Research On The Algorithm For The Generalized Predicative Control Based On Optimization Theory

Generalized predicative control (GPC) is a new computer control method, after it presented, it was got favor by industry and control area. A great many of experts and scholars do a lot of studies on it. Nowadays, it is used broadly in airline, petrol, and so on.Though there are many articles and studies on it, in practice, some control objects are constrained. The main methods are to change the constrained problem into unconstrained problem. This makes the problem become more and more complex, it also involves the problem of computing the the inverse of matrix, even if it does not do that, it concerns the problem of computing the inverse of matrix partly. So the sum of computation and the memory space are large. What's more, the study on the algorithm's convergence is much less.Firstly, for GPC algorithm is one of the representative algorithms in pred- icative control. In this paper, it shows something about predicative control in order to understand what algorithm is predicative control algorithm. It introdu- es three basic principles, then it discusses on predicative control's basic al- gorithm and Diophantine equation deduce solutions, besides, the construct of controlled object's model and the deduce on control rule are included.Secondly, the GPC model is turned into a quadratic problem, which is familiar to us. In this paper, that makes the foundation for the latter algorithm.It has a deep study on trust-region method and it gives a new trust-region method for optimization. It proves the astringency and computes one example to prove the feasibility of the algorithm.Thirdly, it constructs a kind of new algorithm of generalized predicative control with constraints on the base of the former, which is about non-linear programming and predicative control. It introduces Diophantine equation at first, then it use mathematic knowledge to change the model into a model whose object function is quadratic and the constraints are linear equalities and inequalities. The algorithm in this paper is by the combine of penalty function and Lagrange function, It need not find the beginning feasible point and compute the inversion of the matrix, it only need to compute an optimization problem. It reduces the volume of computation and memory.At last, the articles about astringency of GPC algorithm are less by found a lot of articles about it. It is a work that is full of competition, but it is meaningful thing. In this paper, it proves the astringency and gives two theorems on astringency.Besides, an example is computed to prove the feasibility of the algorithm.