Model Identification and State Estimation

The complexity of many technical applications and production processes is continuously increasing, due to growth in the technological possibilities of the produced goods. For biological processes, which are inherently very complex to begin with, complexity has quite different facets, which find their expression, for example, in the linkage of numerous subprocesses, in nonlinear system dynamics, and in combinations of the two.

Moreover, in many cases, the descriptions of the processes and systems are plagued with significant uncertainties. In technical systems, these result from uncertainties regarding the parameters of integrated components and their time-dependent variability during operations, as well as disturbances originating in the external process environment. In biological systems, the natural fluctuations and variability typical of living systems mean that these uncertainties often play an even more important role. Therefore, when developing new medical compounds or devices, or when designing and controlling bioreactors, for example, it is imperative to take them into account.

State estimation as basis of prediction and control

In many technical, medical, and biological processes, mathematical state estimation is an important tool for determining process states that are hidden or not directly measureable, based on the synergetic combination of information from a system simulation and real measurements of various system quantities.

State estimation in dynamic systems provides the basis for model and parameter identification as well as model-based prediction and control. For many years, we have been working in various application contexts with the subject of state estimations. Here, in many cases, existing methods have been adapted to the specific applications. Extensions and brand-new solutions for special problems have also been developed, however.

Our state estimation methods include:

• Extended Kalman-Filter, Constrained Kalman Filter
  
• Sequential Monte Carlo-Methoden (SMC, particle filter)
   

We combine these methods with various approaches for model identification, e.g.:

• Nonlinear optimization
• Maximum Likelihood methods
• Monte Carlo methods (PMCMC)
  
  

and control, e.g.:

• Model predictive control (MPC)
  
• H_∞-control