NOSNOC: A Software Package for Numerical Optimal Control of Nonsmooth Systems

Nurkanović, Armin; Diehl, Moritz

doi:10.1109/lcsys.2022.3181800

Cited by 12 publications

(2 citation statements)

References 12 publications

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“…The Moreau-Jean event-capturing algorithm, which is an extension of ( 86) with a θ-method [55,374,375,6,7] allows to solve numerically generalized equations as (19), with frictional contact. Specific event-capturing schemes inspired from Moreau-Jean are used in [376] to compute optimal controllers (with an application on a jumping robot in [347]). Another, less known, time-stepping scheme is the Schatzman-Paoli algorithm [377,378].…”

Section: Time-discretization For Simulation and Controlmentioning

confidence: 99%

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

Brogliato

2023

Annual Reviews in Control

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Section: Time-discretization For Simulation and Controlmentioning

confidence: 99%

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

Brogliato

2023

Annual Reviews in Control

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“…Smooth penalty methods for some minimax optimal control problems were proposed by Gorelik and Tarakanov [32,33]. An efficient numerical method for optimal control of piecewise smooth systems was recently developed by Nurkanović and Diehl [59], while a method based on discretisation of nonsmooth optimal control problems with state constraints with the use of the so-called pseudospectral knotting technique was presented by Ross and Fahroo [70]. An approach to some nonsmooth optimal control problems based on smoothing approximations was considered by Noori Skandari et al [25,57].…”

Section: Introductionmentioning

confidence: 99%

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Долгополик¹

2023

Preprint

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A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control constraints is presented, in which the the penalty parameter and several line search parameters are adaptively adjusted during the optimisation process. This class of methods is applicable to problems having a known DC (Differenceof-Convex functions) structure and in its core is based on the classical DCA method, combined with the steering exact penalty rules for updating the penalty parameter and an adaptive nonmonotone line search procedure. Under the assumption that all auxiliary subproblems are solved only approximately (that is, with finite precision), we prove the correctness of the proposed family of methods and present its detailed convergence analysis. The performance of several different versions of the method is illustrated by means of a numerical example, in which the methods are applied to a semi-academic optimal control problem with a nonsmooth nonconvex state constraint.

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Finite Elements with Switch Detection for direct optimal control of nonsmooth systems

Nurkanović,

Sperl,

Albrecht

et al. 2024

Numer. Math.

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This paper introduces Finite Elements with Switch Detection (FESD), a numerical discretization method for nonsmooth differential equations. We consider the Filippov convexification of these systems and a transformation into dynamic complementarity systems introduced by Stewart (Numer Math 58(1):299–328, 1990). FESD is based on solving nonlinear complementarity problems and can automatically detect nonsmooth events in time. If standard time-stepping Runge–Kutta (RK) methods are naively applied to a nonsmooth ODE, the accuracy is at best of order one. In FESD, we let the integrator step size be a degree of freedom. Additional complementarity conditions, which we call cross complementarities, enable exact switch detection, hence FESD can recover the high order accuracy that the RK methods enjoy for smooth ODE. Additional conditions called step equilibration allow the step size to change only when switches occur and thus avoid spurious degrees of freedom. Convergence results for the FESD method are derived, local uniqueness of the solution and convergence of numerical sensitivities are proven. The efficacy of FESD is demonstrated in several simulation and optimal control examples. In an optimal control problem benchmark with FESD, we achieve up to five orders of magnitude more accurate solutions than a standard time-stepping approach for the same computational time.

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NOSNOC: A Software Package for Numerical Optimal Control of Nonsmooth Systems

Cited by 12 publications

References 12 publications

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Finite Elements with Switch Detection for direct optimal control of nonsmooth systems

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