Online Identification of Nonlinear Stochastic Spatiotemporal System With Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method

In this paper, we propose a novel kernel method for the online identification of stochastic nonlinear spatiotemporal dynamical systems using the robust control approach. By the difference method, the stochastic spatiotemporal (SST) systems driven by multiplicative noise are first transformed into a class of multi-input-multi-output-partially linear kernel models (PLKMs) with heterogeneous random terms. With the help of techniques established for reproducing kernel Hilbert space, the online learning problem is reasonably considered as an output feedback control problem for a group of time varying linear dynamical systems. We develop an effective algorithm to address the learning problem of PLKM and SST systems by employing the model predictive control theory. Compared with the existing learning methods, the new one can achieve adaptive, robust, and fast convergent online modeling performance for the spatiotemporal dynamics with multiplicative noise, which greatly facilitates the characterization of physical characteristics of the system. Moreover, this investigation for the first time addresses the learning problems for SST systems with novel robust control techniques, which can provide some novel insights into the design of kernel machine learning methods from the perspective of optimal control theory. Numerical studies for benchmark systems are presented to illustrate the effectiveness and efficiency of our new method.

Identification of Nonlinear Spatiotemporal Dynamical Systems With Nonuniform Observations Using Reproducing-Kernel-Based Integral Least Square Regulation

The identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades. Several methods, such as searching principle-based algorithms, partially linear kernel methods, and coupled lattice methods, have been developed to address the identification problems. However, most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains. These are actually not applicable for some practical applications. In this paper, to tackle this issue, a novel kernel-based learning algorithm named integral least square regularization regression (ILSRR) is proposed, which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain. With this technique, a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified. Thereafter, with this novel inverse meshless collocation model, the ILSRR, and a multiple-kernel-based learning algorithm, a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations. Numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method.

Coevolutionary particle swarm optimization using AIS and its application in multiparameter estimation of PMSM

In this paper, a coevolutionary particle-swarmoptimization (PSO) algorithm associating with the artificial immune principle is proposed. In the proposed algorithm, the wholepopulation is divided into two kinds of subpopulations consisting of one elite subpopulation and several normal subpopulations. The best individual of each normal subpopulation will be memorized into the elite subpopulation during the evolution process. A hybrid method, which creates new individuals by using three different operators, is presented to ensure the diversity of all the subpopulations. Furthermore, a simple adaptive wavelet learning operator is utilized for accelerating the convergence speed of the pbest particles. The improved immune-clonal-selection operator is employed for optimizing the elite subpopulation, while the migration scheme is employed for the information exchange between elite subpopulation and normal subpopulations. The performance of the proposed algorithm is verified by testing on a suite of standard benchmark functions, which shows faster convergence and global search ability. Its performance is further evaluated by its application to multiparameter estimation of permanentmagnet synchronous machines, which shows that its performance significantly outperforms existing PSOs. The proposed algorithm can estimate the machine dq-axis inductances, stator winding resistance, and rotor flux linkage simultaneously.

Tracking time-varying causality and directionality of information flow using an error reduction ratio test with applications to electroencephalography data

This paper introduces an error reduction ratio-causality (ERR-causality) test that can be used to detect and track causal relationships between two signals. In comparison to the traditional Granger method, one significant advantage of the new ERR-causality test is that it can effectively detect the time-varying direction of linear or nonlinear causality between two signals without fitting a complete model. Another important advantage is that the ERR-causality test can detect both the direction of interactions and estimate the relative time shift between the two signals. Numerical examples are provided to illustrate the effectiveness of the new method together with the determination of the causality between electroencephalograph signals from different cortical sites for patients during an epileptic seizure.

Classifiability-based discriminatory projection pursuit

Fisher's linear discriminant (FLD) is one of the most widely used linear feature extraction method, especially in many visual computation tasks. Based on the analysis on several limitations of the traditional FLD, this paper attempts to propose a new computational paradigm for discriminative linear feature extraction, named "classifiability-based discriminatory projection pursuit" (CDPP), which is different from the traditional FLD and its variants. There are two steps in the proposed CDPP: one is the construction of a candidate projection set (CPS), and the other is the pursuit of discriminatory projections. Specifically, in the former step, candidate projections are generated by using the nearest between-class boundary samples, while the latter is efficiently achieved by classifiability-based AdaBoost learning from the CPS. We show that the new "projection pursuit" paradigm not only does not suffer from the limitations of the traditional FLD but also inherits good generalizability from the boundary attribute of candidate projections. Extensive experiments on both synthetic and real datasets validate the effectiveness of CDPP for discriminative linear feature extraction.

Online identification of nonlinear spatiotemporal systems using kernel learning approach

The identification of nonlinear spatiotemporal systems is of significance to engineering practice, since it can always provide useful insight into the underlying nonlinear mechanism and physical characteristics under study. In this paper, nonlinear spatiotemporal system models are transformed into a class of multi-input-multi-output (MIMO) partially linear systems (PLSs), and an effective online identification algorithm is therefore proposed by using a pruning error minimization principle and least square support vector machines. It is shown that many benchmark physical and engineering systems can be transformed into MIMO-PLSs which keep some important physical spatiotemporal relationships and are very helpful in the identification and analysis of the underlying system. Compared with several existing methods, the advantages of the proposed method are that it can make full use of some prior structural information about system physical models, can realize online estimation of the system dynamics, and achieve accurate characterization of some important nonlinear physical characteristics of the system. This would provide an important basis for state estimation, control, optimal analysis, and design of nonlinear distributed parameter systems. The proposed algorithm can also be applied to identification problems of stochastic spatiotemporal dynamical systems. Numeral examples and comparisons are given to demonstrate our results.

Identification of finite state automata with a class of recurrent neural networks

A class of recurrent neural networks is proposed and proven to be capable of identifying any discrete-time dynamical system. The application of the proposed network is addressed in the encoding, identification, and extraction of finite state automata (FSAs). Simulation results show that the identification of FSAs using the proposed network, trained by the hybrid greedy simulated annealing with a modified cost function in the training stage, generally exhibits better performance than the conventional identification procedures.