Consistency analysis of subspace identification methods based on a linear regression approach

In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict sufficient assumptions which however does not include important model structures such as, e.g. Box}Jenkins. Based on a simple least-squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions sufficient for consistency and which includes any model structure

Data-driven subspace-based model predictive control

The desire to develop control systems that can be rapidly deployed has resulted in the formulation of algorithms that combine system identification with the development of control technique resulting in a single-step implementation. One such algorithm is Subspace Model Predictive Control (SMPC), which is a combination of results from subspace methods in system identification and model predictive control. In this thesis, novel algorithms of SMPC are investigated and developed. More specifically, a data filtering procedure is proposed in the computation of subspace predictor coefficients, resulting in the suppression of non-stationary disturbance in the identification data and incorporation of integrator in the predictive control law. Computational advantages of parameterization of control input trajectory using Laguerre functions are demonstrated and extended to Multi-input and Multi-output (MIMO) systems. By manipulating the unique structure of subspace data matrices, an efficient recursive algorithm for the updating of subspace predictor coefficients is investigated. This efficient algorithm is then extended to SMPC for time-varying systems, with the proposal of a novel recursive control law. The advantage of this implementation is that recursive updating is only performed when there is plant-predictor mismatch, thus input and output signals need not be persistently exciting at all times. Consequently, unnecessary fluctuations of signals are avoided, resulting in a smoother steady-state response. Finally, an implementation of a variable forgetting factor was introduced in order to facilitate faster convergence. These innovative approaches result in more efficient and reliable SMPC algorithms, thus making this design methodology a promising choice for control system design and implementation. Experimental results obtained from Permanent Magnetic Synchronous Machine and DC motor are used to demonstrate the efficacy of the proposed approaches