Study On Least Square Support Vector Machine Algorithms And Predictive Control Algorithms

The control aspect of non-linear systems is one of the key and challenging issues in the area of control engineering due to the fact that appropriate model is difficult to be obtained in practice. Based on the theory of structural risk minimization, support vector machine (SVM) was proposed as a powerful tool to address the problems of non-linear classification and regression with satisfactory performance. The least squares support vector machine (LSSVM) was developed based on SVM to reduce the computation complexity through transforming inequalities constraints to equalities constraints. In addition, predictive control is an efficient control strategy and predictive functional control (PFC) is effective to make various control input parameters more regular. This dissertation aims to investigate the adoption of LSSVM and PFC control mechanisms along with a set of novel algorithms to address the control issue in non-linear systems. The key contributions of this work can be summarized as follows:1. Compared with SVM, LSSVM eliminates the sparseness property of the support vectors, and thus enables all the training samples to be the support vectors. To reduce the computation complexity, we proposed the approximation approach on all samples based on Lagrange factors cutting. As a result, the samples that contribute less to the model can be removed whilst keep other important samples to build the model. This can significantly reduce the number of support vectors and still maintain satisfactory performance with acceptable computation complexity.2. Super parameters are crucial to the performance of LSSVM and the low quality parameters can deteriorate the model and lead to errors. Thus, we proposed the alternative chaotic particle swarm optimization algorithm to cope with such issue. The particle swarm optimization and global arrival ability of chaos enables the suggested algorithm to fast converge and avoid the sub-optimality in the process of optimization.3. In our approach, we adopt LSSVM to obtain the model and use PFC to perform the control of the non-linear systems. Due to the fact that the system identification models are often with the non-linear and analytical nature, thus, this dissertation suggests the approach to obtain the predictive model by the use of linear approximation, and use novel incremental PFC to obtain the control inputs, which makes the control system inputs more regular, and hence to achieve unbiased control and rapid response.