Long-time average cost control of stochastic systems using sum of squares of polynomials
Long-time average cost control of stochastic systems using sum of squares of polynomials
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DOI：
10.1109/chicc.2015.7260000
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发表时间：
2015-07
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
针对一类确定性动力部分为多项式型的非线性随机系统，提出了一种计算上具有吸引力的长期平均成本控制方法。而不是最小化时间平均成本本身，我们使用它的上界作为控制器设计的目标函数。因此，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来解决优化的固有非凸性，该结构实际上是一个小参数的级数，所有系数都是系统状态的有限阶多项式。通过随机噪声持续扰动下的简单圆柱流模型仿真，验证了所提控制器的有效性。
This paper presents a computationally attractive long-time average cost control approach for a class of nonlinear stochastic systems, where the deterministic dynamical part is of polynomial type. Instead of minimizing the time-averaged cost itself, we use its upper bound as the objective function for controller design. As such, 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 optimisation is resolved 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 system state. The effectiveness of the proposed controller is demonstrated by means of simulation of a simple cylinder flow model under persistent perturbation of random noise.