In this article, a joint adaptive high-gain observer design method is proposed for a class of nonlinear systems subject to sampled output data measurements. The considered class of system is characterized by a nonlinear term coupled with an unknown parameter that enters the system in both the outputs and the states equations. The fact that the considered system involves an output sampling process and an unknown parameter renders the design of the nonlinear adaptive observer more difficult. To overcome this difficulty, a novel closed-loop output predictor is proposed. Based on the well-known decoupling method between the state and unknown parameters, a joint adaptive high-gain observer which can simultaneously guarantee the exponential convergence of the estimation of the unknown state and the unknown parameter is proposed in this article. The structure of the designed observer has been extended to the case of sampled and delayed data measurements. The effectiveness of our proposed observer is demonstrated through numerical simulations and performance comparison with another observer structure proposed in the literature.

Summary In this article, a joint adaptive observer design method is proposed for a class of affine nonlinear systems subject to sampled output data measurements. The considered class of system contains nonlinear terms which depend on unknown parameters. The considered unknown parameters enter the system in both the output and the system states equations which render the design of the sampled data observer for the affine nonlinear system more difficult to conceive. To solve this problem, and based on a new method of decoupling parameter estimation and state observation, a new online output sampling joint adaptive observer is proposed in this article, which can simultaneously guarantees the exponential convergence of the estimation of unknown state and parameter. The structure of the proposed observer has been extended to the case of sampled and delayed data measurements. To illustrate the performance of the proposed observer, a comparison is made with another observer with an output predictor on a satellite navigation system. And the observer proposed in this article is applied to the model‐free control of ultra‐local models.

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SummaryIn this article, a continuous‐discrete high gain observer with a proportional integral (PI) output predictor structure is designed for a class of nonlinear systems subject to sampled‐delayed data measurements. To counteract the effect of the well‐known sensitivity of the high gain observer to the noise measurements, a novel PI output predictor structure is proposed. The uniform ultimate boundedness (UUB) of the proposed observer is demonstrated by means of Lyapunov function and small gain method. The effectiveness of our proposed observer is demonstrated through numerical simulations and performances comparison with previous observer design methods in the literature.