arXiv subjects

Gösta Stomberg

Publications and source records attributed to Gösta Stomberg.

9 recordsLinked to original sources

arXiv2026

A Feedback Stability Theorem for Frequency-dependent Compensation of Excess and Lack of Passivity

This article studies the stability of feedback interconnections of linear time-invariant systems based on frequency-dependent passivity indices. Using these frequency-dependent passivity indices, we show that the feedback interconnection of two systems can be certified to be stable even if both systems have a lack of passivity in terms of their scalar passivity indices. The main contribution of this paper is a new stability theorem based on frequency-dependent passivity indices. Moreover, we discuss the connection of the proposed feedback stability theorem to prior results based on scalar passivity indices. A numerical case study showcases the advantages of frequency-dependent passivity indices over scalar indices for feedback interconnections of linear systems.

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arXiv2026

EMT and RMS Modeling of Thyristor Rectifiers for Stability Analysis of Converter-Based Systems

Thyristor rectifiers are a well-established and cost-effective solution for controlled high-power rectification, commonly used for hydrogen electrolysis and HVDC transmission. However, small-signal modeling and analysis of thyristor rectifiers remain challenging due to their line-commutated operation and nonlinear switching dynamics. This paper first revisits conventional RMS-based modeling of thyristor rectifiers and subsequently proposes a novel nonlinear state-space EMT model in the dq domain that can be linearized for small-signal analysis. The proposed model accurately captures all the relevant dynamic phenomena, including PLL dynamics, the commutation process, and switching delays. It is derived in polar coordinates, offering novel insights into the impact of the PLL and commutation angle on the thyristor rectifier dynamics. We verify the RMS and EMT models against a detailed switching model and demonstrate their applicability through small-signal stability analysis of a modified IEEE 39-bus test system that incorporates thyristor rectifier-interfaced hydrogen electrolyzers, synchronous generators, and grid-forming converters.

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arXiv2025

Decentralized non-convex optimization via bi-level SQP and ADMM

Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high subproblem complexity. We present a novel bi-level SQP method, where the inner quadratic problems are solved via ADMM. A decentralized stopping criterion from inexact Newton methods allows the early termination of ADMM as an inner algorithm to improve computational efficiency. The method has local convergence guarantees for non-convex problems. Moreover, it only solves sequences of Quadratic Programs, whereas many existing algorithms solve sequences of Nonlinear Programs. The method shows competitive numerical performance for an optimal power flow problem.

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arXiv2025

Decentralized Real-Time Iterations for Distributed NMPC

This article presents a Real-Time Iteration (RTI) scheme for distributed Nonlinear Model Predictive Control (NMPC). The scheme transfers the well-known RTI approach, a key enabler for many industrial real-time NMPC implementations, to the setting of cooperative distributed control. At each sampling instant, one outer iteration of a bi-level decentralized Sequential Quadratic Programming (dSQP) method is applied to a centralized optimal control problem. This ensures that real-time requirements are met and it facilitates cooperation between subsystems. Combining novel dSQP convergence results with RTI stability guarantees, we prove local exponential stability under standard assumptions on the MPC design with and without terminal constraints. The proposed scheme only requires neighbor-to-neighbor communication and avoids a central coordinator. A numerical example with coupled inverted pendulums demonstrates the efficacy of the approach.

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arXiv2025

Large problems are not necessarily hard: A case study on distributed NMPC paying off

A key motivation in the development of Distributed Model Predictive Control (DMPC) is to accelerate centralized Model Predictive Control (MPC) for large-scale systems. DMPC has the prospect of scaling well by parallelizing computations among subsystems. However, communication delays may deteriorate the performance of decentralized optimization, if excessively many iterations are required per control step. Moreover, centralized solvers often exhibit faster asymptotic convergence rates and, by parallelizing costly linear algebra operations, they can also benefit from modern multicore computing architectures. On this canvas, we study the computational performance of cooperative DMPC for linear and nonlinear systems. To this end, we apply a tailored decentralized real-time iteration scheme to frequency control for power systems. DMPC scales well for the considered linear and nonlinear benchmarks, as the iteration number does not depend on the number of subsystems. Comparisons with multi-threaded centralized solvers demonstrate competitive performance of the proposed decentralized optimization algorithms.

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arXiv2025

Cooperative distributed model predictive control for embedded systems: Experiments with hovercraft formations

This paper presents experiments for embedded cooperative distributed model predictive control applied to a team of hovercraft floating on an air hockey table. The hovercraft collectively solve a centralized optimal control problem in each sampling step via a stabilizing decentralized real-time iteration scheme using the alternating direction method of multipliers. The efficient implementation does not require a central coordinator, executes onboard the hovercraft, and facilitates sampling intervals in the millisecond range. The formation control experiments showcase the flexibility of the approach on scenarios with point-to-point transitions, trajectory tracking, collision avoidance, and moving obstacles.

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arXiv2023

An essentially decentralized interior point method for control

Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems with non-convex constraints for which classical decentralized optimization algorithms lack convergence guarantees. Moreover, classical decentralized algorithms usually exhibit only linear convergence. This paper presents an essentially decentralized primal-dual interior point method with convergence guarantees for non-convex problems at a superlinear rate. We show that the proposed method works reliably on a numerical example from power systems. Our results indicate that the proposed method outperforms ADMM in terms of computation time and computational complexity of the subproblems.

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arXiv2023

Cooperative Distributed MPC via Decentralized Real-Time Optimization: Implementation Results for Robot Formations

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion with nominal convergence guarantees. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

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arXiv2021

A Distributed Active Set Method for Model Predictive Control

This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An advantage of the proposed method compared to existing distributed model predictive algorithms is the primal feasibility of the iterates. Numerical results show that the proposed method can compete with the alternating direction method of multipliers in terms of communication requirements for a chain of masses example.

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