Recursive Subspace Identification with Predictive Control

a Nuclear Norm approach

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The main contribution of this thesis is the development of an inherently adaptive controller which recursively implements a system identification and control routine. The main idea here, is that if system identification techniques can be made computationally light, and if they can be combined efficiently with a controller formulation, such a framework can be implemented on real world systems to achieve the adaptive nature in control. In the first part of the thesis, we focus on developing a computationally less expensive identification technique, by making various modifications on the N2SID algorithm, a nuclear norm subspace identification method. By allowing for early stopping of the ADMM algorithm (which plays a crucial role in N2SID) and by implementing an efficient alternative to Singular Value Thresholding, we are able to obtain significant reductions in computation time. Furthermore, we allow for a recursive implementation of N2SID by utilizing system information from the previous identification cycle. This results in a significant improvement of the convergence speed of the identification. In order to create an efficient interface between the identification technique and the controller, we formulate an MPC control framework, which does not require the explicit computation of the system matrices at each identification cycle. This helps in reducing the computation time of the recursive algorithm. The overall methodology is such that an inherently adaptive controller is in play at every time instant. To test this algorithm, we implement it on different systems, including LTI and LPV systems.