arXiv subjects

Armin Nurkanovic

Publications and source records attributed to Armin Nurkanovic.

6 recordsLinked to original sources

arXiv2026

Economic Nonlinear Model Predictive Control for Microgrids with Generator Up and Downtime Constraints

Recently there has been a lot of progress in the development of economic nonlinear model predictive control (NMPC) schemes for multistage optimal power flow (OPF) problems. However, the additional inclusion of discrete decision variables to model generator runtimes and generator startup costs can amount to large scale mixed-integer nonlinear programs (MINLPs) that are computationally very challenging. This work investigates the practical approach that replaces the nonlinear AC power flow equations by convex quadratic approximations. In combination with the discrete generator dynamics this leads to a mixed-integer quadratically constrained program (MIQCP) which is of significantly lower complexity and can be solved in reasonable time by off-the-shelf solvers such as CPLEX. We further show that simple terminal constraints are not sufficient to guarantee recursive feasibility of the NMPC scheme if constraints on generator runtime and on the number of generator startup events are present. To address this challenge we propose the use of additional time-coupled constraints and prove the resulting recursive feasibility property. Based on the assumption of periodic dissipativity of the underlying system we can prove stability of the proposed controller. To illustrate our results, we present simulations of a realistic 6-bus microgrid under different demand scenarios.

math.OC↗

arXiv2025

An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints

This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.

math.OC↗

arXiv2024

Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds and Fast Implementation in acados

The Real-Time Iteration (RTI) is an online nonlinear model predictive control algorithm that performs a single Sequential Quadratic Programming (SQP) per sampling time. The algorithm is split into a preparation and a feedback phase, where the latter one performs as little computations as possible solving a single prepared quadratic program. To further improve the accuracy of this method, the Advanced-Step RTI (AS-RTI) performs additional Multi-Level Iterations (MLI) in the preparation phase, such as inexact or zero-order SQP iterations on a problem with a predicted state estimate. This paper extends and streamlines the existing local convergence analysis of AS-RTI, such as analyzing MLI of level A and B for the first time, and significantly simplifying the proofs for levels C and D. Moreover, this paper provides an efficient open-source implementation in acados, making it widely accessible to practitioners.

math.OC↗

arXiv2024

A Long-Short-Term Mixed-Integer Formulation for Highway Lane Change Planning

This work considers the problem of optimal lane changing in a structured multi-agent road environment. A novel motion planning algorithm that can capture long-horizon dependencies as well as short-horizon dynamics is presented. Pivotal to our approach is a geometric approximation of the long-horizon combinatorial transition problem which we formulate in the continuous time-space domain. Moreover, a discrete-time formulation of a short-horizon optimal motion planning problem is formulated and combined with the long-horizon planner. Both individual problems, as well as their combination, are formulated as MIQP and solved in real-time by using state-of-the-art solvers. We show how the presented algorithm outperforms two other state-of-the-art motion planning algorithms in closed-loop performance and computation time in lane changing problems. Evaluations are performed using the traffic simulator SUMO, a custom low-level tracking model predictive controller, and high-fidelity vehicle models and scenarios, provided by the CommonRoad environment.

cs.RO↗

arXiv2022

LCQPow -- A Solver for Linear Complementarity Quadratic Programs

In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in engineering and economics, and they are challenging to solve due to their structural violation of standard constraint qualifications, and highly nonconvex, nonsmooth feasible sets. This work extends a previously presented algorithm based on a sequential convex programming approach applied to a standard penalty reformulation. We examine the behavior of local convergence and introduce new algorithmic features. Competitive performance profiles are presented in comparison to state-of-the-art solvers and solution variants in both existing and new benchmarks.

math.OC↗

arXiv2021

A Sequential Convex Programming Approach to Solving Quadratic Programs and Optimal Control Problems with Linear Complementarity Constraints

Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with linear complementarity constraints. A novel approach to solving a penalty reformulation using sequential convex programming and a homotopy on the penalty parameter is introduced. Linearizing the necessarily nonconvex penalty function yields convex quadratic subproblems, which have a constant Hessian matrix throughout all iterates. This allows solution computation with a single KKT matrix factorization. Furthermore, a globalization scheme is introduced in which the underlying merit function is minimized analytically, and guarantee of descent is provided at each iterate. The algorithmic features and possible computational speedups are illustrated in a numerical experiment.

math.OC↗