategy.

Adaptive output feedback dynamic surface control of nonlinear systems with unmodeled dynamics and unknown high-frequency gain sign

In this paper, a partial tracking error constrained fuzzy output-feedback dynamic surface control (DSC) scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design. With the help of fuzzy logic systems identifying the MIMO unknown nonlinear systems, a fuzzy adaptive observer is established to estimate the unmeasured states. By transforming the tracking errors into new virtual error variables and based on the DSC backstepping recursive design technique, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds. The simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme.

This brief considers the distributed finite-time consensus tracking control problem for nonlinear multi-agent systems with false data injection (FDI) attacks. Firstly, since instability is inevitable when false datas are injected into the researched system, a security control algorithm combining the modified coordinate transformation and the dynamic surface control (DSC) method is developed to eliminate the negative impact of FDI attacks and reduce the burden caused by iterative computations of virtual controls. Besides, there are unknown nonlinearities in the dynamics of each agent, which can not be directly handled by the traditional control design. Thus, the neural-network-based approximation technique is introduced to compensate the unknown nonlinearities. In summary, a novel controller is constructed for each agent, which guarantees the consensus of the outputs of all agents can be achieved and that all the signals of the studied system are bounded within a finite-time period. To prove the correctness of the designed security control algorithm, a simulation example of the multi-agent system composed of multiple single-link robots is presented.

Modular neural dynamic surface control for position tracking of permanent magnet synchronous motor subject to unknown uncertainties

This paper is devoted to addressing the issue of adaptive fuzzy control for single-input single-output (SISO) fractional-order nonlinear systems with uncertainty. In order to avoid the “explosion of terms” caused by solving the fractional derivative of virtual signal, a new fractional-order dynamic surface control (DSC) method is proposed for fractional-order systems. Based on backstepping technique and Lyapunov direct method for fractional derivatives, the stability of closed-loop system is proved, which can ensure that the tracking error can converge to a small region. Finally, a simulation example is provided to reveal the effectiveness of the proposed control scheme.

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In this work, the tracking control problem for a class of nonlinear strict-feedback systems with input nonlinearity is addressed. In response to the influence of input nonlinearity, an auxiliary control system is constructed to compensate for it. To process unknown nonlinear dynamics, radial basis function neural networks (RBFNNs) are introduced to approximate them, and some adaptive updating control laws are designed to estimate unknown parameters. Furthermore, during the dynamic surface control (DSC) design process, first-order low-pass filters are introduced to solve the complexity explosion problems caused by repeated differentiation. After that, an NN-based adaptive dynamic surface tracking controller is proposed to achieve the tracking control. By applying the proposed controller, it can be guaranteed that not only the output of the system can track the desired trajectory, but also that the tracking error can converge to a small neighborhood of zero, while all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed controller is verified through two examples.

To a non-minimum phase nonlinear system, it was supposed that, if there is an output feedback control that stabilizes the auxiliary system, then there is an output feedback that stabilizes the original system. The existing methods base designing output feedback for non-minimum phase nonlinear system on the hypothesis that there exists output feedback for auxiliary system. However, the auxiliary system could be unobservable. Alternatively, this study aims to create a way to design output feedback for auxiliary systems in unobservable situation. An output state is constructed in the last equation of auxiliary system, which artificially makes the internal dynamics of the auxiliary system observable. Then, a cascade high-gain observer is designed for the auxiliary system, consisting of an extended high-gain observer for external dynamics and a high-gain observer for internal dynamics of the auxiliary system. Therefore, the output feedback control for auxiliary system can be designed via the cascade high-gain observer and a state feedback. Finally, the proposed method is demonstrated by an academic example and an inverted pendulum on a cart in the simulation.

This paper presents an adaptive output-feedback control method based on neural networks for flexible link manipulator which is a nonlinear nonminimum phase system. The proposed controller comprises a linear, a neuro-adaptive, and an adaptive robustifying parts. The neural network is designed to approximate the matched uncertainty of the system. The inputs of the neural network are the tapped delays of the system input–output signals. In addition, an appropriate reference signal is proposed to compensate the unmatched uncertainty inherent in the internal system dynamics. The adaptation laws for the neural network weights and adaptive gains are obtained using the Lyapunov’s direct method. These adaptation laws employ a linear observer of system dynamics that is realizable. The ultimate boundedness of the error signals are analytically shown using Lyapunov's method.

In this article, by using the neural-networks (NNs) separation and approximation technique, an adaptive scheme is presented to deliver the prescribed tracking performance for a class of unknown nonaffine switched nonlinear time-delay systems. The nonaffine terms are indifferentiable and the controllability condition is not required for each subsystem, which allows the considered tracking problem to not be efficiently solved by the traditional adaptive control algorithms. To solve the problem, NNs are utilized to separate and approximate the nonaffine functions, and then the dynamic surface control and convex combination method are utilized to construct a controller and a switching strategy. In addition, an adaptive law is considered for each subsystem to reduce the conservativeness. Under the designed controller and switching strategy, all the signals of the resulting closed-loop system are bounded, and the tracking performance is achieved with a prescribed level.