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Center for Nonlinear Studies |
System identification can be viewed as the search (typically by means of an optimization process) for simple equations explaining accurately the observed input-output behavior of a dynamical system. As a rule, achieving high fidelity with a low complexity model requires simultaneous optimization of its forward and feedback loops (in the case of a linear system, this would mean simultaneous optimization of both numerator and denominator of the transfer function). A major challenge in system identification is to incorporate a measure of stability (robustness) of the feedback loop into an overall data matching criterion, without making the resulting optimization problem intractable.
This talk describes the use of dissipation inequalities and convex relaxations in a nonlinear system identification framework which ensures proper (if somewhat conservative) accounting for robustness. Generalized passive models form a set which is both convex and universal (capable of approximating arbitrary stable causal dependencies). The convexity enables the use of semi-definite programming in the derivation of the identified model. Implementation examples and a discussion of alternatives will be given.
Host: Frank Alexander