SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1122-1151, April 2024.
Abstract. Currently, output-feedback control still necessitates severe constraints on systems, e.g., system nonlinearities cannot exceed certain degree and uncertainties should belong to specific types. In this paper, by exploiting dynamic-compensation mechanisms, we essentially extend system nonlinearities and uncertainties. Specifically, the nonlinearities heavily rely on unmeasured states and particularly have unknown arbitrary function-of-output growth rates. Unknown control coefficients whether with known or unknown bounds are admitted, which have been excluded before in the context of such inclusive nonlinearities. The key to our novel solution lies in realizing the potential of filter-based observers, dynamic high gains, design/analysis parameter designation, and composite Lyapunov functions. In detail, two dynamic-high-gain filters are worked out to provide available states for controller design. The filter states, after weighted by the unknown control coefficient, also make up the estimated states which lead to control-free and tractable error dynamics. Two dynamic high gains with new dynamics are put forward to counteract the nonlinearities and uncertainties and, meanwhile, to enable the adaptive controller to own a concise structure. During the controller design, crucial design parameters can no longer be expressed explicitly due to unknown control coefficients, but rather need to be pursued through a recursive algorithm. With a set of analysis parameters, important (dynamic-high-gain) input-to-state stable properties of some vital variables are uncovered, and exhaustive Lyapunov analysis is performed for the closed-loop boundedness and convergence.

中文翻译：

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利用高增益动态补偿机制进行全局输出反馈控制

SIAM 控制与优化杂志，第 62 卷，第 2 期，第 1122-1151 页，2024 年 4 月。
摘要。目前，输出反馈控制仍然需要对系统进行严格的约束，例如系统非线性不能超过一定程度，不确定性应属于特定类型。在本文中，通过利用动态补偿机制，我们本质上扩展了系统的非线性和不确定性。具体来说，非线性严重依赖于未测量的状态，特别是具有未知的任意产出增长率函数。无论边界已知还是未知，未知的控制系数都被允许，这些系数之前在这种包容性非线性的背景下已被排除。我们新颖解决方案的关键在于实现基于滤波器的观测器、动态高增益、设计/分析参数指定和复合李亚普诺夫函数的潜力。具体来说，设计了两个动态高增益滤波器，为控制器设计提供可用状态。滤波器状态经过未知控制系数加权后，也构成了估计状态，从而导致无控制且易于处理的误差动态。提出了两种新动态的动态高增益来抵消非线性和不确定性，同时使自适应控制器具有简洁的结构。在控制器设计过程中，由于控制系数未知，关键设计参数不再能够明确表达，而是需要通过递归算法来求解。通过一组分析参数，揭示了一些重要变量的重要（动态高增益）输入状态稳定属性，并对闭环有界性和收敛性进行了详尽的李亚普诺夫分析。