System identification, observer identification, and data-based controller design

Three basic aspects of modern control are the development of a state space model from data, the development of an observer based on the model and assumed or somehow separately measured plant and measurement noise levels, and the design of an optimal control law. Here we develop algorithms that relate each process more directly to data, and obtain substantially improved results. Regarding identification, in state space model identification a Hankel matrix is needed, which is usually constructed from Markov parameters obtained by some process from data. Here we directly identify the Hankel matrix from data. The resulting algorithm is shown to give significantly improved order determination, which simplifies the model identification process by eliminating the common need for a model reduction step. For observer design, a method of developing observers directly from data is presented, which benefits from the above improved order determination, and in addition eliminates the very troublesome assignment of plant and measurement noise covariances in a Kalman filter design. The data is used to directly determine the needed observer gain without the need to assign values for these covariances. In numerical examples, the performance of the identified estimator is shown to compare very favorably with that of a Kalman filter that knows exactly the true system model and the true measurement and plant noise statistics. Multi-step observers are also developed which are useful in predictive control. The design of a modern controller would normally require model identification, then estimator choice based on the model, and then optimal control design based on the model and using the estimator as part of the control process. Regarding controller design, the contributions in this thesis bypass this multistage process and directly produce the control gains directly from data. There is no need for a model and no need for an observer. The results are optimal predictive control laws. The benefits of each of these new algorithms are demonstrated on real data for the Hubble telescope, or a truss structure at NASA Langley Research Center, or in experiments run on a very flexible spine structure.