arXiv subjects

Emma Tegling

Publications and source records attributed to Emma Tegling.

At least 19 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

Continuous-Time Distributed Learning for Collective Wisdom Maximization

Motivated by the well established idea that collective wisdom is greater than that of an individual, we propose a novel learning dynamics as a sort of companion to the Abelson model of opinion dynamics. Agents are assumed to make independent guesses about the true state of the world after which they engage in opinion exchange leading to consensus. We investigate the problem of finding the optimal parameters for this exchange, e.g. those that minimize the variance of the consensus value. Specifically, the parameter we examine is susceptibility to opinion change. We propose a dynamics for distributed learning of the optimal parameters and analytically show that it converges for all relevant initial conditions by linking to well established results from consensus theory. Lastly, a numerical example provides intuition on both system behavior and our proof methods.

eess.SY↗

arXiv2025

Compositional design for time-varying and nonlinear coordination

This work addresses the design of multi-agent coordination through high-order consensus protocols. While first-order consensus strategies are well-studied -- with known robustness to uncertainties such as time delays, time-varying weights, and nonlinearities like saturations -- the theoretical guarantees for high-order consensus are comparatively limited. We propose a compositional control framework that generates high-order consensus protocols by serially connecting stable first-order consensus operators. Under mild assumptions, we establish that the resulting high-order system inherits stability properties from its components. The proposed design is versatile and supports a wide range of real-world constraints. This is demonstrated through applications inspired by vehicular formation control, including protocols with time-varying weights, bounded time-varying delays, and saturated inputs. We derive theoretical guarantees for these settings using the proposed compositional approach and demonstrate the advantages gained compared to conventional protocols in simulations.

eess.SY↗

arXiv2025

Linear Regulator-Based Synchronization of Positive Multi-Agent Systems

This paper addresses the positive synchronization of interconnected systems on undirected graphs. For homogeneous positive systems, a static feedback protocol design is proposed, based on the Linear Regulator problem. The solution to the algebraic equation associated to the stabilizing policy can be found using a linear program. Necessary and sufficient conditions on the positivity of each agent's trajectory for all nonnegative initial conditions are also provided. Simulations on large regular graphs with different nodal degree illustrate the proposed results.

eess.SY↗

arXiv2025

The diverse and fair structures of growth with scale-free saturations

Real-world growth processes and scalings have been broadly categorized into three growth regimes with distinctly different properties and driving forces. The first two are characterized by a positive and constant feedback between growth and growth rates which in the context of networks lead to scale-free or single-scale networks. The third, sublinear, regime is characteristic of biological scaling processes and those that that are driven by optimization and efficiency. These systems are characterized by a negative feedback in growth rates and as such naturally exhibit saturations, i.e., areas where growth ceases from a lack of resources. Motivated by this observation, we propose and analyze a simple network growth process that is analogous to this sublinear regime and characterize how its scale-free saturations impact the diversity and fairness of its structural properties and give rise to scaling relations observed throughout complex systems and science.

physics.soc-ph↗

arXiv2025

A Minimax Optimal Controller for Positive Systems

We present an explicit solution to the discrete-time Bellman equation for minimax optimal control of positive systems under unconstrained disturbances. The primary contribution of our result relies on deducing a bound for the disturbance penalty, which characterizes the existence of a finite solution to the problem class. Moreover, this constraint on the disturbance penalty reveals that, in scenarios where a solution is feasible, the problem converges to its equivalent minimization problem in the absence of disturbances.

math.OC↗

arXiv2024

Minimax Linear Regulator Problems for Positive Systems

Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work considers a multi-disturbance minimax Linear Regulator (LR) framework for positive linear time-invariant systems in continuous time, which, analogous to the Linear-Quadratic Regulator (LQR) problem, can be utilized for the stabilization of positive systems. The problem is studied for nonnegative and state-bounded disturbances. Dynamic programming theory is leveraged to derive explicit solutions to the minimax LR problem for both finite and infinite time horizons. In addition, a fixed-point method is proposed that computes the solution for the infinite horizon case, and the minimum L1-induced gain of the system is studied. We motivate the prospective scalability properties of our framework with a large-scale water management network.

