The Research On Online Modeling And Control Method Based On Least Squares Support Vector Machines

Some algorithms about least squares support vector machines(LSSVM) and applying methods for system online modeling and control based on LSSVM are studied in this dissertation.The main contents are outlined as follows:The existing LSSVM incremental and decremental learning algorithms by the formula of solving inversion of partitioned matrix are analyzed, and some speeding up implementing tactics are designed for the algorithms; consequently, a fast online LSSVM learning algorithm is obtained. The numerical simulation of multiple-input multiple-output(MIMO) system online modeling employing the fast online LSSVM shows these speedy tactics can heighten time performance of the existing LSSVM online learning algorithm; the tactics only require space of several additional buffer arrays.To reduce the computation amount of basic pruning algorithm(BPA) for LSSVM, a fast pruning algorithm(FPA) is proposed. The connection between two coefficient matrices of linear equations corresponding to LSSVM before pruning and to one after doing is analyzed, and the recursive relation between inversions of sub-matrices of the two coefficient matrices is derived by property of elementary matrix attained through swapping two columns or two rows that its inversion equalling to itself and by the calculation formula of solving inversion of partitioned matrix, therefore repeat calculation of inversion of higher order matrices is avoided in pruning process, and computation amount is decreased. FPA products the same resultant sparse LSSVM as BPA theoretically, when recursive calculating error is neglected. The numerical simulation results show the presented algorithm is quicker than BPA, and the more the training samples, the greater FPA’s speedup rate to BPA is.To reduce the computation time and storage space of online LSSVM with time window, an online sparse LSSVM with time window is proposed. It only takes samples ranking at partial moments among sliding time window as training samples set(TSS). The new sample is learned necessarily; when sample elimination is performed, if the sample ranking at the oldest moment among sliding time window exists in TSS, then it will be removed during decremental learning, otherwise, the sample with the smallest leave-one-out predicting error among TSS is selected and deleted. Compared with the existing online LSSVM, the presented online sparse LSSVM can learn more characteristic of system using less samples, and heighten time-space efficiency; compared with the existing online spare LSSVM, it can get rid of the obsolete sample, and adapt to time-variant properties of system better. The numerical simulation results for system modeling show the presented online sparse LSSVM can save time and space, provide accurate prediction.For non-bias LSSVM(NB-LSSVM), computing process to delete the least important sample or any one is given, and sparse online non-bias LSSVM (SONB-LSSVM) is designed. The skill for deleting sample can improve diversity and representative capacity of the training sample set. Compared with online non-bias LSSVM(ONB-LSSVM), SONB-LSSVM can study system properties in longer time horizon; generalization of SONB-LSSVM is less affected by the input signal frequency when it is employed for dynamic system online modeling.Aiming at the problem that predicting accuracy of LSSVM is influenced easily by gross errors and noises overriding on measure value of plant output when LSSVM applied to the dynamic process online modeling directly, a robust online process modeling method using NB-LSSVM is presented after characteristics of samples sequence structure and of noises action are analyzed. Abnormal measure data are recognized and eliminated, and measure data carrying noises are detected and rectified according to relation between predicting error and set threshold value during per predicting period, consequently less noises enter into samples, and obtained online LSSVM can track dynamics of process better. The modeling method is robust, can decrease effect of gross error and Gaussian white noise on LSSVM predicting accuracy and improve predicting accuracy. The numerical simulation shows the validity and advantage of the method.To tackle the difficulty in setting the kernel parameter and in adjusting it to varying process employing LSSVM to identify time-varying nonlinear process online, an online process identification approach based on LSSVM using regulated kernel parameter during different term is proposed in this paper. Three LSSVMs are utilized and the whole modeling predicting times is divided into starting stage and working periods, at the end of which the LSSVM with smallest sum of predicting error is selected as working LSSVM for successive working period, and kernel parameters are reset for other two LSSVM according to heuristic rules and they become comparative LSSVMs during the following working period. The method is easy to set kernel parameters and has adjustability to a certain extent. The numerical simulation shows the adaptability of the method is better than that of traditional method statistically.For the predictive control of nonlinear systems, a constrained single-step-ahead predictive control(PC) algorithm is proposed utilizing SONB-LSSVM. The presented control algorithm uses SONB-LSSVM to model online and to forecost the plant output value; the control values are obtained by the rolling optimization of particle swarm optimization(PSO) or Brent optimization. During starting stage of control, the control values are calculated through proportional-integral-derivative(PID) controller, and the plant input-output values are acquired to form samples and to train initial NB-LSSVM incrementally, which facilitates the usage of the presented PC. Because SONB-LSSVM can study new dynamic properties of process in time, the predictive control strategy possesses excellent adaptation. Simulation results of liquid-level process control, continuous stirred tank reactor(CSTR) concentration control and temperature control of water tank show the validity of the predictive control algorithm.The applications of SONB-LSSVM and ONB-LSSVM in nonlinear inverse control are investigated. An adaptive direct inverse control is proposed utilizing SONB-LSSVM. SONB-LSSVM is used to build the nonlinear inverse model for the controlled object and to compute control value during per control period. The approach is suit for time-invariant ivertible system and one with parameters(or properties) time-varying slightly. For the invertible system with parameters(or properties) time-varying in wide range, a composite control strategy combining ONB-LSSVM inverse model with PID control is designed. During per controlling period, control signal is compounded from inverse control value and PID control value, and compound ratio of them changes automatically. Inverse control plays more important role in high frequency range, and PID control does so in low frequency range. Consequently, the control approach possesses wide frequency adaptation range and good control performances to time-varying systems. In both methods the initial NB-LSSVM is trained online, which facilitates the usage of the proposals. Simulation results indicate the feasibility and validity of the control methods.