An adaptive learning controller for MIMO uncertain feedback linearizable nonlinear systems

Most of available results in adaptive learning controllers (ALCs) with input learning technique have considered the single-input single-output nonlinear systems. This paper presents an ALC for MIMO uncertain feedback linearizable systems whose uncertainty is in their linear parameters. Since only an output signal is available for measurement, a high gain observer is used to estimate the unmeasurable state. The estimated state is then utilized to implement the ALC. The proposed ALC learns the input gain parameters of the state equation as well as the internal parameters. In addition, the desired input is also learned using an input learning rule to track the whole command history. In the proposed ALC, the tracking errors are bounded and the mean-square tracking error is $$O(\epsilon )$$O(ϵ) as the task is repeated. Single-link and two-link manipulators are presented as simulation examples to confirm the feasibility and the performance of the proposed ALC.

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