Henning Schlüter

Abstract

We present a Stochastic Model Predictive Control (SMPC) framework for linear systems subject to Gaussian disturbances. In order to avoid feasibility issues, we employ a recent initialization strategy, optimizing over an interpolation of the initial state between the current measurement and previous prediction. By also considering the variance in the interpolation, we can employ variable-size tubes, to ensure constraint satisfaction in closed-loop. We show that this novel method improves control performance and enables following the constraint closer, then previous methods. Using a DC-DC converter as numerical example we illustrated the improvement over previous methods.

Abstract

Goal: Skeletal muscle mechanics can be assessed in vivo using shear wave elastography. However, the impact of pennation angle on shear wave velocity (SWV) remains unclear. This study aims to quantify the effect by automatically aligning the ultrasound probe with muscle fiber orientation. Methods: We propose an automatic ultrasound probe alignment system and compare it to manual and no alignment. SWV of the gastrocnemius medialis muscle of ten volunteers was measured during rest and isometric contractions. Results: The SWV was different between the conditions ($p~=~0.008$). The highest SWV was obtained during the automatic alignment and differences between the conditions were most pronounced during high-level contractions. The automatic system yielded more accurate alignment compared to a manual operator ($p~=~0.05$). Conclusions: The present study indicates that pennation angle affects SWV, hence muscle fiber orientation must be considered to reliably interpret SWV. Using automatic alignment systems allows for more accurate alignment, improving the methodology of ultrasound elastography in skeletal muscles.

Abstract

This paper deals with stochastic model predictive control (SMPC) based on polynomial chaos expansion (PCE) for linear systems with time-invariant stochastic parametric uncertainties and time-varying stochastic additive disturbances subject to chance constraints on states and inputs. Exploiting terminal ingredients in the SMPC problem and a hybrid update strategy, a recursively feasible optimization problem is formulated. Moreover, stability of the system of PCE coefficients can be shown. Furthermore, in the paper the performance and computational complexity of SMPC based on PCEs is compared to tube-based SMPC and robust model predictive control (RMPC) is analyzed and benefits are demonstrated in simulation.

Abstract

We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets to design the MPC. The scheme avoids the infeasibility issues arising from unbounded disturbances by including the initial state as a decision variable. We show that the stabilizing control scheme can guarantee constraint satisfaction in closed loop, assuming unimodal disturbances. In addition to illustrating these guarantees, the numerical example indicates further advantages of optimizing over the initial state for the transient behavior.

Abstract

When models are inaccurate, the performance of model-based control will degrade. For linear quadratic control, an event-triggered learning framework is proposed that automatically detects inaccurate models and triggers the learning of a new process model when needed. This is achieved by analyzing the probability distribution of the linear quadratic cost and designing a learning trigger that leverages Chernoff bounds. In particular, whenever empirically observed cost signals are located outside the derived confidence intervals, we can provably guarantee that this is with high probability due to a model mismatch. With the aid of numerical and hardware experiments, we demonstrate that the proposed bounds are tight and that the event-triggered learning algorithm effectively distinguishes between inaccurate models and probabilistic effects, such as process noise. Thus, a structured approach is obtained that decides when model learning is beneficial.

Abstract

This paper presents a nonlinear model predictive control strategy for stochastic systems with state- and input-dependent, finite-support disturbances subject to individual chance constraints. Our approach uses an online computed stochastic tube to ensure stability, constraint satisfaction, and recursive feasibility in the presence of stochastic uncertainties. The shape of the tube and the constraint backoff is based on an offline computed incremental Lyapunov function.

Abstract

This paper studies the problem of penalizing rule violation in the context of logic-based motion planning. Translating a given Linear Temporal Logic (LTL) rule into a penalty structure requires a design decision, since the discrete automata obtained from the rule do not provide a straightforward method to penalize rule violation. We propose a design method that explicitly specifies violation to allow for more flexibility in parametrization of desired behaviors and differentiation of penalty semantics. Case study results are shown in the context of an autonomous driving scenario.