|BIANCHI FEDERICO||Cycle: XXXII |
Section: Systems and Control
Tutor: GARATTI SIMONE
Advisor: PIRODDI LUIGI Major Research topic
:A randomized model structure selector for complex dynamical systemsAbstract:
In this thesis, the identification from experimental data of dynamical systems is considered with focus on parametric methods. In the parametric case, when the model structure is known, the identification problem consists essentially in estimating a finite number of unknown parameters. If, on the other hand, the model structure is unknown, one has also to carry out the task of model structure selection (MSS). The aim of MSS is to find the form of the dependence between data, within a family of functions which is usually parameterized by means of a finite-dimensional parameter vector. This is a combinatorial problem which consists in selecting, among all the model terms that could be included into the model, only those providing good accuracy in approximating the system behavior but at the same time preserving model parsimony. Ultimately, MSS is the most difficult problem in identifying the model in view of its combinatorial nature, and hence it has aroused great interest in the scientific community. Most of the proposed model selection algorithms consist of a policy to explore the model structure space and compare different model structures in terms of their performance. Several approaches have been proposed, ranging from greedy incremental strategies and evolutionary algorithms, to randomized techniques based on probabilistic reformulations of the selection problem. The last class is the one that is pursued in this thesis, where the problem of MSS is investigated with respect to the identification of nonlinear systems via distributed computation and the identification of hybrid (nonlinear) systems.
- The problem of identifying a model of a nonlinear system from input/output observations is typically formulated as an optimization problem over all available data that are collected by a central unit, in the same operating conditions. However, the massive diffusion of networked systems is changing this paradigm: data are collected separately by multiple agents and cannot be made available to some central unit due to, e.g., privacy constraints. Therefore, we address this novel set-up and consider the case in which multiple agents are cooperatively aiming at identifying a model for a system, by local computations based on private data sets. This problem is particularly challenging because the combinatorial nature of the problem of identifying the structure hampers the application of classical distributed schemes. In this thesis, we propose a method that overcomes this limit by adopting a probabilistic reformulation of the model structure selection problem and seeking for the consensus among agents on both the model structure and the parameter estimates.
- Hybrid dynamical systems (HSs) whose behavior can be described by the interaction of time- and event-driven dynamics, provide a unified framework for the representation of many physical processes whose behavior is characterized by different continuous dynamics (modes) among which the system can switch. Many control systems can also be considered as switching systems, such as thermal process where a thermostat controlling the temperature switches heating or cooling choices on or off. Also in technological systems, such as robotic system or component mounter continuous dynamics, representing the behavior of the physical and mechanical part, interact with discrete dynamics, representing the software and logical behavior. In such cases, a single dynamical model, not even a nonlinear one, is often not suitable to capture the real dynamics of the system. The optimization problem induced by the identification task is of a mixed-integer type, since it involves the identification of discrete variables (representing the mapping of the samples to the modes and the model structure associated to each mode), as well as continuous ones (the parameters of the models describing the continuous dynamics associated to the various system conditions). Many approaches have been proposed over the last two decades for the case of affine dynamics. Surprisingly fewer works have tackled the case of nonlinear continuous dynamics associated to the modes, in spite of its importance in modeling complex applications. In this thesis, we consider the identification of switched nonlinear systems in input-output form, namely Switched Nonlinear ARX (SNARX), in the case of unknown model structures. We propose a black-box iterative identification method.