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

Performance bounds for multi-vehicle networks with local integrators

In this work, we consider the problem of coordinating a collection of $n$th-order integrator systems. The coordination is achieved through the novel serial-consensus design, which can be seen as a method for achieving a stable closed-loop while only using local relative measurements. Earlier work has shown that second-order serial consensus can stabilize a collection of double integrators with scalable performance conditions, independent of the number of agents and topology. In this paper, we generalize these performance results to an arbitrary order $n\geq 1$. The derived performance bound depends on the condition number, measured in the vector-induced maximum matrix norm, of a general diagonalizing matrix. We provide an exact characterization of how a minimal condition number can be achieved. Third-order serial consensus is illustrated through a case study of PI-controlled vehicular formation, where the added integrators are used to mitigate the effect of unmeasured load disturbances. The theoretical results are illustrated through examples.

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↗

arXiv2024

Closed-loop design for scalable performance of vehicular formations

This paper presents a novel control design for vehicular formations, which is an alternative to the conventional second-order consensus protocol. The design is motivated by the closed-loop system, which we construct as first-order systems connected in series, and is therefore called serial consensus. The serial consensus design will guarantee stability of the closed-loop system under the minimum requirement of the underlying communication graphs each containing a connected spanning tree -- something that is not true in general for the conventional consensus protocols. Here, we show that the serial consensus design also gives guarantees on the worst-case transient behavior of the formation, which are independent of the number of vehicles and the underlying graph structure. In particular this shows that the serial consensus design can be used to guarantee string stability of the formation, and is therefore suitable for directed formations. We show that it can be implemented through message passing or measurements to neighbors at most two hops away. The results are illustrated through numerical examples.

math.OC↗

arXiv2024

Scalable Reinforcement Learning for Linear-Quadratic Control of Networks

Distributed optimal control is known to be challenging and can become intractable even for linear-quadratic regulator problems. In this work, we study a special class of such problems where distributed state feedback controllers can give near-optimal performance. More specifically, we consider networked linear-quadratic controllers with decoupled costs and spatially exponentially decaying dynamics. We aim to exploit the structure in the problem to design a scalable reinforcement learning algorithm for learning a distributed controller. Recent work has shown that the optimal controller can be well approximated only using information from a $\kappa$-neighborhood of each agent. Motivated by these results, we show that similar results hold for the agents' individual value and Q-functions. We continue by designing an algorithm, based on the actor-critic framework, to learn distributed controllers only using local information. Specifically, the Q-function is estimated by modifying the Least Squares Temporal Difference for Q-functions method to only use local information. The algorithm then updates the policy using gradient descent. Finally, we evaluate the algorithm through simulations that indeed suggest near-optimal performance.

eess.SY↗

arXiv2023

Minimax Linear Optimal Control of Positive Systems

We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the Bellman equation can be obtained, revealing that the optimal control policy (among all possible policies) is linear. This policy can in turn be computed through standard value iterations. Moreover, the feedback matrix of the optimal controller inherits the sparsity structure from the constraint matrix of the problem statement. This permits structural controller constraints in the problem design and simplifies the application to large-scale systems. We use a simple example of voltage control in an electric network to illustrate the problem setup.

math.OC↗

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↗

arXiv2023

A closed-loop design for scalable high-order consensus

This paper studies the problem of coordinating a group of $n$th-order integrator systems. As for the well-studied conventional consensus problem, we consider linear and distributed control with only local and relative measurements. We propose a closed-loop dynamic that we call serial consensus and prove it achieves $n$th order consensus regardless of model order and underlying network graph. This alleviates an important scalability limitation in conventional consensus dynamics of order $n\ge 2$, whereby they may lose stability if the underlying network grows. The distributed control law which achieves the desired closed loop dynamics is shown to be localized and obey the limitation to relative state measurements. Furthermore, through use of the small-gain theorem, the serial consensus system is shown to be robust to both model and feedback uncertainties. We illustrate the theoretical results through examples.

math.OC↗