Modifications of Optimization Algorithms Applied in Multivariable Predictive Control

摘要

Non-linear optimization, particularly quadratic programming (QP), is a mathematical method which is widely applicable in model predictive control (MPC). It is significantly important if constraints of variables are considered in MPC and the optimization task is then computationally demanding. The result of the optimization is a vector of future increments of a manipulated variable. The first element of this vector is applied in the next sampling period of MPC in the framework of a receding horizon strategy. In practical realization of a multivariable MPC, the optimization is characterized by higher computational complexity. Therefore, reduction of the computational complexity of the optimization methods has been widely researched. Besides the generally used numerical Hildreth's method of QP, a possible suitable modification is based on precomputing operations proposed by Wang, L. This general optimization strategy is further modified. Two modifications, which could be applied separately each, were interconnected in this paper. The first modification was published previously; however, its application can be more efficient in connection with the second proposed approach, which modifies precomputing operations. Decreasing of the computational complexity of the optimization by using of the proposal is discussed and analyzed by measurements of floating point operations and control quality criterions using hypotheses tests - paired T-test and Wilcoxon test.