Nonlinear Hybrid Systems Identification using Kernel-Based Techniques
Abstract Hybrid systems can describe in an unified setting many processes which combine continuous/discrete dynamics and logic rules. Their identification from input/output data is however difficult since it requires to jointly solve a classification and estimation problem. Restricting the attention to piecewise linear models, recent research has shown how these difficulties can be successfully faced combining Gaussian regression and stochastic simulation techniques. In this paper we extend this approach to systems composed by nonlinear submodels. Numerical examples regarding estimation of discontinuous functions and identification of piecewise nonlinear dynamic systems are then included to illustrate the potential of the new approach.
This chapter is mainly devoted to practical applications. In particular we present an application concerning the facial expression of emotion along with a case study aimed at analyzing aortic valve morphology. We also introduce two innovative topics: biometric morphing and nonparametric iterated combination for paired data. In practice, the result of the application of the NPC tests described in the previous chapters depends also on the choice of the combining function. Every combining function has its own characteristics and can be preferable to others in specific situations. As a consequence, results may differ slightly depending on which combining function is used. Sometimes, especially with categorical variables, different combining functions may lead to different results in terms of statistical significance. To remove these differences and assess the useful properties of many different types of combinations, the iterated combining procedure can be applied.