Expensive Control of Long-Time Averages Using Sum of Squares and Its Application to A Laminar Wake Flow
Expensive Control of Long-Time Averages Using Sum of Squares and Its Application to A Laminar Wake Flow
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使用平方和对长时间平均值的昂贵控制及其在层流尾流中的应用
DOI：
10.1109/tcst.2016.2638881
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发表时间：
2016-02
影响因子：
4.8
通讯作者：
Tutty Owen
中科院分区：
文献类型：
--
作者：
Huang Deqing;Jin Bo;Lasagna Davide;Chernyshenko Sergei;Tutty Owen
本文提出了一种非线性状态反馈控制设计方法，用于长时间的平均成本控制，其中控制努力被假定为昂贵的。该方法是基于平方和和半定规划技术。它适用于其右手边的状态变量和控制是一个多项式函数的动力系统。Chernyshenko等人首先描述但未实现的关键思想，优化涉及长时间平均值的成本函数的困难问题被相同平均值的上限的优化所取代。因此，控制器设计需要同时优化控制律和可调函数，类似于李雅普诺夫函数。本文介绍了一种解决这类优化问题的方法。该方法是基于正式的假设，控制是昂贵的，从它遵循的最优控制是小的。由此产生的渐近优化问题是凸的。根据状态相关线性不等式和双线性不等式的可解性条件，导出了控制器中所有多项式系数的表达式。所提出的方法被施加到设计一个全信息反馈控制器，通过旋转振荡，减轻在层流状态下的圆柱体的尾涡脱落的问题。报告了驱动尾流降阶模型和直接数值模拟的控制结果。
This paper presents a nonlinear state-feedback control design approach for long-time average cost control, where the control effort is assumed to be expensive. The approach is based on sum-of-squares and semidefinite programming techniques. It is applicable to dynamical systems whose right-hand side is a polynomial function in the state variables and the controls. The key idea, first described but not implemented by Chernyshenko et al., is that the difficult problem of optimizing a cost function involving long-time averages is replaced by an optimization of the upper bound of the same average. As such, a controller design requires the simultaneous optimization of both the control law and a tunable function, similar to a Lyapunov function. This paper introduces a method resolving the well-known inherent nonconvexity of this kind of optimization. The method is based on the formal assumption that the control is expensive, from which it follows that the optimal control is small. The resulting asymptotic optimization problems are convex. The derivation of all the polynomial coefficients in the controller is given in terms of the solvability conditions of state-dependent linear and bilinear inequalities. The proposed approach is applied to the problem of designing a full-information feedback controller that mitigates vortex shedding in the wake of a circular cylinder in the laminar regime via rotary oscillations. Control results on a reduced-order model of the actuated wake and in direct numerical simulation are reported.
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影响因子：
7.7
作者：
Jian-xin Xu;Zhao-Qin Guo;Tong-heng Lee
通讯作者：
Jian-xin Xu;Zhao-Qin Guo;Tong-heng Lee
影响因子：
27.7
作者：
John Kim;T. Bewley
通讯作者：
John Kim;T. Bewley
DOI：
10.1007/bf00046603
发表时间：
1983-09
期刊：
Acta Applicandae Mathematica
影响因子：
--
作者：
M. Robin
通讯作者：
M. Robin
DOI：
10.1007/978-1-4613-0265-0_27
发表时间：
2002
期刊：
--
影响因子：
--
作者：
M. Mendiondo;R. Stockbridge
通讯作者：
M. Mendiondo;R. Stockbridge
影响因子：
3.9
作者：
Dan Zhao;Jianliang Wang
通讯作者：
Dan Zhao;Jianliang Wang