arXiv subjects

Alba Gurpegui

Publications and source records attributed to Alba Gurpegui.

7 recordsLinked to original sources

arXiv2026

General-Sum Linear Regulator Games for Positive Systems

This paper studies a continuous-time general-sum non-cooperative game with linear costs, positive linear system dynamics, and elementwise linear input constraints. In the finite-horizon case, we present a verification theorem characterizing feedback Nash equilibria, in terms of absolutely continuous solutions of a coupled system of vector-valued ordinary differential equations, realized by time-varying feedback laws. Unlike linear-quadratic differential games, whose Riccati-based equilibria scale quadratically with the state dimension, this formulation scales linearly. However, the resulting piecewise-constant feedback saturates between its constraint bounds rather than varying smoothly, and additional mathematical challenges arise when characterizing the solutions of the differential equations, which are generally discontinuous due to the switching nature of the feedback gains. In this work, we study the case where switching occurs only at isolated time instants. In the infinite-horizon case, under stabilizability assumptions, the equilibrium is characterized by coupled vector-valued algebraic equations. For this game, we propose iterative methods to compute both finite and infinite-horizon equilibria. The approach is illustrated through a large-scale pollution game.

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arXiv2026

L1 Optimal Control of Continuous-Time Stochastic Positive Systems

We present an L1-optimal control problem class with linear nonnegative costs subject to multiplicative It\^o diffusion processes with elementwise linear input constraints. Forward invariance of the positive orthant is established for the considered stochastic dynamics, and a simulation method consistent with this invariance property is proposed. Both finite-horizon and discounted infinite-horizon stochastic L1-optimal control problems are considered. These problems admit explicit solutions characterized by a vector-valued ordinary differential equation in the finite-horizon case and by an algebraic equation in the infinite-horizon case. Notably, the optimal value function and feedback policy coincide with those of the corresponding deterministic problem, demonstrating robustness to multiplicative stochastic uncertainty. A portfolio example illustrates our results.

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arXiv2026

Scalable Design of Attack-Resilient Controllers for Positive Systems

This paper proposes a framework for secure and resilient controller design for positive systems against cyber-attacks. In particular, we consider a network-controlled system where an adversary injects false data into the actuator channels to increase the control cost (performance measure) while penalizing the attack effort and subject to state-dependent constraints. Using a minimax formulation, we analyze the worst-case performance loss caused by such adversaries, which is given by the solution of a difference equation, and an algebraic equation when the time horizon is infinite. We show that the optimal attack policy, among possible nonlinear policies, is linear. Despite the lack of explicit stealthiness constraints, we also show that when the measured output has an unstable zero which is not an unstable zero of the performance measure, the attacks can induce unbounded performance degradation. The proposed framework is also extended to systems with model uncertainty. Numerical examples illustrate the results and demonstrate how tools from positive systems and linear regulator theory can be used to mitigate cyber-attacks with low computational effort.

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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.

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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.

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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.

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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.

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