In this paper, we investigate the model reference adaptive control approach for uncertain piecewise affine systems with performance guarantees. The proposed approach ensures the error metric, defined as the weighted Euclidean norm of the state tracking error, to be confined within a user-defined time-varying performance bound. We introduce an auxiliary performance function to construct a barrier Lyapunov function. This auxiliary performance signal is reset at each switching instant, which prevents the transgression of the barriers caused by the jumps of the error metric at switching instants. The dwell time constraints are derived based on the parameters of the user-defined performance bound and the auxiliary performance function. We also prove that the Lyapunov function is non-increasing even at the switching instants and thus does not impose extra dwell time constraints. Furthermore, we propose the robust modification of the adaptive controller for the uncertain piecewise affine systems subject to unmatched disturbances. A Numerical example validates the correctness of the proposed approach.

中文翻译：

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具有状态跟踪性能保证的分段仿射系统模型参考自适应控制。

在本文中，我们研究了具有性能保证的不确定分段仿射系统的模型参考自适应控制方法。所提出的方法确保将误差度量（定义为状态跟踪误差的加权欧几里得范数）限制在用户定义的时变性能范围内。我们引入辅助性能函数来构造障碍Lyapunov函数。该辅助性能信号在每个切换时刻都会重置，这可以防止由于错误指标在切换时刻的跳跃而导致的屏障越界。停留时间约束是根据用户定义的性能范围和辅助性能函数的参数得出的。我们还证明，即使在切换瞬间，Lyapunov函数也不会增加，因此不会施加额外的停留时间约束。此外，我们提出了针对不确定的分段仿射系统的自适应控制器的鲁棒修改，该系统具有不受匹配的干扰。数值例子验证了所提方法的正确性。