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首页> 外文期刊>IEEE Transactions on Industrial Electronics >A Min–Max Approach to Event- and Self-Triggered Sampling and Regulation of Linear Systems
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A Min–Max Approach to Event- and Self-Triggered Sampling and Regulation of Linear Systems

机译:线性系统的事件触发和自触发采样与调节的最小最大值方法

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摘要

This paper presents both an event-and a self-triggered sampling and regulation scheme for continuous time linear dynamic systems by using zero-sum game formulation. A novel performance index is defined wherein the control policy is treated as the first player and the threshold for control input error due to aperiodic dynamic feedback is treated as the second player. The optimal control policy and sampling intervals are generated using the saddle point or Nash equilibrium solution, which is obtained from the corresponding game algebraic Riccati equation. To determine the optimal event-based sampling scheme, an event-triggering condition is derived by utilizing the worst case control input error as the threshold. To avoid the additional hardware for the event-triggering mechanism, a near optimal self-triggering condition is derived to determine the future sampling instants given the current state vector. To guarantee Zeno-free behavior in both the event-and self-triggered closed-loop systems, the minimum intersample times are shown to be lower bounded by a nonzero positive number. Asymptotic stability of the closed-loop system is ensured using Lyapunov stability analysis. Finally, simulation examples are provided to substantiate the analytical claims.
机译:本文采用零和博弈公式给出了连续时间线性动力系统的事件和自触发采样与调节方案。定义了一种新颖的性能指标,其中将控制策略视为第一玩家,并将因非周期性动态反馈导致的控制输入错误的阈值视为第二玩家。最优控制策略和采样间隔是使用鞍点或纳什均衡解决方案生成的,该解决方案是从相应的博弈代数Riccati方程获得的。为了确定最佳的基于事件的采样方案,通过利用最坏情况的控制输入错误作为阈值来推导事件触发条件。为了避免事件触发机制使用额外的硬件,在给定当前状态向量的情况下,得出了接近最佳的自触发条件,以确定未来的采样时刻。为了在事件和自触发的闭环系统中都保证没有零基的行为,最小的采样间时间显示为下限为非零正数。使用Lyapunov稳定性分析可确保闭环系统的渐近稳定性。最后,提供了仿真示例以证实分析要求。

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