In this article a new algorithm for the design of stationary input sequences for system identification is presented. The stationary input signal is generated by optimizing an approximation of a scalar function of the information matrix, based on stationary input sequences generated from prime cycles, which describe the set of finite Markov chains of a given order. This method can be used for solving input design problems for nonlinear systems. In particular it can handle amplitude constraints on the input. Numerical examples show that the new algorithm is computationally attractive and that is consistent with previously reported results.Index Terms-System identification, input design, Markov chains.

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We study the problem of estimating the largest gain of an unknown linear and time-invariant filter, which is also known as the H∞ norm of the system. By using ideas from the stochastic multi-armed bandit framework, we present a new algorithm that sequentially designs an input signal in order to estimate this quantity by means of input-output data. The algorithm is shown empirically to beat an asymptotically optimal method, known as Thompson Sampling, in the sense of its cumulative regret function. Finally, for a general class of algorithms, a lower bound on the performance of finding the H∞ norm is derived.

Applications oriented input design for closed-loop system identification: a graph-theory approach.In Abstract-A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.

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