A new kernel-based approach for overparameterized Hammerstein system identification

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$ coefficients of the nonlinearity together with the first $n$ samples of the impulse response of the linear system by estimating an $np$-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and $p$ coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201

Adaptive cancelation of self-generated sensory signals in a whisking robot

Sensory signals are often caused by one's own active movements. This raises a problem of discriminating between self-generated sensory signals and signals generated by the external world. Such discrimination is of general importance for robotic systems, where operational robustness is dependent on the correct interpretation of sensory signals. Here, we investigate this problem in the context of a whiskered robot. The whisker sensory signal comprises two components: one due to contact with an object (externally generated) and another due to active movement of the whisker (self-generated). We propose a solution to this discrimination problem based on adaptive noise cancelation, where the robot learns to predict the sensory consequences of its own movements using an adaptive filter. The filter inputs (copy of motor commands) are transformed by Laguerre functions instead of the often-used tapped-delay line, which reduces model order and, therefore, computational complexity. Results from a contact-detection task demonstrate that false positives are significantly reduced using the proposed scheme

About the maximum entropy principle in non equilibrium statistical mechanics

The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make predictions in physics and other disciplines, which constitutes an alternative and more general method than the traditional ones of statistical mechanics. Actually, careful inspection shows that such a success is due to a series of fortunate facts that characterize the physics of equilibrium systems, but which are absent in situations not described by Hamiltonian dynamics, or generically in nonequilibrium phenomena. Here we discuss several important examples in non equilibrium statistical mechanics, in which the MEP leads to incorrect predictions, proving that it does not have a predictive nature. We conclude that, in these paradigmatic examples, the "traditional" methods based on a detailed analysis of the relevant dynamics cannot be avoided

Multimodal person recognition for human-vehicle interaction

Next-generation vehicles will undoubtedly feature biometric person recognition as part of an effort to improve the driving experience. Today's technology prevents such systems from operating satisfactorily under adverse conditions. A proposed framework for achieving person recognition successfully combines different biometric modalities, borne out in two case studies

On Optimal Input Design for Feed-forward Control

This paper considers optimal input design when the intended use of the identified model is to construct a feed-forward controller based on measurable disturbances. The objective is to find a minimum power excitation signal to be used in system identification experiment, such that the corresponding model-based feed-forward controller guarantees, with a given probability, that the variance of the output signal is within given specifications. To start with, some low order model problems are analytically solved and fundamental properties of the optimal input signal solution are presented. The optimal input signal contains feed-forward control and depends of the noise model and transfer function of the system in a specific way. Next, we show how to apply the partial correlation approach to closed loop optimal experiment design to the general feed-forward problem. A framework for optimal input signal design for feed-forward control is presented and numerically evaluated on a temperature control problem