To do so, our input trajectories are parametrized in consecutive sections, e.g. as consecutive piecewise ramps or splines.

Abstract: Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior over the continuous-time dynamics and latent state trajectory in state-space form and updating it through a targeted marginal Metropolis-Hastings sampler equipped with a numerical ODE integrator. The resulting posterior samples are used to formulate a scenario-based optimal control problem that accounts for both model and measurement uncertainty and is solved using standard nonlinear programming methods. The approach is validated in a numerical case study on glucose regulation using a Type 1 diabetes model. Keywords: Probabilistic and Bayesian methods for system identification, Nonlinear system identification, Time series modeling, Statistical inference, Learning methods for optimal control, Model predictive control, Data-driven control theory 1. INTRODUCTION Accurate dynamical models are fundamental for the predictive and optimal control of nonlinear systems. Although first-principles models may describe the general structure of many systems, important parameters or effects often remain unknown, limiting their direct use for control.

For time-series modeling we employ a Gaussian process with a nonlinear exogenous input structure.

We introduce MIO, a transformer-based model for inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories of a dynamical system. By combining multiple instance learning with transformer-based symbolic regression, the model effectively leverages repeated observations of the same system to learn more generalizable representations of the underlying dynamics. We investigate different instance aggregation strategies and show that even simple mean aggregation can substantially boost performance. MIO is evaluated on systems ranging from one to four dimensions and under varying noise levels, consistently outperforming existing baselines.

Biomolecular Neural Networks (BNNs), artificial neural networks with biologically synthesizable architectures, achieve universal function approximation capabilities beyond simple biological circuits. However, training BNNs remains challenging due to the lack of target data. To address this, we propose leveraging Signal Temporal Logic (STL) specifications to define training objectives for BNNs. We build on the quantitative semantics of STL, enabling gradient-based optimization of the BNN weights, and introduce a learning algorithm that enables BNNs to perform regression and control tasks in biological systems. Specifically, we investigate two regression problems in which we train BNNs to act as reporters of dysregulated states, and a feedback control problem in which we train the BNN in closed-loop with a chronic disease model, learning to reduce inflammation while avoiding adverse responses to external infections. Our numerical experiments demonstrate that STL-based learning can solve the investigated regression and control tasks efficiently.

Optimal trajectories that minimize a user-defined cost function in dynamic systems require the solution of a two-point boundary value problem. The optimization process yields an optimal control sequence that depends on the initial conditions and system parameters. However, the optimal sequence may result in undesirable behavior if the system's initial conditions and parameters are erroneous. This work presents a data-driven fuzzy controller synthesis framework that is guided by a time-optimal trajectory for multicopter tracking problems. In particular, we consider an aggressive maneuver consisting of a mid-air flip and generate a time-optimal trajectory by numerically solving the two-point boundary value problem. A fuzzy controller consisting of a stabilizing controller near hover conditions and an autoregressive moving average (ARMA) controller, trained to mimic the time-optimal aggressive trajectory, is constructed using the Takagi-Sugeno fuzzy framework.

Stem cell therapy is a promising approach to treat heart insufficiency and benefits from automated myocardial injection which requires highly precise motion of a robotic manipulator that is equipped with a syringe. This work investigates whether sufficiently precise motion can be achieved by combining a SCARA robot and learning control methods. For this purpose, the method Autonomous Iterative Motion Learning (AI-MOLE) is extended to be applicable to multi-input/multi-output systems. The proposed learning method solves reference tracking tasks in systems with unknown, nonlinear, multi-input/multi-output dynamics by iteratively updating an input trajectory in a plug-and-play fashion and without requiring manual parameter tuning. The proposed learning method is validated in a preliminary simulation study of a simplified SCARA robot that has to perform three desired motions. The results demonstrate that the proposed learning method achieves highly precise reference tracking without requiring any a priori model information or manual parameter tuning in as little as 15 trials per motion. The results further indicate that the combination of a SCARA robot and learning method achieves sufficiently precise motion to potentially enable automatic myocardial injection if similar results can be obtained in a real-world setting.

Useful robot control algorithms should not only achieve performance objectives but also adhere to hard safety constraints. Control Barrier Functions (CBFs) have been developed to provably ensure system safety through forward invariance. However, they often unnecessarily sacrifice performance for safety since they are purely reactive. Receding horizon control (RHC), on the other hand, consider planned trajectories to account for the future evolution of a system. This work provides a new perspective on safety-critical control by introducing Forward Invariance in Trajectory Spaces (FITS). We lift the problem of safe RHC into the trajectory space and describe the evolution of planned trajectories as a controlled dynamical system. Safety constraints defined over states can be converted into sets in the trajectory space which we render forward invariant via a CBF framework. We derive an efficient quadratic program (QP) to synthesize trajectories that provably satisfy safety constraints. Our experiments support that FITS improves the adherence to safety specifications without sacrificing performance over alternative CBF and NMPC methods.

This work proposes Autonomous Iterative Motion Learning (AI-MOLE), a method that enables systems with unknown, nonlinear dynamics to autonomously learn to solve reference tracking tasks. The method iteratively applies an input trajectory to the unknown dynamics, trains a Gaussian process model based on the experimental data, and utilizes the model to update the input trajectory until desired tracking performance is achieved. Unlike existing approaches, the proposed method determines necessary parameters automatically, i.e., AI-MOLE works plug-and-play and without manual parameter tuning. Furthermore, AI-MOLE only requires input/output information, but can also exploit available state information to accelerate learning. While other approaches are typically only validated in simulation or on a single real-world testbed using manually tuned parameters, we present the unprecedented result of validating the proposed method on three different real-world robots and a total of nine different reference tracking tasks without requiring any a priori model information or manual parameter tuning. Over all systems and tasks, AI-MOLE rapidly learns to track the references without requiring any manual parameter tuning at all, even if only input/output information is available.

Validating robotic systems in safety-critical appli-cations requires testing in many scenarios including rare edgecases that are unlikely to occur, requiring to complement real-world testing with testing in simulation. Generative models canbe used to augment real-world datasets with generated data toproduce edge case scenarios by sampling in a learned latentspace. Autoencoders can learn said latent representation for aspecific domain by learning to reconstruct the input data froma lower-dimensional intermediate representation. However, theresulting trajectories are not necessarily physically plausible, butinstead typically contain noise that is not present in the inputtrajectory. To resolve this issue, we propose the novel Physics-Informed Trajectory Autoencoder (PITA) architecture, whichincorporates a physical dynamics model into the loss functionof the autoencoder. This results in smooth trajectories that notonly reconstruct the input trajectory but also adhere to thephysical model. We evaluate PITA on a real-world dataset ofvehicle trajectories and compare its performance to a normalautoencoder and a state-of-the-art action-space autoencoder.