MPC uses a prediction model to make decisions regarding the current actuation taking into account input, state and output constraints. In practice, model inaccuracies or disturbances usually cause a violation of the nominal system dynamics, which will lead to performance degradation and, most importantly, infeasibility when using nominal MPC approaches neglecting the uncertainty. This issue is addressed in robust and stochastic MPC schemes.
Our current work focuses on
- Soft constraints
Whereas input constraints are hard constraints and can never be exceeded, state or output constraints often represent desired bounds that can in practice be briefly violated if necessary. Soft constrained MPC approaches are based on the idea that, due to the nature of the state constraints, violation can often be tolerated for short time periods, thereby ensuring feasibility at all times.
A key goal in all methods is to provide not only a feasibility but also a stability guarantee. While asymptotic stability can often not be achieved in the presence of persistent disturbances, a practical concept employed for the stability analysis of uncertain systems is that of input-to-state stability, requiring the effect of the disturbance to be bounded and to depend on the size of the disturbance.
- Stochastic MPC
While most robust MPC methods consider bounded disturbances/uncertainties and design the problem for the worst-case scenario, stochastic MPC approaches take into account an stochastic probability distribution over observed disturbances. This additional knowledge provides the capability of being significantly less conservative than classic approaches, and we have been developing computationally efficient methods that exploit this information.