A modified Riccati approach to analytic interpolation with applications to system identification and robust control

Multivariable analytic interpolation with complexity constraints: A modified Riccati approach

Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the scalar case. This turns out to be quite nontrivial, as it poses many new problems. A basic step in the procedure is to solve a Riccati type matrix equation. To this end, an algorithm based on homotopy continuation is provided.

The Covariance Extension Equation: A Riccati-type Approach to Analytic Interpolation

Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type equation. The rank of the solution matrix is the same as the degree of the interpolant, thus providing a natural approach to model reduction. A homotopy continuation method is presented and applied to some problems in modeling and robust control. We also address a question on the positive degree of a covariance sequence originally posed by Kalman.

Partial Realization Theory and System Identification Redux

Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that the nonstandard matrix Riccati equation is universal in the sense that it can be used to solve more general analytic interpolation problems by only changing certain parameters. Such interpolation problems are ubiquitous in systems and control. In this context we also discuss a question posed by R.E. Kalman in beginning of the 1970s.

基于解析插值的同时镇定问题通用解法

A general solution to the simultaneous stabilization problem by analytic interpolation

本文针对控制系统同时镇定难题，提出基于解析插值的通用解法，推导标量与多变量场景下的充要条件，结合协方差扩展方程实现解的参数化，通过数值算例验证了方法的高效可靠性。

一种基于插值的快速频域系统辨识方案

An Interpolation-based Scheme for Rapid Frequency-Domain System Identification

本研究提出一种基于重心插值与权重优化的频域系统辨识方案，采用自适应频率点选择与瞬态数据优化权重，构建凸优化问题可保证系统稳定性，能减少正弦测试次数，在高阶低阻尼结构系统上验证了有效性。

离散时间逆线性二次型调节器问题中代数Riccati方程的数据驱动估计

Data-driven Estimation of the Algebraic Riccati Equation for the Discrete-Time Inverse Linear Quadratic Regulator Problem

针对未知离散时间系统，提出直接从观测数据估计代数Riccati方程的方法，无需系统辨识，利用先验信息减少数据需求，并通过数值实验验证其高效性。