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Multiple Model Adaptive Control With Mixing

机译：混合多模型自适应控制

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摘要

Despite the remarkable theoretical accomplishments and successful applications of adaptive control, the field is not sufficiently mature to solve challenging control problems where strict performance and robustness guarantees are required. Critical to the design of practical control systems for these challenging applications, and currently lacking in parameter estimation-based adaptive control schemes, is an approach that explicitly accounts for robust-performance and stability specifications. Towards this goal, this paper describes a robust adaptive control approach called adaptive mixing control that makes available the full suite of powerful design tools from LTI theory, e.g., mixed-$mu$ synthesis. The stability and robustness properties of adaptive mixing control are analyzed. It is shown that the mean-square regulation error is of the order of the modeling error provided the unmodeled dynamics satisfy a norm-bound condition. And when the parameter estimate converges to its true value, which is guaranteed if a persistence of excitation condition is satisfied, the adaptive closed-loop system converges exponentially fast to a closed-loop system comprising the plant and some LTI controller that satisfies the control objective. A benchmark example is presented, which is used to compare the adaptive mixing controller with other adaptive schemes.
机译：尽管自适应控制取得了卓越的理论成就和成功的应用，但该领域还不够成熟，无法解决需要严格的性能和鲁棒性保证的挑战性控制问题。对于这些具有挑战性的应用，实际控制系统的设计至关重要，而目前尚缺乏基于参数估计的自适应控制方案，该方法明确考虑了鲁棒性能和稳定性指标。为了实现这一目标，本文介绍了一种鲁棒的自适应控制方法，称为自适应混合控制，该方法可利用LTI理论提供全套功能强大的设计工具，例如，混合混合。分析了自适应混合控制的稳定性和鲁棒性。结果表明，如果未建模的动力学满足范数约束条件，则均方根调节误差约为建模误差。当参数估计值收敛到其真实值时（如果满足激励条件的持久性则可以保证），自适应闭环系统将指数级收敛到一个闭环系统，该闭环系统包括设备和一些满足控制目标的LTI控制器。给出了基准示例，该基准示例用于将自适应混合控制器与其他自适应方案进行比较。

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