AI 中文总结
研究调制函数方法这一代数框架，通过引入对偶调制函数等，表明其不仅是估计框架，也是LTV系统控制器设计框架，给出控制律存在条件并提出新固定时间控制律。
AI 中文摘要
调制函数方法是一种代数框架，用于线性、分数阶、分布式及一些非线性系统的状态和参数估计以及故障检测。本文通过引入对偶调制函数和对偶调制，表明该框架不仅是估计框架，也是LTV系统的控制器设计框架，给出相关控制律存在的充要条件，提出新的固定时间控制律并进行数值模拟。
英文摘要
The modulating function method is an algebraic framework that, thus far, has been used for state and parameter estimation, as well as fault detection, of linear, fractional-order, distributed, and some nonlinear systems. At the core of the method lies the modulating function, which can either be selected directly or be obtained as a solution to an auxiliary system. By introducing the notion of dual modulating functions and dual modulations using auxiliary systems and duality, this paper shows that this framework is not only an estimation framework, but also a controller design framework for LTV systems. In particular, necessary and sufficient conditions for the existence of the associated control laws are introduced; the well-known state feedback law is obtained as a particular case of the dual modulation approach, along with output feedback, LTI sliding mode control, the reachability gramian, and the state-transition matrix; and a new fixed-time control law is proposed for both LTI and LTV systems, including an estimate of the transient behavior. Moreover, numerical simulations of the newly proposed control law are performed, indicating similar performance levels to a benchmark LQR even when handling unmatched disturbances.
Comments16 pages, 8 figures
