arXiv subjects

Mark Jeeninga

Publications and source records attributed to Mark Jeeninga.

5 recordsLinked to original sources

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↗

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↗

arXiv2020

DC power grids with constant-power loads -- Part I: A full characterization of power flow feasibility, long-term voltage stability and their correspondence

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. In Part I of this paper we present a detailed introduction to the problem of power flow feasibility of such power grids, and the associated problem of selecting a desirable operating point which satisfies the power flow equations. We introduce and identify all long-term voltage semi-stable operating points, and show that there exists a one-to-one correspondence between such operating points and the constant power demands for which the power flow equations are feasible. Such operating points can be found by solving an initial value problem, and a parametrization of these operating points is also obtained. In addition, we give a full characterization of the set of all feasible power demands, and give a novel proof for the convexity of this set. Moreover, we present a necessary and sufficient LMI condition for the feasibility of a vector of power demands under small perturbation, which extends a necessary condition in the literature.

eess.SY↗

arXiv2020

DC power grids with constant-power loads -- Part II: nonnegative power demands, conditions for feasibility, and high-voltage solutions

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part I. In particular, we refine several results in Part I to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which is cheaper to compute than the necessary and sufficient LMI condition in Part I. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. In addition, we prove that the unique long-term voltage semi-stable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is also obtained, along with a parametrization of the boundary of the set of feasible power demands.

math.OC↗

arXiv2019

Plug-and-play Solvability of the Power Flow Equations for Interconnected DC Microgrids with Constant Power Loads

In this paper we study the DC power flow equations of a purely resistive DC power grid which consists of interconnected DC microgrids with constant-power loads. We present a condition on the power grid which guarantees the existence of a solution to the power flow equations. In addition, we present a condition for any microgrid in island mode which guarantees that the power grid remains feasible upon interconnection. These conditions provide a method to determine if a power grid remains feasible after the interconnection with a specific microgrid with constant-power loads. Although the presented condition are more conservative than existing conditions in the literature, its novelty lies in its plug-and-play property. That is, the condition gives a restriction on the to-be-connected microgrid, but does not impose more restrictions on the rest of the power grid.

math.OC↗