## Predictive Control & Youla-Kucera Parametrisation

Predictive control has become a very succesful control design, mainly due tu direct constraint handling capabilities. Its main drawback is stability. This research tries to solve the stability problem by applying the following simple idea. Assume that a system is already controlled by some nominal controller and the closed-loop is already stable. By the use of the Youla-Kucera paramtrisation, a general formula for all stabilising controllers can be found. Within these a controller (or an optimal YK polynomial) is searched that minimises a quadratic function and simultaneously satisfies constraints.

The first approach is to use finite horizon cost function. However, by applying this idea to a finite horizon cost function the overall Youla-Kucera predictive controller (YKPC) becomes time-variant. The stability analysis of such a system is performed. Stability proofs lead to minimum possible horizon lenghts. These are given as number of unstable poles (control horizon) and number of unstable zeros (output horizon) plus the degree of optimised YK polynomials.

Another possibilty how to overcome stability problem is to use infinite horizon cost function. In that case the controller is time-invariant when constraints are inactive. Constrained stability is as in the previous case assured if the corresponding optimisation problem is feasible.

The third approach to stability is based on the following idea. Let us assume that the loop is already closed and controlled by a controller. The question is what is the minimum number of control moves, or control error moves that still lead to stable closed-loop behaviour and to a time-invariant controller. Again, the minimum number if steps is directly related to the number of unstable poles and zeros.

### Journals and book chapters

• Fikar, M., Kucera, V.: On minimum finite length control problem. Int. J. Control, 73(2), 152-158, 2000. Abstract
• Fikar, M., Engell, S., Dostál, P.: Design of Predictive LQ Controller. Kybernetika 35(4), 459-472, 1999. Abstract
• Fikar, M., Engell, S.: Receding horizon predictive control based upon Youla-Kucera parametrisation. European Journal of Control, 3 (4), 304 - 316, 1997. Abstract
• Fikar, M., Jorgensen, S. B.: Multivariable Constrained Control Based upon all Stabilizing Controllers, In: D. W. Clarke (Ed.) Advances in Model-Based Predictive Control, Oxford University Press, 1994, 260 - 275. Abstract
• Fikar, M. Jorgensen, S. B.: Multivariable constrained adaptive predictive control based on pole placement design. In: Wawrick, Kárný (Eds.) Mutual Impact of Computing Power and Control Theory, Plenum Pub. Corp., London, 1993, 301 - 310.

### Conferences

• Fikar, M., Morari, M., Mikleš, J.: On Youla-Kuèera parametrisation approach to predictive control. ECC99, Karlsruhe, CD-ROM Proceedings, F163, 1999. Abstract, Presentation, Article:PS.ZIP
• Fikar, M., Kucera, V.: On stable finite length control problem. Proceedings of the 12th Int. Conference Process Control '99, Tatranske Matliare, Slovakia, 31.5-3.6.1999, Vol. 1, 11-15. Abstract, Presentation, Article:PS.ZIP
• Fikar, M., Engell, S., Dostál, P.: Design of Infinite Horizon Predictive LQ Controller. Proceedings ECC'97, Bruxelles, Paper No. 698, 1997. Abstract, Presentation:PS.ZIP
• , Article:PS.ZIP

### Technical Reports

• M. Fikar, On Minimum Degree Finite Length Control Error Problem, Technical Report MF9901, Control Engineering Laboratory, FEE, Ruhr-University Bochum, 1999. Abstract, Report:PS.ZIP
• M. Fikar, On Minimum Degree Finite Length Control Problem, Technical Report KAMF9802, Department of Process Control, FCT STU, 1998. Abstract, Report:PS.ZIP
• Fikar, M.: Control of Multivariable Systems. Parametrization of all Stabilizing controllers. PhD thesis, Dep. of Process Control CHTF STU, 1994. Abstract, PHD:PS.ZIP
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