In modern technologies such as autonomous vehicles and service robots, control engineering plays a crucial role for the overall performance and safety of the system. However, the control design becomes often very time-consuming or unfeasible due to the increasing complexity of recent technological advancements. The classical control approaches, which are based on models of the systems using first-order principles, are not satisfactory in the presence of complex dynamics, e.g., for highly nonlinear systems or interaction with prior unknown environment.
Recent findings in the area of computational intelligence and machine learning have shown that data-driven approaches lead to very promising results in a wide application range as they require only a minimal prior knowledge for the modeling of complex dynamics. However, the major drawback in data-driven approaches frequently manifests as unpredictable outcomes. Thus, guarantees about the stability and performance of the control loop are absent which is translated as compromised safety in control systems. As a consequence, the current application of data-driven models in control scenarios is limited to non-critical and low performance systems due to their unpredictable blackbox-behavior. My research focuses on
Bridging the gap between machine learning and control theory to develop new algorithms towards safe, robust, and intelligent control of physical systems.
For this purpose, I use Gaussian process models as a data-driven technique due to many beneficial properties such as the bias-variance trade-off and the strong connection to Bayesian mathematics. My research allows to answer the following questions:
How to use GP models as dynamical systems and what are the control-theoretic properties of dynamical GP models
How to select the underlying kernel function to give the maximum control performance and how to deal with a misselection
How to apply GP models in control approaches with safety and performance guarantees for the closed-loop
In the following, you find a selection of my work. Some code is publicly available on my Github repo.
Underactuated vehicles have gained much attention in the recent years due to the increasing amount of aerial and underwater vehicles as well as nanosatellites. Trajectory tracking control of these vehicles is a substantial aspect for an increasing range of application domains. However, external disturbances and parts of the internal dynamics are often unknown or very time-consuming to model. To overcome this issue, we present a tracking control law for underactuated rigid-body dynamics using an online learning-based oracle for the prediction of the unknown dynamics. We show that Gaussian process models are of particular interest for the role of the oracle. The presented approach guarantees a bounded tracking error with high probability where the bound is explicitly given.
T. Beckers, L. Colombo, S. Hirche, and G. Pappas. “Online learning-based trajectory tracking for underactuated vehicles with uncertain dynamics”.
The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often challenging or even infeasible due to the complexity of the system dynamics. In contrast, data-driven approaches need only a minimum of prior knowledge and scale with the complexity of the system. In particular, Gaussian process dynamical models (GPDMs) provide very promising results for the modeling of complex dynamics. However, the control properties of these GP models are just sparsely researched, which leads to a "blackbox" treatment in modeling and control scenarios. In addition, the sampling of GPDMs for prediction purpose respecting their non-parametric nature results in non-Markovian dynamics making the theoretical analysis challenging. In this article, we present approximated GPDMs which are Markov and analyze their control theoretical properties. Among others, the approximated error is analyzed and conditions for boundedness of the trajectories are provided. The outcomes are illustrated with numerical examples that show the power of the approximated models while the the computational time is significantly reduced.
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model. Classically, these hyperparameters are optimized to minimize the prediction error of the model but this process totally neglects its later usage in the control loop. In this work, we present a framework to optimize the kernel and hyperparameters of a kernel-based model directly with respect to the closed-loop performance of the model. Our framework uses Bayesian optimization to iteratively refine the kernel-based model using the observed performance on the actual system until a desired performance is achieved.
T. Beckers, S. Bansal, C. J. Tomlin, and S. Hirche. “Closed-loop model selection for kernel based models via Bayesian Optimization”. In: Proceedings of the Conference on Decision and Control. 2019. doi: 10.1109/CDC40024.2019.9029690. [Preprint] [bibtex]
Perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows to maintain good tracking performance at low feedback gains. However, accurate models are often difficult to obtain. In this article, we address the problem of stable high-performance tracking control for unknown Euler-Lagrange systems. In particular, we employ Gaussian Process regression to obtain a data-driven model that is used for the feed-forward compensation of unknown dynamics of the system. The model fidelity is used to adapt the feedback gains allowing low feedback gains in state space regions of high model confidence. The proposed control law guarantees a globally bounded tracking error with a specific probability.
T. Beckers, D. Kulić, and S. Hirche. “Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems”. In: Automatica 103 (2019), pp. 390–397.
doi: 10.1016/j.automatica.2019.01.023. [Preprint] [bibtex]