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This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

This article investigates the consensus problem for a class of fractional-order multi-agent systems with input delay. Each follower is modeled as a system with input delay and nonlinear dynamics. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, dynamic surface control technology is introduced into an adaptive neural network backstepping controller. A dynamic event-triggered scheme without Zeno behavior is considered, which can reduce the utilization of communication resources. The sliding mode control technology is introduced to enhance robustness. The Pade delay approximation method is extended to fractional-order systems, which converts the original systems into systems without input delay. The stability of systems is ensured by the constructed Lyapunov functions. Examples and simulation results show that the consensus tracking errors can quickly converge and all the followers can synchronize to the leader by the proposed method.

The aim of this paper is to develop state estimation and sliding mode control schemes for the vibration suppression of an underactuated wing aeroelastic system in the presence of a gust load disturbance. Ignoring structural elastic deformation and using the concentrated elastic system (spring) to simulate the overall elastic deformation, this aeroelastic model consists of a straight wing and spring system, describing flap and pitch freedoms. The corresponding dynamic motion equation is established using the Lagrange method, and the gust is modeled as a typical "1-cosine" gust. The aerodynamic lift and moment on the wing are computed by strip theory. The open loop system exhibits the limit cycle oscillations (LCOs) at a certain freestream velocity. The objective is to design a control system for suppressing the LCOs. For the purpose of control, a single trailing-edge control surface is used. It is assumed that only the pitch angle is measured and the remaining state variables needed for full state feedback are estimated by the designed observer. Then an integral sliding surface is put forward on the estimation space; a new continuous reaching law is proposed to reduce the chattering phenomena. The finite-time reachability of the predesigned sliding surface is proved and guaranteed by the designed sliding mode control law. The sufficient condition for the asymptotic stability of the closed-loop system composed of the sliding mode dynamics and the error dynamical system is derived in terms of linear matrix inequality (LMI). The effectiveness of the proposed strategy is finally demonstrated by simulation results.

In this paper, the containment control problem of a class of fractional-order nonlinear multi-agent systems is studied, in which the multi-agent system contains unmeasured states and system nonlinearity. An adaptive neural network backstepping controller combined with event-triggered mechanism is proposed to ensure all followers can converge to the convex hull spanned by the leaders. The command filter is introduced into the proposed fractional-order control system to obtain fractional derivatives for virtual control functions continuously and avoid “explosion of complexity.” From the Lyapunov stability theory, all the signals can remain semi-global uniformly ultimately bounded in the closed-loop system. Numerical example and simulation results confirm the feasibility of the proposed control method.