Stable Linear System Identification with Prior Knowledge by Elastic Riemannian Sequential Quadratic Optimization
Stable Linear System Identification with Prior Knowledge by Elastic Riemannian Sequential Quadratic Optimization
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发表时间：
2021
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通讯作者：
Mitsuaki Obara;Member Ieee Kazuhiro Sato;Takayuki Okuno;Akiko Takeda
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作者：
Mitsuaki Obara;Member Ieee Kazuhiro Sato;Takayuki Okuno;Akiko Takeda
- 我们考虑一种根据有噪状态观测识别线性连续时不变自治系统的方法。特别地，我们着重于在某些先验知识下满足系统渐近稳定性的识别。为此，我们首先以黎曼非线性优化（RNLO）问题的形式提出了新的建模。我们通过使用黎曼流形来确保稳定性，并额外考虑非线性约束的识别艾德系统，以满足先验知识。为了解决这个问题，我们提出了一个弹性黎曼序列二次优化（eRSQO）方法。eRSQO是Obara，Okuno和Takeda（2020）提出的RSQO的改进，关于子问题的可行性以获得搜索方向;如果算法检测到不可行性，eRSQO解决替代子问题，该子问题总是有一个可行点，并计算搜索方向。在比RSQO更弱的假设下证明了eRSQO的全局收敛性。最后，我们通过数值实验证明了所提出的RNLO建模和eRSQO方法的有效性。
—We consider an identification method for a linear continuous time-invariant autonomous system from noisy state observations. In particular, we focus on the identification to satisfy the asymptotic stability of the sys-tem with some prior knowledge. To this end, we first pro-pose novel modeling in the form of a Riemannian nonlinear optimization (RNLO) problem. We ensure the stability by using a Riemannian manifold and additionally consider nonlinear constraints for the identified system to meet the prior knowledge. To solve the problem, we propose an elastic Riemannian sequential quadratic optimization (eRSQO) method. eRSQO is an improvement of RSQO proposed by Obara, Okuno, and Takeda (2020) with respect to the feasibility of subproblems to obtain a search direction; if the algorithm detects the infeasibility, eRSQO solves an alternative subproblem, which always has a feasible point, and computes a search direction. We prove the global convergence property of eRSQO under weaker assumptions than RSQO. Finally, we demonstrate the effectiveness of the proposed RNLO modeling and eRSQO method through numerical experiments.