Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.

Online Sequential Fuzzy Extreme Learning Machine for Function Approximation and Classification Problems

Abstract: In this correspondence, an online sequential fuzzy extreme learning machine (OS-fuzzy-ELM) has been developed for function approximation and classification problems. The equivalence of a Takagi-Sugeno-Kang (TSK) fuzzy inference system (FIS) to a generalized single hidden-layer feedforward network is shown first, which is then used to develop the OS-fuzzy-ELM algorithm. This results in a FIS that can handle any bounded nonconstant piecewise continuous membership function. Furthermore, the learning in OS-fuzzy-ELM can be done with the input data coming in a one-by-one mode or a chunk-by-chunk (a block of data) mode with fixed or varying chunk size. In OS-fuzzy-ELM, all the antecedent parameters of membership functions are randomly assigned first, and then, the corresponding consequent parameters are determined analytically. Performance comparisons of OS-fuzzy-ELM with other existing algorithms are presented using real-world benchmark problems in the areas of nonlinear system identification, regression, and classification. The results show that the proposed OS-fuzzy-ELM produces similar or better accuracies with at least an order-of-magnitude reduction in the training time.

Robust Stability and Stabilization of Linear Switched Systems With Dwell Time

Abstract: Sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, which is non-increasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs. It becomes time invariant afterwards. This function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties. The method proposed is then applied to stabilization via state-feedback both for the nominal and the uncertain cases.

Multiple Change-Point Estimation With a Total Variation Penalty

Abstract: We propose a new approach for dealing with the estimation of the location of change-points in one-dimensional piecewise constant signals observed in white noise. Our approach consists in reframing this task in a variable selection context. We use a penalized least-square criterion with a l1-type penalty for this purpose. We explain how to implement this method in practice by using the LARS / LASSO algorithm. We then prove that, in an appropriate asymptotic framework, this method provides consistent estimators of the change points with an almost optimal rate. We finally provide an improved practical version of this method by combining it with a reduced version of the dynamic programming algorithm and we successfully compare it with classical methods.