Issue 1 (203), article 3


Cybernetics and Computer Engineering, 2021, 1(203)


GUBAREV V.F.2, DSc. (Engineering), Corresponding Member of NAS of Ukraine,
Head of the Dynamic Systems Control Department

1National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” 37, Peremohy av., 03056, Kyiv, Ukraine
2Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine
40, Acad. Glushkova, 03187, Kyiv, Ukraine


Introduction. There is a wide range of systems describable as multi input multi variable systems evolving in discrete time. This mathematical model is often used in engineering, but it can also be applied in many other fields. The problem of stabilization of this kind of system frequently arises. In this paper we consider the model predictive control approach to this problem. Its main principle is to generate control signals by optimizing consequent system’s future dynamics on limited prediction horizon. While it demonstrates some good results, in practice we are always limited in terms of computational resources. Thus, we can optimize outcomes of our future control sequence only for limited horizon lengths. That is why it is valuable to understand how this limit affects control quality.

The purpose of the paper is to propose a way to appraise drawbacks of limiting of the prediction horizon to certain length for a particular system, so that we can make informed choice of such limit and therefore choose controller’s microprocessor with sufficient computing power.

Methods. Several indexes which characterize the stabilization process are defined. Their heatmaps built against system’s initial state are used as a convenient visualization of how system’s stabilization dynamics changes depending on its initial state and of drawbacks induced by prediction horizon length limiting. Such heatmaps were built for several prominent example systems with different structures by performing corresponding series of computational experiments.

Results. Drawbacks of prediction horizon length limiting vary from severe to completely nonexistent depending on the system’s structure and representation. These drawbacks relax with increase of this limit. Simple future state’s norm minimizing objective function gives best results with systems whose natural response matrix is not defective and is represented in real Jordan form. Otherwise results worsen dramatically.

Conclusions. The stabilization dynamics depends largely on the system’s structure. Therefore, it is advised to take it into account and build heatmaps of aforementioned indexes to decide on prediction horizon length limit. A good system’s representation can improve stabilization time with limited prediction horizon length. Also, the function of minimum required stabilization time for initial state can be treated as an ideal objective function, but finding this function for a particular system is problematic.

Keywords: MPC, MIMV, heatmap, control synthesis, discrete controllable system, linear system.

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Received 24.12.2020