Structure-based optimization problem for model predictive control in linear multi-input multi-value systems

Abstract

Various technical and other realworld systems can be modelled with decent precision as linear systems. This approach is the core of the long established control theory, whose mathematical apparatus is ubiquitous when it comes to controlling some kind of system. While it is hard to underestimate importance of this approach, long history of research in this field showed some of its shortcomings which may hinder its application in various ways. For example, it does not allow to incorporate constraints on control signal’s magnitude into the system’s model. Thus, engineers are forced to manually tune controller’s parameters adhoc in order to satisfy these constraints. This paper is dedicated to development of an alternative control algorithm based on the model predictive control approach. Its core idea is to generate control sequences by solving an optimization problem which objective function depends on predicted future state. It allows to generate fast stabilization trajectories without additional tuning by using the classic linear system’s evolutionary equation as a future state predictor and constraints on controls as optimization problem’s constraints. Meaningfully defined objective function is crucial in order to make this control algorithm work properly. It appeared that defining an objective function with good enough properties in general case is not a trivial task. This paper leverages modern nonstandard analysis in order to achieve this feat.