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Transient bounds for adaptive control systems

机译：自适应控制系统的瞬态界限

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摘要

Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. In this note, we consider how these theories may be applied to adaptive control to quantify transient response. This involves the explicit description of the constants appearing in the passivity theorem and/or the small gain theorem which characterize both system gains and initial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which connects initial state conditions with the input-output analysis. Applying these general theorems to adaptive control, we are able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response. The implication of these sufficient results is that without both bounds upon initial conditions and guarantees of excitation, potentially extreme transient excursions of system variables are possible even though global convergence and asymptotic performance are guaranteed.
机译：自适应控制系统本质上是非线性的，分析其稳定性和瞬态响应的机制通常来自更通用的非线性理论，例如小增益参数或无源性。在本说明中，我们考虑如何将这些理论应用于自适应控制以量化瞬态响应。这涉及对无源定理和/或小增益定理中出现的常数的明确描述，这些常数表征了系统增益和初始条件效应。结果是瞬态响应范围和统一的工厂可控性之间的基本联系，这将初始状态条件与投入产出分析联系起来。将这些一般性定理应用到自适应控制中，我们能够将统一的可控制性条件解释为激励要求的持续性，从而为瞬态响应提供局部边界。这些充分结果的含义是，即使在保证全局收敛和渐近性能的情况下，也没有初始条件的限制和激励的保证，系统变量的潜在极端瞬态偏移还是可能的。

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