R. Findeisen

J. Pohlodek, H. Alsmeier, B. Morabito et al.

Integrating measurements and historical data can enhance control systems through learning-based techniques, but ensuring performance and safety is challenging. Robust model predictive control strategies, like stochastic model predictive control, can address this by accounting for uncertainty. Gaussian processes are often used but have limitations with larger models and data sets. We explore Bayesian neural networks for stochastic learning-assisted control, comparing their performance to Gaussian processes on a wastewater treatment plant model. Results show Bayesian neural networks achieve similar performance, highlighting their potential as an alternative for control designs, particularly when handling extensive data sets.

Roland Schurig, David Ohlin, Anders Rantzer et al.

Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear cost. The addition of capacity constraints on states (storage) and inputs (flows between nodes) significantly increases the problem complexity. Leveraging the analytic structure of the unconstrained problem, an explicit suboptimal admissible controller is constructed. This yields graph-computable performance bounds and a minimum stabilising horizon length for a model predictive controller without terminal conditions. A convex program enables efficient computation of the optimal bound and horizon. These results highlight how system structure enables explicit MPC guarantees that are typically not available.

Alexander Rose, Lukas Theiner, Rolf Findeisen

Applying model predictive control on embedded systems remains challenging due to the high computational cost of solving optimal control problems. To address this limitation, computationally efficient Gaussian process approximations of the implicit model predictive control law can be employed. However, for trajectory-tracking applications, the large amount of training data required for successful generalization across distinct reference trajectories poses a significant challenge. To improve data efficiency, we propose to transform the model into curvilinear coordinates around the reference trajectory. Secondly, we use a nominal feedforward component, allowing the Gaussian process to learn only the residual control input, making the approximation of a trajectory-tracking controller feasible. To underline the applicability of the approach, we deploy the controller on a Raspberry Pi in a small-scale vehicle and validate it experimentally. Compared to a model predictive control implementation using real-time iterations, the Gaussian process based approximation computes control inputs about five times faster while achieving similar closed-loop tracking performance.