### Abstract

The application of novel adaptive predictive optimal controllers of low order, that

involve a multi-step cost index and future set-point knowledge, is considered. The usual predictive controller is of high order and the aim is to utilise simpler structures, for applications where PID controllers might be employed for example. A non-linear system is assumed to be represented by multiple linear discrete-time state-space models, where n of these models are linearisations of the underlying non-linear system at an operating point, determined o-line. One extra model is identied on-line. The optimisation is then performed across this range of Nf + 1 models to produce a single low order control law. One advantage of this approach is that it is very straightforward to generate a much lower order predictive controller and thereby simplify implementation. Also, with

respect to the adaptive nature of the algorithm, the solution is rather cautious. Each new update of the controller involves averaging the cost function across both xed and currently identied models, providing robust adaptive control action.

The method is applied to a piecewise non-linear system, implemented by switching between several linear systems, and results are given.

involve a multi-step cost index and future set-point knowledge, is considered. The usual predictive controller is of high order and the aim is to utilise simpler structures, for applications where PID controllers might be employed for example. A non-linear system is assumed to be represented by multiple linear discrete-time state-space models, where n of these models are linearisations of the underlying non-linear system at an operating point, determined o-line. One extra model is identied on-line. The optimisation is then performed across this range of Nf + 1 models to produce a single low order control law. One advantage of this approach is that it is very straightforward to generate a much lower order predictive controller and thereby simplify implementation. Also, with

respect to the adaptive nature of the algorithm, the solution is rather cautious. Each new update of the controller involves averaging the cost function across both xed and currently identied models, providing robust adaptive control action.

The method is applied to a piecewise non-linear system, implemented by switching between several linear systems, and results are given.

Original language | English |
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Number of pages | 15 |

Publication status | Published - Aug 2002 |

Event | Fifteenth International Symposium on Mathematical Theory of Networks and Systems - South Bend, Indiana, United States Duration: 12 Aug 2002 → 16 Aug 2002 |

### Conference

Conference | Fifteenth International Symposium on Mathematical Theory of Networks and Systems |
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Country | United States |

City | South Bend, Indiana |

Period | 12/08/02 → 16/08/02 |

### Keywords

- predictive control
- restricted structure

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## Cite this

Grimble, M. J., & Martin, P. (2002).

*Adaptive predictive control with controllers of restricted structure*. Paper presented at Fifteenth International Symposium on Mathematical Theory of Networks and Systems, South Bend, Indiana, United States.