A Direct Multiple Shooting Method for Real-Time Optimization of Nonlinear DAE Processes

Bock, Hans Georg; Diehl, Moritz; Leineweber, Daniel B.; Schlöder, Johannes P.

doi:10.1007/978-3-0348-8407-5_14

Cited by 88 publications

(44 citation statements)

References 13 publications

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“…The scheme was introduced in its present form in Diehl et al [19] going back to ideas presented in Bock et al [10]. In its actual implementation it is able to treat differential algebraic equation (DAE) models (Leineweber [31]), as they often arise in practical applications.…”

Section: Introductionmentioning

confidence: 99%

A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control

Diehl¹,

Bock²,

Schlöder³

2005

SIAM J. Control Optim.

479

288

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Abstract. An efficient Newton-type scheme for the approximate on-line solution of optimization problems as they occur in optimal feedback control is presented. The scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process. The contractivity of this real-time iteration scheme is proven, and a bound on the loss of optimality-compared with the theoretical optimal solution-is given. The robustness and excellent real-time performance of the method is demonstrated in a numerical experiment, the control of an unstable system, namely, an airborne kite that shall fly loops. 1. Introduction. Feedback control based on the real-time optimization of nonlinear dynamic process models, also referred to as nonlinear model predictive control (NMPC), has attracted increasing attention over the past decade, particularly in chemical engineering [4,27,1,28]. Based on the current system state, feedback is provided by an online optimization of the predicted system behavior, using the mathematical model. The first part of the optimized control trajectory is implemented at the real system, and a sampling time later the optimization procedure is repeated. Among the advantages of this approach are the flexibility provided in formulating the objective and in modeling the process using ordinary or partial differential equations (ODEs or PDEs), the capability of directly handling equality and inequality constraints, and the possibility of treating large disturbances quickly.One important precondition, however, is the availability of reliable and efficient numerical optimal control algorithms. One particularly successful algorithm that is designed to achieve this aim, the recently developed real-time iteration scheme, will be the focus of this paper. In the literature, several suggestions have been made on how to adapt off-line optimal control algorithms for use in on-line optimization. For an overview and comparison of important approaches, see, e.g., Binder et al. [6]. We particularly mention here the "Newton-type control algorithm" proposed by Li and Biegler [32] and de Oliveira and Biegler [15] and the "feasibility-perturbed SQP" approach to NMPC by Tenny, Wright, and Rawlings [38]. Both approaches keep even intermediate optimization iterates feasible. This is in contrast to the simultaneous dynamic optimization methods, as the collocation method proposed in Biegler [5] or the direct multiple shooting method in Bock et al. [7] and in Santos [37], which allow

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Section: Introductionmentioning

confidence: 99%

A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control

Diehl¹,

Bock²,

Schlöder³

2005

SIAM J. Control Optim.

479

288

View full text Add to dashboard Cite

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“…The problem as formulated requires the solution of a nonlinear program, a computationally demanding, although tractable, problem. If the process model is stiff or has unstable dynamics, a simultaneous strategy, in which the discretization and optimization are performed simultane-Ž ously, is often advantageous Biegler 1997Biegler , 1998Bock et al . 1998 .…”

Section: Moving-horizon Estimationmentioning

confidence: 99%

Constrained process monitoring: Moving‐horizon approach

2002

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“…Multiple shooting is one of many methods which integrate, discretize and reshapes the problem formulation to a form accepted by NLP solvers [8,9,10]. In the multiple shooting method the time domain is divided into smaller time intervals and the DAE (Differential Algebraic Equation) models are integrated separately in each interval.…”

Section: B Direct Multiple Shootingmentioning

confidence: 99%

Management of harmonic propagation in a marine vessel by use of optimization

Skjong

Ochoa-Gimenez

Molinas

et al. 2015

2015 IEEE Transportation Electrification Conference and Expo (ITEC)

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Abstract-Advances in power electronics drive systems for variable speed operation has enabled extensive use of such solutions in the propulsion and thruster systems of marine vessels. These solutions however introduce current and voltage distortions that compromises the overall power quality of the onboard electrical system. This paper presents and discusses one approach for generating the harmonic current reference for an active filter based on optimization. Two relevant results are revealed by this study: 1) lower THD values are attained by performing system optimization compared to local compensation of one load, and 2) the lower THD values are achieved with a smaller active filter rating than the one required for local load compensation.

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A Direct Multiple Shooting Method for Real-Time Optimization of Nonlinear DAE Processes

Cited by 88 publications

References 13 publications

A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control

A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control

Constrained process monitoring: Moving‐horizon approach

Management of harmonic propagation in a marine vessel by use of optimization

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