In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multi-agent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multi-agent systems. In this scheme, asymptotic consensus of a second-order uncertain multi-agent system is achieved in a network of directed graph.
This paper studies the real-time parameter estimation and adaptive tracking control problem for a six degrees of freedom (6-DOF) of quadrotor unmanned aerial vehicle (UAV) as an under-actuated system. A virtual proportional derivative (PD) is proposed to maintain position dynamics. Two adaptive control schemes are designed and compared to maintain the attitude dynamics of UAV while several parameters of UAV are unknown. In the first scheme, a classical adaptive scheme using the certainty equivalence principle is extended and designed for tracing control of the systems with unknown time-varying parameters. To improve the performance of the first scheme, a new control scheme is designed in the second scheme by proposing additional continuous function to handle the unknown parameters. An additional robust term is designed in both schemes to handle the perturbation caused by unknown time-varying parameters. The rigorous analytical proof and numerical simulation analysis are provided to support the efficacy of the proposed controller.INDEX TERMS Quadrotor, unmanned aerial vehicle, unknown time-varying parameter, classical adaptive scheme, certainty equivalence principle, adaptive control.
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