Abstract: The project aims at developing novel techniques for designing well-performing controllers which could be implemented on a cheap hardware. Using Model Predictive Control (MPC) and parametric programming, one can synthesize so-called explicit MPC controllers in form of a look-up table. Although such controllers provide very fast implentation, they suffer from the fact that if the prediction model changes, the whole look-up table needs to be re-computed, which is time-consuming. Therefore in this project we aim at synthesizing so-called universal explicit MPC controllers which can be adapted to changing parameters of the prediction model on-the-fly. This task will be achieved by transforming the prediction model into the Brunovsky canonical form, in which the state update is a bilinear function of the states and the time-varying model parameters. The universal controllers will subsequently be obtained by either replacing the bilinear term by auxiliary variables, or by approximating the bilinearity by a piecewise affine function.
Main scientific objective of the project is to develop novel theoretical methods leading to synthesis of explicit MPC controllers which can be adapted, on-the-fly, to time-varying changes of the model parameters.
Achieving the main goal involves solving three particular tasks:
- Transformation of the prediction model into the Brunovsky's canonical form.
- Synthesis of explicit MPC controllers for prediction models in the Brunovsky's form.
- Reduction of complexity of explicit MPC controllers such that they could be implemented on control platforms with severe limitations on available memory and CPU speed.
Principal researcher: Michal Kvasnica