arXiv subjects

David Ohlin

Publications and source records attributed to David Ohlin.

8 recordsLinked to original sources

arXiv2026

Model Predictive Control for Constrained Linear Positive Systems on Graphs

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.

math.OC↗

arXiv2026

Positive Observers Revisited

The paper shows that positive linear systems can be stabilized using positive Luenberger-type observers. This is achieved by structuring the observer as monotonically converging upper and lower bounds on the state. Analysis of the closed-loop properties under linear observer feedback gives conditions that cover a larger class than previous observer designs. The results are applied to nonpositive systems by enforcing positivity of the dynamics using feedback from the upper bound observer. The setting is expanded to include stochastic noise, giving conditions for convergence in expectation using feedback from positive observers.

math.OC↗

arXiv2025

Multipolar dynamics of social segregation: Data validation on Swedish vaccination statistics

We perform a validation analysis on the multipolar model of opinion dynamics. A general methodology for using the model on datasets of two correlated variables is proposed and tested using data on the relationship between COVID-19 vaccination rates and political participation in Sweden. The model is shown to successfully capture the opinion segregation demonstrated by the data and spatial correlation of biases is demonstrated as necessary for the result. A mixing of the biases on the other hand leads to a more homogeneous opinion distribution, and greater penetration of the majority opinion, which here corresponds to a decision to vote or vaccinate.

eess.SY↗

arXiv2025

On Exact Solutions to the Linear Bellman Equation

This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the class of Linearly Solvable MDP is reformulated as a continuous-state optimal control problem. It is shown that this class naturally satisfies the conditions for explicit solution of the Bellman equation, motivating the extension of previous results to semilinear dynamics to account for input nonlinearities. The applicability of the given conditions is illustrated in scenarios with linear and quadratic cost, corresponding to the Stochastic Shortest Path and Linear-Quadratic Regulator problems.

math.OC↗

arXiv2024

Heuristic Search for Linear Positive Systems

This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain class of linear systems. This is used to construct a heuristic search framework for linear {positive} systems inspired by existing methods for SSP. {We propose a heuristics-based algorithm for {efficiently} finding local solutions to the analyzed class of optimal control problems with {a given initial} state and {positive} linear dynamics.} {By leveraging the bound on optimality in each state provided by the heuristics, we also derive a novel distributed algorithm for calculating local controllers within a specified performance bound, with a distributed condition for termination.} More fundamentally, the results allow for analysis of the conditions for explicit solutions to the Bellman equation utilized by heuristic search methods.

math.OC↗

arXiv2024

Achieving consensus in networks of increasingly stubborn voters

We study opinion evolution in networks of stubborn agents discussing a sequence of issues, modeled through the so called concatenated Friedkin-Johnsen (FJ) model. It is concatenated in the sense that agents' opinions evolve for each issue, and the final opinion is then taken as a starting point for the next issue. We consider the scenario where agents {also take a vote at the end of each issue} and propose a feedback mechanism from the result (based on the median voter) to the agents' stubbornness. Specifically, agents become increasingly stubborn during issue $s+1$ the more they disagree with the vote at the end of issue $s$. We analyze {this model} for a number of special cases and provide sufficient conditions for convergence to consensus stated in terms of permissible initial opinion and stubbornness. In the opposite scenario, where agents become less stubborn when disagreeing with the vote result, we prove that consensus is achieved{, and we demonstrate the faster convergence of opinions compared to constant stubbornness.

math.OC↗

arXiv2024

Multipolar opinion evolution in biased networks

Motivated by empirical research on bias and opinion formation, we formulate a multidimensional nonlinear opinion-dynamical model where agents have individual biases, which are fixed, as well as opinions, which evolve. The dimensions represent competing options, of which each agent has a relative opinion, and are coupled through normalization of the opinion vector. This can capture, for example, an individual's relative trust in different media. In special cases including where biases are uniform across agents our model achieves consensus, but in general, behaviors are richer and capture multipolar opinion distributions. We examine general fixed points of the system, as well as special cases such as zero biases toward certain options or partitioned decision sets. Lastly, we demonstrate that our model exhibits polarization when biases are spatially correlated across the network, while, as empirical research suggests, a mixed community can mediate biases.

eess.SY↗

arXiv2023

Optimal Control of Linear Cost Networks

We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be computed by linear programming. Our framework admits a range of network routing problems with underlying linear dynamics. These dynamics can be used to model traditional graph-theoretical problems like shortest path as a special case, but can also capture more complex behaviors. We provide an asynchronous and distributed value iteration algorithm for obtaining the optimal cost function and control law.

math.OC↗