基于均方小增益定理的随机时滞飞控系统稳定与镇定研究

Stochastic delay is a prevailing scene in engineered systems. Except on rare instances, stochastic delays are likely to bring great difficulties to the stability and stabilization of control systems. Systems with stochastic delay, however, is intricate to analysis by nature because of the complex uncertainty of stochastic systems. Consequently, results on the stability and stabilization of linear systems with stochastic delays are limited. The existing results are predominantly time-domain conditions, obtained by the construction of Lyapunov functionals and as the solutions to large-scale linear matrix inequality problems. Considering the degraded performance, reduced robustness and instability in flight control systems with stochastic delays, the project builds up a symmetric analysis model for linear systems with stochastic delays. This project seeks to answer the fundamental question: What is the largest range of delays such that there exists a feedback controller that can stabilize all the plants subject to a stochastic delay within the range? Upon that, the project measures the performances and limitations based on mean-square small-gain theorem for systems with both input and state stochastic delays, given the existence of input saturation, parametric uncertainty and random noises. The project proposes a multiple -constraints based optimization control mechanism. The project aims to develop new theories, new approaches, and new control schemes on systems with stochastic delays, and provide theoretical supports for flight control applications. In one word, the project is of great theoretical and practical value.

随机时滞在工程应用中广泛存在，为控制系统的稳定与镇定带来很大困难。由于随机时滞的复杂不确定性，分析难度大，既有成果十分有限。当前研究大多基于Lyapunov函数，将稳定性问题转为大规模线性矩阵不等式的可实现问题。本项目着眼随机时滞在飞控应用中引起的性能降低、鲁棒性减少、失稳等实际问题，以飞控系统为研究对象展开建模、分析与控制研究。本项目欲探究的的本质性意义问题是：针对具有随机时滞和多重复杂约束的飞行控制系统，存在反馈控制器使得在整个时滞范围内系统都可被镇定的最大时滞范围为多少？基于此，本项目通过构建均方小增益定理分析模型，探究输入饱和、参数不确定和随机扰动等因素对控制性能的影响，提出基于多指标约束的优化控制方法。本项目期望从基础理论、研究方法和调控方法上有所创新和突破，为解决飞行控制中的实际问题提供必要的理论支撑，具有重要的理论价值和现实意义。

时滞现象在工业生产、航空航天等实际应用中广泛存在，为控制系统的稳定、镇定与性能实现带来很大困难。由于时滞，尤其是时变时滞的复杂性与不确定性，时滞系统稳定性与性能分析难度大，既有成果十分有限。本项目聚焦时滞在飞控应用中引起的性能降低、鲁棒性减少、失稳等实际问题，针对具有随机时滞、时变时滞、输入饱和等多重复杂约束的飞行控制系统，从鲁棒控制的角度展开分析，探究输入饱和、参数不确定和随机扰动等因素对控制性能的影响，构建基于小增益定理和自适应动态规划的时滞系统稳定性分析模型和最优控制模型，提出基于多指标约束的优化控制方法。此外，本项目亦构建了基于主成分分析和深度置信网络的轴承系统智能故障诊断方案，相关故障诊断成果可以进一步推广到分布式控制系统、多飞行器控制系统、无人机编队协同控制系统、近空间飞行器系统等工程与航天应用中，具有重要的理论与应用价值。