Data-based Approximation And Optimal Tracking Control Of Nonlinear Systems

Due to the strong nonlinearity and complexity of industrial process, the researchon optimal tracking control of nonlinear system has always been a hot topic in thecontrol field. This paper uses the idea of viewing the problem from data in Big DataTime, starts with researching the classic data-driven control methods, proposing acreative approach to solve the approximation and optimal tracking control of a classof nonlinear system. This original method adopts the least square support vectormachines(LS-SVMs) which is the specialty of support vector machines(SVMs) toaccomplish our research work.This paper employs the LS-SVMs to solve the approximation of the affinenonlinear systems with partially unknown functions through a set of measured datapoints. Firstly, the known part of the affine nonlinear systems is mapped into highdimensional feature spaces and can be expressed as some linear equations with squarematrices coefficient; meanwhile, the system approximate solution in LS-SVMs formis given. Via the system transformation, the original problem is formulated as anoptimization problem using kernel trick with LS-SVMs and we can obtain thecontinuous and differential approximate solution. Furthermore, after solving theoptimization problem, the unknown part can be identified by its relationship to theknown part and the approximate solution of affine nonlinear systems.Moreover, this paper researches the data-based approach to optimal trackingcontrol of a class of nonlinear systems using LS-SVMs. Two LS-SVMs are used asparametric structures to implement the optimal tracking data-driven control scheme,which aim at figuring out the optimal tracking trajectory and then obtaining theoptimal tracking controller with a set of discrete points. This approach can obtainexplicit and continuous optimal tracking controller through a set of discrete desiredtrajectory data points. Specifically, in order to make sure that the tracking trajectoryoscillates mildly, we introduce a weight function between the complexities ofLS-SVMs and tracking errors in the framework of the first LS-SVMs.In Big Data Time, we have researched the approximate solution and optimaltracking data-driven control of a class of nonlinear systems from the angle of data.This paper has proposed the creative method of solving the problem using LS-SVMs. Based on this, we try to construct the new data-driven control theory using themachine learning.