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Start of funding 01.07.2018

Stability and performance guarantees for data-driven control methods

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In modern control applications such as soft robotics or human-robot-interaction, the control design and modelling process becomes very time-consuming or even infeasible due to the complexity of the models. A solution to overcome these issues is provided by data-driven models which require only a minimum of prior knowledge since the complexity of the model scales with the amount of training data. However, a general problem of data-driven models is the estimation of the model accuracy which is usually necessary for robust control design and stability. In this project, we use Gaussian Process models since they provide not only a mean prediction, but also a variance as uncertainty measure of the model. We exploit this uncertainty to derive control laws which guarantee the stability of the closed loop. In addition, the control error based on the number and distribution of training points is determined. As consequence, more advanced control strategies can be applied to safety-critical systems which results in an improved overall performance.

Final report:
The project made it possible for Mr. Beckers to visit the University of California, Berkeley for 6 weeks. During this time, the project partners focused mainly on two subprojects:

1. Gaussian processes are a very powerful tool for model-based control approaches of nonlinear systems. In contrast to parametric models, the prediction is based on the underlying data which offers a highly flexible modeling technique. However, the selection of the kernel and its hyperparameters is a crucial step since it strongly influences the quality of the model. Classically, they are optimized based on the data but totally neglecting the later usage of the model in the control loop. We worked on a framework to optimize the Gaussian process with respect to the closed loop performance using Bayesian optimization. The approach preserves the stability of the control loop.

2. Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. This requires a precise model of the system since otherwise the guarantees are lost. Parametric models are often limited in the applicability for modeling complex systems and do not provide any information about the quality of the regression. Therefore, we use a data-driven approach, i.e. Gaussian processes, to achieve a probabilistic model of the actual system based on samples of the process. The results are probabilistic safety guarantees for the closed loop that allows the application in more safety-critical environments.

Results and future work: We derived two approaches with data-driven based control methods that guarantee a safe behavior of the closed loop system with an increased performance. The results of the first subproject will be submitted in the very near future as

Thomas Beckers, Somil Bansal, Claire J. Tomlin and Sandra Hirche: „Closed loop model selection for kernel-based regression methods“.

The publication of the second subproject’s results will be afterwards.