A linear programming approach for multivariable feedback control with inequality constraints

Chang, Ting-Wei; Seborg, Dale E.

doi:10.1080/00207178308932994

Cited by 58 publications

(14 citation statements)

References 8 publications

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“…For example, Zadeh and Whalen [9] and Propoi [10] introduce the approaches to solve MPC problem based on linear programming in the early sixties. And some other authors published their investigation concerning the linear programming based MPC [11]- [14].…”

Section: B Linear Programming Formulationmentioning

confidence: 99%

Two neural network approaches to model predictive control

Pan

Wang

2008

2008 American Control Conference

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Model predictive control (MPC) is a powerful technique for optimizing the performance of control systems. However, the high computational demand in solving optimization problem associated with MPC in real-time is a major obstacle. Recurrent neural networks have various advantages in solving optimization problems. In this paper, we apply two recurrent neural network models for MPC based on linear and quadratic programming formulations. Both neural networks have good convergence performance and low computational complexity. A numerical example is provided to illustrate the effectiveness and efficiency of the proposed methods and show the different control behaviors of the two neural network approaches.

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Section: B Linear Programming Formulationmentioning

confidence: 99%

Two neural network approaches to model predictive control

Pan

Wang

2008

2008 American Control Conference

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“…Define Xsp to contain a sequence of set-points for the outputs up to the time horizon, so that the open-loop error may be calculated in advance as XOL -XSP. Then the ideal control sequence Lim will be the one which minimises the magnitudes of the elements of the residual r =xoL-xsp+BLim Transforming and adding a term for move suppression (Morshedi et ai, 1985), we minimise rather the magnitude of Minimisation of the size of each term in p , yet keeping Lim, m and XCL within defined upper and lower constraints, is achieved using the linear programming technique of Chang and Seborg (1983).…”

Section: Control Algorithmmentioning

confidence: 99%

“…Both control actions will affect the entire concentration profile, so some minimisation of future deviations from setpoint over a time horizon is essential. A constrained multivariable Linear Dynamic Matrix Controller (LDMC), based on the linear programming solution of Chang and Seborg (1983), and the formulation ofMorshedi et at (1985), has been formulated as follows:…”

Section: Control Algorithmmentioning

confidence: 99%

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Constrained predictive control of a counter-current extractor

Mulholland

Narotam

1996

System Modelling and Optimization

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Continuous counter-current liquid-liquid extraction of copper from an acidic aqueous solution is performed in a 6m pulsed packed column. Bubbles of an immiscible organic phase, containing the complexing agent LIX 64N, move upward as the continuous aqueous phase moves downward. It is desired to regulate the residual copper content of the departing aqueous phase, using as control actions the organic feed rate and the pulse frequency. In this distributed system, profiles of copper concentration become imprinted on the descending aqueous phase as a result of the history of controls and disturbances acting during the passage of a parcel. Initial work has involved the development of a dynamic model of the extractor, and the proving of a constrained model predictive controller on this model. The model is based on a spectral solution along the discretised column length, with special treatments of convection and the boundary conditions. The Linear Dynamic Matrix Controller (LDMC) minimises the summed magnitudes of deviation from setpoint, over a time horizon of up to 50 steps. The algorithm used is based on the method of Chang and Seborg (1983).

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“…This MPC approach is also applied in general resource allocation or scheduling problems as done in Ferrari-Trecate et al (2004), Lee et al (2007), Lee and Lee (2006), Munawar and Gudi (2005), van Staden, Zhang, andZafra-Cabeza et al (2008) MPC algorithm needs to solve an optimization problem in each iteration. Studies on the connections of MPC with optimization were conducted since the 1960's (see Chang and Seborg (1983) and Zadeh and Whalen (1962)). Modern MPC approaches for resource allocation problems do not take the relationship of the MPC solutions and the global optimal resource allocation solutions into consideration.…”

Section: Introductionmentioning

confidence: 99%

A model predictive control approach to the periodic implementation of the solutions of the optimal dynamic resource allocation problem

Zhang

Xia

2011

Automatica

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Available online xxxx Keywords:Model predictive control Perfect optimal dynamic resource allocation problem Energy optimization a b s t r a c t This paper proposes a model predictive control (MPC) approach to the periodic implementation of the optimal solutions of a class of resource allocation problems in which the allocation requirements and conditions repeat periodically over time. This special class of resource allocation problems includes many practical energy optimization problems such as load scheduling and generation dispatch. The convergence and robustness of the MPC algorithm is proved by invoking results from convex optimization. To illustrate the practical applications of the MPC algorithm, the energy optimization of a water pumping system is studied.

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A linear programming approach for multivariable feedback control with inequality constraints

Cited by 58 publications

References 8 publications

Two neural network approaches to model predictive control

Two neural network approaches to model predictive control

Constrained predictive control of a counter-current extractor

A model predictive control approach to the periodic implementation of the solutions of the optimal dynamic resource allocation problem

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