A Novel Framework for System Identification, Simulation and Control

Abstract

This research is aimed at making contributions in three fundamental problems in systems and control. The problems are broadly known as system identification, optimal simulation and data-based control. The system identification problem involves the inverse problem of developing the dynamics model of a system from input/output experimental data. The system simulation problem pertains to the use of numerical simulations in predicting model response for a complex dynamical system, while the data-based control problem is aimed at deriving certain control inputs based on empirical response data to direct the system to elicit a desired response from it.

Q-Markov covariance equivalent realization (QMC) is a system identification approach that matches exactly the first q Markov parameters and covariance parameters of a system with a prespecified positive scalar q. Existing QMC methods possess two deficiencies. First, they are not applicable system identification of unstable systems. Second, they find infinite numbers of solutions and do not provide a means to choose the best solution. The first result of this research develops a new QMC formulation that extends the existing QMC methods for identification of unstable systems. This new QMC formulation is derived over closed-loop dynamics as an observer and does not pose any constraints on the stability of the system to identify. In addition, this research presents a methodology to determine an efficient QMC solution and a general algorithm for system identification applications using the QMC method.

When dynamic systems are simulated on the computer, the numerical values of the outputs and states are corrupted by round-off errors. The second set of results of this research aims at finding the simulation model that gives optimal performance under finite precision computing. This research provides two approaches to tackle this problem. The first approach formulates the problem into three linear matrix inequalities (LMIs) plus a non-convex constraint and transforms it into a feedback control problem. It becomes solvable numerically via the LMI toolbox after convexification and guarantees convergence to a local optimum. The second approach focuses on simulation applications of flexible structures in modal coordinates. It finds the simulation model with the optimal size via truncation of modes.

A data-based control law for reference tracking applications is developed as the third result of this research. This control law finds an optimal input sequence that minimizes a quadratic weighted cost function consisting of tracking errors and input increments. Its effectiveness is demonstrated using an application involving the morphing control of a tensegrity airfoil.