论文标题
通过凸优化的随机非线性系统的强大控制器设计
Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization
论文作者
论文摘要
本文介绍了基于凸优化的随机稳态跟踪误差最小化（CV-STEM），这是一类ITO随机非线性系统和拉格朗日系统的新状态反馈控制框架。它的创新在于通过最佳收缩度量计算控制输入，该指标贪婪地最大程度地减少了系统轨迹的稳态平方跟踪误差的上限。尽管最小化结合的问题是非凸，但它使用非线性系统方程的状态依赖性系数参数化提出了同等的凸公式。使用随机增量收缩分析显示，CV-STEM提供了足够的保证，可以通过L2-bobustness属性来实现误差的指数界限。为了基于抽样的实施，我们就状态和时间依赖性度量及其与连续时间案例的明确连接介绍了离散时间随机收缩分析。我们验证了CV-STEM对PID，H-含量和基线非线性控制器的优越性，以控制航天器态度控制和同步问题。
This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is non-convex, its equivalent convex formulation is proposed utilizing state-dependent coefficient parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L2-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H-infinity, and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.
