Analysis of modified optimization in multivarible predictive control with regards to control quality

Abstract

Model predictive control (MPC) has been a widely researched strategy in the modern control theory. Various modifications of MPC are focused on improving of two subsystems – the predictor and the optimizer, which cooperate mutually on the receding horizon. In constrained predictive control, the optimization is a quadratic programming problem, which has to be solved numerically. Namely, in constrained multivariable MPC, the constraints and the multi-variability of the process cause excessive increasing of the computational complexity. Reducing of computational time and decreasing of a number of numerical operations are particularly desirable. This is the reason for efforts to modify algorithms of numerical optimization. These modifications can influence control quality. This paper deals with one modification of the Hildreth optimization method and accurate analysis of its impact to quality of control. For analysis of impact to control quality, descriptive statistical methods are frequently used; particularly, methods based on analysis of floating point operations are complemented with their regression analysis for expression of complexity function O. However, the regression analysis of these results belongs only to non-inductive statistical methods depending on particular measurements of a computational complexity. For purposes of increasing responsibility of control quality indicators, set of specific statistical methods aimed on testing hypotheses is recommended in this paper. Testing hypotheses can be applied with strictly defined significance level. Practical implementation of modified MPC algorithm is statistically analyzed in comparison with unmodified MPC using proposed set of particular statistical methods. © 2019, Cefin Publishing House. All rights reserved.