Quadratic programming algorithms for large-scale model predictive control

Bartlett, Roscoe; Biegler, Lorenz T.; Backström, Johan U.; Gopal, Vipin

doi:10.1016/s0959-1524(02)00002-1

Cited by 74 publications

(55 citation statements)

References 16 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%

Fast Model Predictive Control Using Online Optimization

Wang

Boyd

2008

IFAC Proceedings Volumes

487

765

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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%

Fast Model Predictive Control Using Online Optimization

Wang

Boyd

2008

IFAC Proceedings Volumes

487

765

View full text Add to dashboard Cite

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“…Efficient interior point algorithms [25,26] and active set algorithms [2] have been tailored for the control of cross-directional variations using model predictive control. Both reported approaches exploit the sparse structure that arises if robustness considerations are ignored.…”

Section: Discussion Of Computationmentioning

confidence: 99%

Design of cross-directional controllers with optimal steady state performance

Heath

Wills

2003

2003 European Control Conference (ECC)

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Actuator constraint handling is necessary for many cross-directional controllers. We discuss how optimal steady state performance can be guaranteed by modifying an internal model control structure with a non-linear element. For the simple dynamics associated with most web processes this also gives good closed-loop dynamic behaviour. Thus unconstrained control design techniques may be applied directly to the constrained control problem.

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“…This section presents a fast QP solver, called QPSchur, which is specifically designed to solve a large scaled CD-MPC problem. QPSchur is a dual space algorithm, where an unconstrained optimal solution is found first and violated constraints are added until the solution is feasible (Bartlett 2002). Let's consider the Lagrangian of the constrained QP in (32)…”

Section: Fast Qp Solvermentioning

confidence: 99%