arXiv subjects

Pablo Krupa

Publications and source records attributed to Pablo Krupa.

22 records · Page 2Linked to original sources

arXiv2021

Implementation of MPC in embedded systems using first order methods

This Ph.D. dissertation contains results in two different but related fields: the implementation of model predictive control (MPC) in embedded systems using first order methods, and restart schemes for accelerated first order methods (AFOM). We start by presenting three novel restart schemes for AFOM. These schemes can improve the convergence of the AFOM by suppressing the undesirable oscillations that they are prone to present. The schemes we develop have theoretical guarantees and do not require knowledge of difficult-to-obtain parameters of the optimization problem. Next, we present sparse solvers for various MPC formulations which take advantage of the structures of the optimization problems. The solvers have been made available in an open-source toolbox for Matlab called SPCIES (https://github.com/GepocUS/Spcies). Finally, we present a novel MPC formulation that displays a larger domain of attraction and better performance than other MPC formulations, especially when using small prediction horizons. This, along with its recursive feasibility and asymptotic stability, makes it especially suitable for its implementation in embedded systems.

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arXiv2021

Real-time implementation of MPC for tracking in embedded systems: Application to a two-wheeled inverted pendulum

This article presents the real-time implementation of the model predictive control for tracking formulation to control a two-wheeled inverted pendulum robot. This formulation offers several advantages over standard MPC formulations at the expense of the addition of a small number of decision variables, which complicates the inner structure of the matrices of the optimization problem. We implement a sparse solver, based on an extension of the alternating direction method of multipliers, in the system's embedded hardware. The results indicate that the solver is suitable for controlling a real system with sample times in the range of milliseconds using current, readily-available hardware.

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arXiv2021

Harmonic based model predictive control for set-point tracking

This paper presents a novel model predictive control (MPC) formulation for set-point tracking. Stabilizing predictive controllers based on terminal ingredients may exhibit stability and feasibility issues in the event of a reference change for small to moderate prediction horizons. In the MPC for tracking formulation, these issues are solved by the addition of an artificial equilibrium point as a new decision variable, providing a significantly enlarged domain of attraction and guaranteeing recursive feasibility for any reference change. However, it may suffer from performance issues if the prediction horizon is not large enough. This paper presents an extension of this formulation where a harmonic artificial reference is used in place of the equilibrium point. The proposed formulation achieves even greater domains of attraction and can significantly outperform other MPC formulations when the prediction horizon is small. We prove the asymptotic stability and recursive feasibility of the proposed controller, as well as provide guidelines for the design of its main ingredients. Finally, we highlight its advantages with a case study of a ball and plate system.

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arXiv2019

Restart FISTA with Global Linear Convergence

Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some applications that slows its convergence. Restart schemes seek to improve the convergence of FGM algorithms by suppressing the oscillatory behaviour. Recently, a restart scheme for FGM has been proposed that provides linear convergence for non strongly convex optimization problems that satisfy a quadratic functional growth condition. However, the proposed algorithm requires prior knowledge of the optimal value of the objective function or of the quadratic functional growth parameter. In this paper we present a restart scheme for FISTA algorithm, with global linear convergence, for non strongly convex optimization problems that satisfy the quadratic growth condition without requiring the aforementioned values. We present some numerical simulations that suggest that the proposed approach outperforms other restart FISTA schemes.

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