Data-driven Iterative Optimal Control And Application

With the rapid development of modern industries, computer technology are becoming increasingly powerful and degree of automation increase gradually, optimization of industrial process control are received more and more attention. To make the system performance index more accurately and quickly to achieve optimal value, it is necessary to study the optimal control theory and methods.This paper first introduced a new approach for the optimal control with constraints to achieve a desired performance index for nonlinear processes based on new kernel extreme learning machine (KELM). The contributions of the method are as follows:(1) In existing iterative learning control (ILC) algorithm, the model was built only between manipulated input variables and output variables without considering the state variables. In this paper, the variables are divided into state variables, manipulated input variables and output variables in the process of modeling in view of important of states variables in the industrial processes. Then variation of input variables can be gotten by batch-to-batch ILC separately.(2) Constraints of state variables and the input variables are considered in the current version. Particle swarm optimization (PSO) is used to solve the optimization problem.(3) Kernel trick is introduced to improve accuracy of ELM modeling, new KELM algorithm is proposed in the current version. The input trajectory for the next batch is accommodated by searching for the optimal value through the error feedback at a minimum cost. The PSO algorithm is used to search for the optimal value base on ILC. The proposed approach has shown its effectiveness and feasibility by applying to bulk polymerization of the styrene batch process and fused magnesium furnace.Then, a two-step modeling approach based on kernel partial least squares (KPLS) is proposed. The relationship between manipulated input variables and output variables can be gotten by respectively building models between manipulated input variables and operating state variables and between operating state variables and manipulated input variables. The new approach can tackle nonlinear systems because it can efficiently compute regression coefficients in high-dimensional feature spaces by using kernel trick. Applying the approach to temperature control of bulk polymerization of styrene and fused magnesium furnace base on ILC, the proposed approach has shown its effectiveness and feasibility.There are some errors in the KELM for regress target. In order to change the quality of the regress, modified kernel extreme learning machine (MKELM) is Proposed. Analyzing the processes of MKELM and KPLS can find that KPLS’s maximum correlation and MKELM are actually consistent. KELM and KPLS are equivalent for building regression relationship from the standard optimization method point of view, but KELM has faster learning speed due to its special separability feature and KPLS has higher accuracy when used for modeling. The two methods are separately applied to bulk polymerization of styrene and fused magnesium furnace, analysis in theory is further verified by the simulation results.