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Application of Set Membership Identification to Controller Design


M. Tanaskovic


The topic of this thesis is the application of set membership identification to controller design. Set membership identification is a method for building a mathematical model of a dynamic system from experimental data. Based on the initially available information on the plant that is being identified, the knowledge of a bound on the disturbance signal that affects the obtained measurements and the measurements themselves, it provides a set of all possible plant models that are consistent with the available data. The resulting uncertainty model obtained when set membership identification is used is deterministic in contrast to the probability density function which represents the identification uncertainty when probabilistic identification is used. The assumptions made by set membership identification are often less restrictive than the assumptions made by probabilistic identification. In addition, the deterministic uncertainty description can be very useful when used for robust controller design or in control design tasks in which constraint satisfaction is required. Furthermore, in direct controller design, where the controller is directly designed from experimental data, the deterministic uncertainty set obtained when the set membership identification is used can be exploited in order to provide stability and performance guarantees for the designed controller. However, set membership identification is less used in controller design compared to the probabilistic identification. The main reason for this lies in the fact that the set membership identification received less research attention than the probabilistic identification and is hence not so well known and understood by control engineers. Therefore, in order to enable greater exploitation of all the benefits that the use of set membership identification can bring to controller design, further research is required. As a contribution to these research efforts, three topics related to set membership identification and its application to controller design are considered in this thesis. The first contribution presents new theoretical results related to the worst-case identification experiment design in the set membership context for constrained linear systems with multiple inputs. The presented results can be seen as a generalization of the theory related to experiment design for set membership identification that already exists in the literature to the case of constrained systems with multiple inputs. Based on the presented theoretical derivations, a computationally tractable algorithm for experiment design that is based on convex optimization is proposed. This algorithm calculates the input sequence that is guaranteed to satisfy the input constraints and at the same time minimizes a measure of the worst-case identification uncertainty that can be obtained in any particular experiment. The effectiveness of the proposed approach is demonstrated by a numerical case study which shows that there are clear advantages of using the proposed scheme with respect to more traditional experiment design methods that are based on generating random signals. Therefore, the proposed methodology could be used to systematically design identification experiments that lead to small identification uncertainty when set membership identification is used and hence better performance of the controllers designed on the basis of such models. The second contribution is an adaptive model predictive control algorithm for constrained, multiple input, multiple output linear systems that is based on set membership identification. This algorithm relies on recursive set membership identification in order to update the set of all plant models that are consistent with initial assumptions on the system and available measurements at each time step. The controller then enforces the constraints for all the models in this set and hence also for the actual plant. %This algorithm is computationally efficient as it requires only the solution of linear and quadratic programs that are guaranteed to be recursively feasible. Furthermore, it exhibits integral action which allows offset free reference tracking. In addition to the base algorithm, several extensions that can be used in order to reduce computational complexity of the overall adaptive approach, introduce exploring property in order to facilitate faster identification and introduce forgetting of old information in order to apply the algorithm to time varying systems are presented. The proposed approach is experimentally tested on a quad-tank laboratory setup in various operating conditions which include a non-minimum phase behavior and the presence of non-negligible nonlinearity. In addition, the possibility for its use in building climate control is considered and illustrated by a simulation case study. Experiments and simulations show that, for the sake of constraint satisfaction, it is more beneficial to use the proposed adaptive scheme than to use a non-adaptive or a certainty equivalence adaptive model predictive control algorithm that uses least squares. The third contribution of the thesis is a novel on-line direct controller design method for nonlinear systems that uses set membership identification. The technique does not derive explicitly a model of the system, rather it delivers directly the feedback controller by combining an on-line and an off-line scheme. Like in other on-line algorithms, the measurements collected in closed-loop operation are exploited to modify the controller in order to improve the tracking performance over time. At the same time, a predictable closed-loop behavior is guaranteed by making use of a batch of available data, which is a characteristic of off-line algorithms. The feedback controller is parameterized with kernel functions and the design approach exploits results in set membership identification and learning by projections in order to provide guarantees on the stability and reference tracking performance of the designed controller. In addition to theoretical analysis of its properties, the tuning of the algorithm is discussed in detail and a method to adapt some of the tuning parameters on-line while retaining the stability guarantees is presented.


Type of Publication:

(03)Ph.D. Thesis

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2015:IFA_5369,
    author={M. Tanaskovic},
    title={{Application of Set Membership Identification to Controller
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