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| Parameter and State Estimation |
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Model based control and optimization strategies rely on the availability of accurate dynamic mathematical models and estimates of the system states [1]. In many real-world applications, white-box models based on first principles are preferred, since they provide additional insight in the system behavior, allow to analyze the influence of real design parameters on the system behavior, and are not limited to available measurement ranges. To calibrate these possibly nonlinear, large-scale and/or multi-scale engineering models, model parameters and unmeasurable state variables have to be estimated based on system measurements obtained either on-line (i.e., during normal operation), or off-line (e.g., from carefully designed experiments). Moreover, the simultaneous availability of model uncertainty information (e.g., confidence levels on parameter and state estimates) is required to statistically guarantee the optimality and feasibility of any model-based optimal solution later on, which is of high importance in industrial practice.
The aim of the research is to advance white-box on-line and off-line parameter and state estimation and experiment design techniques for multi-scale, large-scale, or nonlinear engineering models.
The focus of the research is:
- Fast on-line nonlinear model parameter and state estimation: Develop moving horizon estimation (MHE) algorithms for on-line estimation of parameters and states of nonlinear systems. Since MHE formulates the estimation problem as a dynamic optimization problem, it can take various constraints into account, and it can cope with nonlinear dynamics, two shortcomings/limitations of more classical estimators such as Kalman filters. The main challenge is to develop numerical solution methods, in close collaboration with WP1, such that these MHE algorithms can run at sampling frequencies that approach the 1kHz range, which is necessary in mechatronics and robotics applications. The MHE algorithms will be experimentally validated on a KUKA Lightweight robot arm, (i) for the on-line identification of highly nonlinear dynamic robot models, including joint flexibilities and time-varying parameters such as those of complex pre-sliding friction models [2], and (ii) for the on-line estimation of the state of the robot environment during autonomous and multi-sensor based execution of robot tasks in uncertain and/or continuously changing and human-populated environments, including tasks involving dynamic human-robot interaction.
- Efficient off-line parameter estimation for (non)linear large-scale and multi-scale models: Design algorithms that provide not only the globally best parameters but also their uncertainty levels (e.g., confidence levels) for different classes of multi-scale and large-scale (non)linear models. Hereto, the estimation procedure is formulated as the minimization of the difference between model predictions and available measurements, while uncertainty levels can be derived from sensitivity information of the optimum.
- Optimal Experiment Design for highly informative experiments: Limit the experimental burden and costs by carefully designing experimental procedures [2; 3] (e.g., optimal positioning of sensors in robotics or dynamic testing of civil engineering structures [4], optimal dynamic feeding profiles in bioreactors [5]). In the field of optimal experiment design, measures quantifying the information content of experiments are specified based on the variance/co-variance matrix. Hence, the development of efficient techniques to optimise these measures given experimental constraints is asset for a use in practical applications.
