Interior point SQP strategies for large-scale, structured process optimization problems

Albuquerque, J. Sodré; Gopal, Vipin; Staus, George H.; Biegler, Lorenz T.; Ydstie, B. Erik

doi:10.1016/s0098-1354(98)00292-0

Cited by 35 publications

(18 citation statements)

References 10 publications

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“…Previous work that addresses efficient solution of the QPs that arise in MPC includes [27]- [29], and [63]; for efficient methods for large-scale MPC problems arising in chemical process control, see [30]- [32]. Efficient methods for robust MPC are addressed by [33]- [35].…”

Section: A Related Workmentioning

confidence: 99%

“…It can be factored efficiently using a specialized method described below for block tridiagonal matrices (which is related to the Riccati recursion in control theory) [27]- [29], [55], [56], or by treating it as a banded matrix, with bandwidth . Both of these methods require order flops ( [3], [4], [29]- [32], [55], [56] flops. The cost of step 3 is dominated by the other steps, since the Cholesky factorization of was already computed in step 1.…”

Section: Fast Computation Of the Newton Stepmentioning

confidence: 99%

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Fast Model Predictive Control Using Online Optimization

Wang

Boyd

2008

IFAC Proceedings Volumes

487

768

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Abstract-A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well-known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than five), few constraints, and short time horizons. In this paper, we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1284 constraints) in around 5 ms, allowing MPC to be carried out at 200 Hz.Index Terms-Model predictive control (MPC), real-time convex optimization.

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Section: A Related Workmentioning

confidence: 99%

Section: Fast Computation Of the Newton Stepmentioning

confidence: 99%

Fast Model Predictive Control Using Online Optimization

Wang

Boyd

2008

IFAC Proceedings Volumes

487

768

View full text Add to dashboard Cite

show abstract

“…Of course, many other nonlinear optimization techniques have been proposed in the literature to handle nonlinear MPC and some of these could also potentially mitigate/eliminate the convergence problems (e.g., sequential quadratic (SQP) approaches using PD IPM to solve the subproblems [40], feasibility-perturbed SQP programming [41], active set quadratic programming [42], reduced space interior point strategy [43]). …”

Section: F Other Mpc Solversmentioning

confidence: 99%

Reinforcement Learning Versus Model Predictive Control: A Comparison on a Power System Problem

Ernst

Glavić

Capitanescu

et al. 2009

IEEE Trans. Syst., Man, Cybern. B

183

112

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“…z,ż,z, · · · , z (r) are the flat output and its derivatives, and the order of derivative r corresponds to the controllability index satisfying Equation (5). In this formulation, the model reduces to a trivial dynamics Equation (5).…”

Section: Nonlinear Mpc For Flat Systemsmentioning

confidence: 99%

“…In [4], a direct multiple shooting approach is adapted to meet the specific requirements of NMPC. Sequential quadratic programming has also been successfully applied to this problem, e.g., [5,6]. A recent approach is sensitivity-based NMPC [7], whereby an approximate solution is calculated and then subsequently adjusted based on the sensitivity of the NLP to perturbations.…”

Section: Introductionmentioning

confidence: 99%

Fast Wavelet-Based Model Predictive Control of Differentially Flat Systems

2015

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A system is differentially flat if it is Lie-Bäcklund (L-B) equivalent to a free dynamical system that has dimensions equal to that of the input of the original system. Utilizing this equivalence, the problem of nonlinear model predictive control of a flat system can be reduced to a lower dimensional nonlinear programming problem with respect to the flat outputs. In this work, a novel computational method based on Haar wavelets in the time-domain for solving the resulting nonlinear programming problem is developed to obtain an approximation of the optimal flat output trajectory. The Haar wavelet integral operational matrix is utilized to transform the nonlinear programming problem to a finite dimensional nonlinear optimization problem. The proposed approach makes use of flatness as a structural property of nonlinear systems and the convenient mathematical properties of Haar wavelets to develop an efficient computational algorithm for nonlinear model predictive control of differentially flat systems. Further improvement on computational efficiency is achieved by providing solutions with multiple resolutions (e.g., obtaining high resolution solutions only for the near future, but allowing coarse approximation for the later stage in the prediction horizon).

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Interior point SQP strategies for large-scale, structured process optimization problems

Cited by 35 publications

References 10 publications

Fast Model Predictive Control Using Online Optimization

Fast Model Predictive Control Using Online Optimization

Reinforcement Learning Versus Model Predictive Control: A Comparison on a Power System Problem

Fast Wavelet-Based Model Predictive Control of Differentially Flat Systems

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