Numerical Methods for Efficient and Fast Nonlinear Model Predictive Control

Bock, Hans Georg; Diehl, Moritz; Kühl, Peter; Kostina, Ekaterina; Schiöder, Johannes P.; Wirsching, Leonard

doi:10.1007/978-3-540-72699-9_13

Cited by 20 publications

(24 citation statements)

References 11 publications

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“…, N − 1, in which λ k i denotes the current value of the Lagrange multi-pliers for the nonlinear continuity constraints in (3c). Note that the linearized KKT conditions in (6) correspond to the KKT optimality conditions for the QP in (7), for a fixed active set A. In addition, each QP subproblem is convex because H k 0, e.g., for the Gauss-Newton Hessian approximation.…”

Section: Sqp Algorithm With Inexact Jacobiansmentioning

confidence: 99%

“…The function (·) defines the stage cost and the nonlinear system dynamics are formulated as an implicit system of ordinary differential equations (ODE) in (1c), which could additionally be extended with implicit algebraic equations. A common assumption is that the resulting system of differential-algebraic equations (DAE) is of index 1 [7]. The optimization problem is parametric, since it depends on the state estimatex 0 at the current sampling instant, through the initial value condition in (1b).…”

Section: Introductionmentioning

confidence: 99%

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Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control

Hespanhol

Quirynen

2019

Optimization Methods and Software

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Nonlinear model predictive control (NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or that may include implicit algebraic equations. This paper provides a local convergence analysis for the recently proposed adjoint-based sequential quadratic programming (SQP) algorithm that is based on a block-structured variant of the twosided rank-one (TR1) quasi-Newton update formula to efficiently compute Jacobian matrix approximations in a sparsity preserving fashion. A particularly efficient algorithm implementation is proposed in case an implicit integration scheme is used for discretization of the optimal control problem, in which matrix factorization and matrix-matrix operations can be avoided entirely. The convergence analysis results as well as the computational performance of the proposed optimization algorithm are illustrated for two simulation case studies of nonlinear MPC.

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Section: Sqp Algorithm With Inexact Jacobiansmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control

Hespanhol

Quirynen

2019

Optimization Methods and Software

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“…Therefore, a tight integration between optimization solver and simulator is desired to limit communication overhead. This tight integration comes as a result of problem-structure exploitation, decomposition techniques, and parallelization (Bock et al 2007). Some research efforts on reservoir-management control optimization focus attention on methods that reduce the search-space and memory requirements at the cost of solution accuracy; examples are proper orthogonal decomposition (van Doren et al 2006) and trajectory piecewise linearization (Cardoso 2009;Cardoso and Durlofsky 2010).…”

Section: Introductionmentioning

confidence: 99%

Output-Constraint Handling and Parallelization for Oil-Reservoir Control Optimization by Means of Multiple Shooting

2015

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We propose to formulate and solve the reservoir-control optimization problem with the direct multiple-shooting method. This method divides the optimal-control problem prediction horizon in smaller intervals that one can evaluate in parallel. Further, output constraints are easily established on each interval boundary and as such hardly affect computation time. This opens new opportunities to include state constraints on a much broader scale than is common in reservoir optimization today. However, multiple shooting deals with a large number of variables because it decides on the boundary-state variables of each interval. Therefore, we exploit the structure of the reservoir simulator to conceive a variable-reduction technique to solve the optimization problem with a reduced sequential quadratic-programming algorithm. We discuss the optimization-algorithm building blocks and focus on structure exploitation and parallelization opportunities. To demonstrate the method's capabilities to handle output constraints, the optimization algorithm is interfaced to an open-source reservoir simulator. Then, on the basis of a widely used reservoir model, we evaluate performance, especially related to output constraints. The performance of the proposed method is qualitatively compared with a conventional method.

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“…In this article, the ideas presented in [Diehl, 2002, Bock et al, 2005 are further developed. We propose an optimization algorithm for NMPC problems based on adjoints and inexact constraint Jacobians that follows the principles of real-time iterations.…”

Section: Introductionmentioning

confidence: 99%

An Adjoint-based Numerical Method for Fast Nonlinear Model Predictive Control

Wirsching

Albersmeyer

Kühl

et al. 2008

IFAC Proceedings Volumes

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The application of optimization-based control methods such as nonlinear model predictive control (NMPC) to real-world process models is still a major computational challenge. In this paper, we present a new numerical optimization scheme suited for NMPC. The SQP-type approach uses an inexact constraint Jacobian in its iterations and is based on adjoint derivatives, that can be computed very efficiently. In comparison to a similar real-time algorithm based on directional sensitivities and an exact constraint Jacobian, the computational complexity is significantly reduced. Both algorithms are applied to the model of a thermally coupled distillation column for disturbance rejection. The results provide a proof-of-principle for the proposed adjoint-based optimization approach.

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Numerical Methods for Efficient and Fast Nonlinear Model Predictive Control

Cited by 20 publications

References 11 publications

Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control

Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control

Output-Constraint Handling and Parallelization for Oil-Reservoir Control Optimization by Means of Multiple Shooting

An Adjoint-based Numerical Method for Fast Nonlinear Model Predictive Control

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