Low-order state-feedback controller design for long-time average cost control of fluid flow systems: A sum-of-squares approach
Low-order state-feedback controller design for long-time average cost control of fluid flow systems: A sum-of-squares approach
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DOI：
10.1109/chicc.2015.7260020
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发表时间：
2015-09
期刊：
影响因子：
--
通讯作者：
Deqing Huang;Chernyshenko Sergei
中科院分区：
文献类型：
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作者：
Deqing Huang;Chernyshenko Sergei
提出了一种新的状态反馈控制器设计方法，用于流体流动的长时间平均成本控制。由于流体动力系统的高维性，直接设计控制器会导致高阶状态反馈，这在实际应用中可能不适用。为了解决这个问题，首先将原始系统转换为降阶不确定系统，其中对所涉及的不确定性进行多项式界的解析计算。同时，我们不是将时间平均代价本身最小化，而是将其上界作为控制器设计的目标函数。然后，在基于平方和优化的框架下，同时优化控制律和类似Lyapunov函数的可调函数。通过假设控制器采用小反馈结构，克服了优化的固有非凸性，该结构实际上是一个小参数的级数，所有系数都是降阶系统状态的有限阶多项式。该诱导控制器的主要特点是具有低阶结构和鲁棒性。
This paper presents a novel state-feedback controller design approach for long-time average cost control of fluid flows. Due to the high dimensionality of fluid dynamical system, direct controller design renders to high-order state feedback that might not be applicable in practice. To resolve this, the original system is first transformed into a reduced-order uncertain system, where polynomial bounds for the involved uncertainties are evaluated analytically. Meanwhile, instead of minimizing the time-averaged cost itself, we use its upper bound as the objective function for controller design. Then, under the framework of sum-of-squares-based optimization, the control law and a tunable function similar to the Lyapunov function are optimized simultaneously. The inherent non-convexity of the optimization is overcome by assuming that the controller takes a small-feedback structure, which actually is a series in a small parameter with all the coefficients being finite-order polynomials of the reduced-order system state. The main characteristics of the induced controller lie in its low-order structure and robustness.