arXiv subjects

Jan Olucak

Publications and source records attributed to Jan Olucak.

5 recordsLinked to original sources

arXiv2026

Safe-by-Design: Approximate Nonlinear Model Predictive Control with Real Time Feasibility

This paper proposes a computationally lightweight, continuous-time receding-horizon nonlinear model predictive control (MPC) approach with infinitesimal prediction horizon. Unlike discrete-time one-step MPC schemes, this methodology permits the formulation of small-sized convex quadratic pro- grams (QPs) for feedback yet recovers the theoretical guarantees of quasi-infinite horizon MPC. The convex QP comes with a small computational footprint, which is advantageous for real- time application where runtime guarantees must be given. We demonstrate the effectiveness of the proposed approach when compared to other constrained control techniques through numerical experiments for nonlinear constrained spacecraft control.

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arXiv2026

Input-to-state Stable Approximate Nonlinear Model Predictive Control with Realtime Feasibility

In this paper, a computationally lightweight approximate robust nonlinear model predictive control (NMPC) law is proposed based on a pair of input-to-state control Lyapunov function and robust control barrier function. The result builds upon and augments a recently introduced nominal infinitesimal- horizon NMPC scheme which permits small-sized quadratic programs to compute the feedback law for nonlinear constraint systems on embedded hardware in real time. Numerical experiments for nonlinear constrained spacecraft control and comparison to other robust NMPC schemes from the literature demonstrate the effectiveness of the proposed scheme.

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arXiv2026

On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems

Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs. However, in case of nonconvex problems iterative procedures are needed. Yet tractable and efficient solution methods are still lacking, limiting their application, for instance, in control engineering. To address this gap, we propose a filter line search algorithm that solves a sequence of quadratic subproblems. Numerical benchmarks demonstrate that the algorithm can significantly reduce the number of iterations, resulting in a substantial decrease in computation time compared to established methods for nonconvex SOS programs

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arXiv2024

CaΣoS: A nonlinear sum-of-squares optimization suite

We present Ca$Σ$oS, the first MATLAB software specifically designed for nonlinear sum-of-squares optimization. A symbolic polynomial algebra system allows to formulate parametrized sum-of-squares optimization problems and facilitates their fast, repeated evaluations. To that extent, we make use of CasADi's symbolic framework and realize concepts of monomial sparsity, linear operators (including duals), and functions between polynomials. Ca$Σ$oS currently provides interfaces to the conic solvers SeDuMi, Mosek, and SCS as well as methods to solve quasiconvex optimization problems (via bisection) and nonconvex optimization problems (via sequential convexification). Numerical examples for benchmark problems including region-of-attraction and reachable set estimation for nonlinear dynamic systems demonstrate significant improvements in computation time compared to existing toolboxes. Ca$Σ$oS is available open-source at https://github.com/ifr-acso/casos.

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arXiv2023

Real-time Nonlinear Model Predictive Control using One-step Optimizations and Reachable Sets

Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded hardware. To solve this problem, this paper proposes to compute a sequence of one-step optimizations aided by pre-computed inner approximations of reachable sets rather than solving the full-horizon optimal control problem at once. This feature can be used to virtually predict the future system behavior with a low computational footprint. Proofs for recursive feasibility and for the sufficient conditions for asymptotic stability under mild assumptions are given. The presented approach is demonstrated in simulation for functional verification.

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