arXiv subjects

Franz Rußwurm

Publications and source records attributed to Franz Rußwurm.

5 recordsLinked to original sources

arXiv2026

Polytopic Inner Approximation of Admissible Sets for Linear Systems

This paper presents a method for computing inner polytopic approximations of admissible sets for continuous-time linear control systems subject to multiple affine state constraints, with a particular concern on computational tractability for large dimensional problems. In place of globally computing the admissible set and the part of its boundary called the barrier, we compute the so-called individual admissible sets and the corresponding barriers for each single constraint. We then use the exact sampling of linear systems and generate polytopes in half-space representation that provide an approximation of the individual admissible sets, to finally intersect them. We provide a complexity analysis of the whole procedure to evaluate its efficiency. The approach is illustrated by two examples -a triple integrator and a mass-spring-damper chain considered in 4, 6, 8, and 10 dimensions- with corresponding runtimes evaluated for both.

math.OC↗

arXiv2026

On the Boundary of the Robust Admissible Set in State and Input Constrained Nonlinear Systems

In this paper, we consider nonlinear control systems subject to bounded disturbances and to both state and input constraints. We introduce the definition of robust admissible set - the set of all initial states from which the state and input constraints can be satisfied for all times against all admissible disturbances. We focus on its boundary that can be decomposed into the usable part on the state constraint boundary and the barrier, interior to the state constraints. We show that, at the intersection of these two components, the boundary of the robust admissible set must be tangent to the state constraint set and separate the interior of the robust admissible set and its complement, a property that we call the ultimate locally separating hyperplane condition. Moreover, we prove that the barrier must satisfy a saddle-point principle on a Hamiltonian, based on Pontryagin's maximum principle, whose final condition is precisely the ultimate locally separating condition, thus providing a set of differential equations made of the system and its adjoint for a direct construction of the barrier. Lastly, we illustrate our results by calculating the robust admissible set for an adaptive cruise control example.

math.OC↗

arXiv2022

Critical Clearing Time Estimates of Power Grid Faults via a Set-Based Method

This paper is concerned with estimating critical clearing times in the transient stability problem of power grids without extensive time-domain simulations. We consider a highdimensional post-fault system (the grid after the fault is cleared) which we decouple into many smaller subsystems. Then, for each subsystem, we find the so-called safety sets and simulate the faulted system once to deduce the so-called safe and unsafe critical clearing times, which specify the intervals of time over which the fault may remain active before safety is compromised. We demonstrate the approach with a numerical example involving the IEEE 14 bus system.

eess.SY↗

arXiv2021

On MPC without terminal conditions for dynamic non-holonomic robots

We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.

eess.SY↗

arXiv2021

Optimal control of centrifugal spreader

Achieving an evenly distributed fertilization spread pattern is a complex technical task. A corresponding control algorithm must account for the tractor movement, the settings of the spreader, the prescribed dosage as well as machine constraints. It dictates, in particular, the fertilization process needs be estimated ahead to achieve an optimized spread pattern. The presented work is concerned with the development of a predictive control scheme for optimized fertilizer application using modeling of the tractor moving on the field and the spread pattern in form of a crescent behind the tractor. In particular, the form of the spread pattern is modeled via four normal distributions, two for each side of the pattern. The control goal is to achieve a desired fertilizer distribution on the field. The study presents three algorithms for comparison: a one-step optimization and two approaches using model-predictive control, one with a simplified model of the spread pattern in the prediction horizon, and one with a comprehensive one model, respectively. The best results are obtained with model-predictive control using the comprehensive model.

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