Backstepping PDE design, Volterra and Fredholm operators: A convex optimization approach
Backstepping PDE design, Volterra and Fredholm operators: A convex optimization approach
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反推偏微分方程设计、Volterra 和 Fredholm 算子：凸优化方法
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
T. Parisini
中科院分区：
文献类型：
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作者：
Pedro Ascencio;A. Astolfi;T. Parisini
本文将边界偏微分方程控制器/观测器的反推设计问题转化为凸优化问题。对一类抛物型和双曲型偏微分方程，分析了沃尔泰拉和Fredholm算子.由此产生的核偏微分方程的多项式函数，其中的参数进行了优化，使用平方和（SOS）技术，并通过半定规划求解。本文证明了实解析函数空间中多项式核的Fredholm型变换的唯一性和可逆性。逆核近似为SOS和矩问题的最优解。数值仿真结果表明了该方法的有效性。
This paper deals with backstepping design for boundary PDE control/observer as a convex optimization problem. Both Volterra and Fredholm operators are analysed for a class of parabolic and hyperbolic PDEs. The resulting Kernel-PDEs are formulated in terms of polynomial functions, the parameters of which are optimized using Sum-of-Squares (SOS) techniques and solved via semidefinite programming. Uniqueness and invertibility of the Fredholm-type transformation are proven for polynomial Kernels in the space of real-analytic functions. The inverse kernels are approximated as the optimal solution of a SOS and moment problem. The effectiveness of this approach is illustrated by numerical simulations.