Štrbské Pleso, Slovak Republic, June 11-14, 2019


Plenary lectures

D. Dochain (UCLouvain, Belgium): Survey of parameter and state estimation for (bio)chemical systems - A personal perspective

Abstract: A key question in process control is how to monitor reactant and product concentrations in a reliable and cost effective manner. However, it appears that, in many practical applications, only some of the concentrations of the components involved and critical for quality control are available for on-line measurement. For instance, dissolved oxygen concentration in bioreactors, temperature in non-isothermal reactors and gaseous flow rates are available for on-line measurement while the values of the concentrations of products, reactants and/or biomass are often available via on-line analysis. An interesting alternative which circumvents and exploits the use of a model in conjunction with a limited set of measurements is the use of state observers.

Historically state observers have been designed for linear systems more in the context of the duality controllability/observability and often included in a closed loop, but little attention had been paid on the issue of coming up with reliable estimates of the state, i. e. with respect to model uncertainty in particular. The design of robust observers is yet an central issue for (bio)chemical systems, especially when considering the sensitivity of the proposed models with respect to the system kinetics in particular.

The present plenary lecture will first review some of the limitations of Luenberger/Kalman observers, and then propose a number of alternatives that have been proposed over the years.

S. Engell (TU Dortmund, Germany): Robust NMPC by Multistage Optimization - Basic idea and further developments

Abstract: In model predictive control (MPC), the next input move is computed by an open-loop optimization of the input sequence for a given plant model. Inevitably, a plant model does not represent the behavior of the plant exactly, there will always be a mismatch between the prediction of the model and the true behavior of the controlled system. In MPC based on a nominal model, this error is only accounted for by taking into account the observed plant-model mismatch (bias correction) or by updating the state of the model. The effect of the deficiencies of the model will be a deterioration of the performance of the closed loop, violation of constraints, or even instability.

Robust (N)MPC formulations take the plant-model mismatch into account systematically. One assumes a set of possible plant behaviours (models) and optimizes the performance e.g. for the worst-case model, satisfying the constraints for the complete set of models. A fundamental question in this context is how to include the presence of future feedback into the optimization of the next control move. For fixed controller structures, It is possible to optimize over the controller parameters, but this introduces a significant restriction. Another option is to compute a nominal trajectory by the MPC controller and to use a second, ancillary controller to keep the real trajectory close to the nominal one (tube-based NMPC). This however to some extent gives away optimality.

Multi-stage (N)MPC is a robust MPC formulation that includes the future feedback actions into the open-loop optimization at the current point in time, by including recourse actions. It is formulated on a discrete tree of possible future evolutions of the controlled system. For this discrete set of uncertainties, the formulation provides the optimal closed-loop performance. The multistage NMPC has been demonstrated to lead to efficient robust control for many examples.

Practically the full state of the controlled system is rarely measurable. To cope with this situation, the original multi-stage MPC concept has been extended to output feedback based on state estimators. The inclusion of the estimation error however significantly enlarges the scenario tree which leads to a rapid growth of the computational effort. Tube-enhanced multi-stage MPC combines the handling of large uncertainties by multi-stage MPC with the regulation against small disturbances and estimation errors using a tube-based approach.

Multi-stage MPC can also be combined with the estimation of model-error models to reduce the conservativeness of the approach for non-parametric model mismatch. It also can be employed in dual control formulations where the explicit formulation of a trade-off between model improvement and control performance is avoided and replaced by an integrated formulation where the model error influences the performance via the resulting scenario tree.

Workshops - free of charge, available to all participants

M. E. Villanueva (ShanghaiTech, China): Robust Model Predictive Control for Nonlinear Systems using Sets

Abstract: This workshop aims to give a tutorial introduction to robust feedback control using model-predictive control, together with set-theoretic techniques. This talk will first discuss conservative but tractable approximations of a robust optimal feedback control problem for nonlinear continuous-time systems. In particular, the focus will be on Tube Model Predictive Control strategies. Here, state trajectories are replaced by set-valued functions (Robust Forward Invariant Tubes) in the state space, enclosing all future states of the system independently of the uncertainty realization. We will show how, using techniques from reachability analysis, one can arrive to a standard optimal control problem, whose solution provides a conservative approximation to the robust feedback control problem. The talk will also discuss applications of the tube approach to real-time robust MPC and optimal control synthesis for periodic processes.

G. Hulkó (STU, Slovakia): Control of Distributed Parameter Systems - An Engineering Approach

Abstract: In the scope of this tutorial a basic structure of an engineering approach in control of distributed parameter systems will be presented based on numerical models of controlled technological and manufacturing processes. The decomposition of the dynamics and synthesis of control into time and space components will be introduced along with the distributed parameter open loop control, feedback control loop and feedback control loop with an internal model. Moreover, the software support DPS Blockset for Simulink a third-party software product of The MathWorks Company will be demonstrated with automatized design of distributed parameter control loops. Finally, some specific model control tasks and temperature field control in shape and continuous casting processes will be discussed.