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A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimization to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimization to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor. 

It is well known that text-based passwords are hard to remember and that users prefer simple (and non-secure) passwords. However, despite extensive research on the topic, no principled account exists for explaining when a password will be forgotten. This paper contributes new data and a set of analyses building on the ecological theory of memory and forgetting. We propose that human memory naturally adapts according to an estimate of how often a password will be needed, such that often used, important passwords are less likely to be forgotten. We derive models for login duration and odds of recall as a function of rate of use and number of uses thus far. The models achieved a root-mean-square error (RMSE) of 1.8 seconds for login duration and 0.09 for recall odds for data collected in a month-long field experiment where frequency of password use was controlled. The theory and data shed new light on password management, account usage, password security and memorability.