On the design of exact penalty functions for MPC using mixed integer programming

Hovd, Morten; Stoican, Florin

doi:10.1016/j.compchemeng.2013.07.001

Cited by 15 publications

(9 citation statements)

References 24 publications

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“…On the other hand, in [4], additional constraints were imposed on the binary variables in order to force the uniqueness of λ (via the selection of rows from C). We consider this later approach superior and we will adapt it in the following subsection.…”

Section: Programmingmentioning

confidence: 99%

A linear MPC algorithm for embedded systems with computational complexity guarantees

Necoara

Stoican

Clipici

et al. 2014

2014 18th International Conference on System Theory, Control and Computing (ICSTCC)

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In this paper we propose a linear MPC scheme for embedded systems based on the dual fast gradient algorithm for solving the corresponding control problem. We establish computational complexity guarantees for the MPC scheme by appropriately deriving tight convergence estimates of order O(1/k 2 ) for an average primal sequence generated by our proposed numerical optimization algorithm. We also show that these estimates rely heavily upon the dual optimal variables (Lagrange multipliers). Since convergence certification in embedded MPC is essential, we also derive tight bounds on the norm of these dual optimal variables. However, computing the norm for the Lagrange multipliers associated to multi-parametric optimization problems can quickly become intractable for high dimension and/or a large set of constraints. Therefore, we recast the problem in a mixed integer formulation by using auxiliary binary variables to characterize the complementarity conditions. We also show that this problem can be solved numerically efficiently.

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Section: Programmingmentioning

confidence: 99%

A linear MPC algorithm for embedded systems with computational complexity guarantees

Necoara

Stoican

Clipici

et al. 2014

2014 18th International Conference on System Theory, Control and Computing (ICSTCC)

Self Cite

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“…Selecting a numerical value for µ may, however, be difficult. It is generally undesirable to assign an arbitrary high value to µ to ensure exactness of the penalty function, as this may lead to violent control action, possibly harmful to the actuators [11], as well as numerical ill-conditioning. We therefore seek to find a lower bound on µ in order to guarantee that the penalty function is exact.…”

Section: A Computing the Penalty Parametermentioning

confidence: 99%

“…Consequently, to computeμ for (6a), the maximum value of the ∞ norm of the Lagrangian multipliers for the hard-constrained problem for all initial states x ∈ S j must be calculated. To perform this computation, we use the mixed-integer linear programming (MILP) approach developed by [11]. Note that this computation must be performed for each safety set S j , corresponding to isolated actuators faults as well faults in several actuators simultaneously.…”

Section: A Computing the Penalty Parametermentioning

confidence: 99%

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An exact penalty-function approach to proactive fault-tolerant economic MPC

Knudsen

Brusevold

Foss

2016

2016 European Control Conference (ECC)

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Abstract-This paper presents a fault-tolerant economic model predictive control scheme for proactive handling of incipient actuator faults. The scheme applies an 1 exact penalty function with a set of switching rules in order to steer the system by a minimum-time approach inside a controlled invariant set where stability of the system can be preserved during loss of actuation from the faulty actuator. We consider the approach for linear control systems, thereby allowing computation of a lower bound for the penalty parameter to ensure exactness of the penalty function. We prove nominal asymptotic stability of the modes of the proposed model predictive control scheme, and illustrate the approach by a numerical example.

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“…The third single objective function is to adjust the three loopers' abundance when welding, trimming, or roll changing is taking place. However, in the restricted problem with equality constrained and inequality constrained conditions in equation (2), to simplify the solving process and easy programming, speed penalty index could be added to the objective function to transform constrained optimization problem into an unconstrained optimization problem, [12][13][14] then the objective function can be expressed as equation (3), where, v il and v iu are the lower and upper speed limit values of the ith section in m/s, and N is the penalty index coefficient (N = 20). When the setup speed v i is in the authorized range, the value of penalty index is approximately zero.…”

Section: Objective Function Designmentioning

confidence: 99%

A new speed optimization algorithm with application in pickling and rolling line

Zhu

Wang

Zhang

et al. 2016

Advances in Mechanical Engineering

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In order to reduce equipment wear and operator pressure, as well as to improve the production efficiency of combined continuous pickling line and tandem cold rolling mill units, four sections' speeds should be automatically optimized to control the three loopers' abundance, which include the entry loopers' entry speed, pickling speed, trimming speed, and tandem cold rolling mill entry speed. According to the optimal speed principle, a new optimization algorithm was proposed based on objective function. In this work, Nelder-Mead simplex method is applied to find the optimal solution by minimizing the objective function. In addition, the calculation of four initial speeds is specified, especially the initial tandem cold rolling mill entry speed. The proposed speed optimization algorithm was successfully applied to a 1450 mm continuous pickling line and tandem cold rolling mill. The acceleration and deceleration are smooth and steady when welding, trimming, or roll changing takes place in practice, the three loopers' abundance are controlled in suitable range. Results show that the continuous pickling line unit could provide the material in maximum capacity to ensure that the tandem cold rolling mill unit's production is efficient, and the rolling yield is greatly improved due to the decrease in the number of stops.

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On the design of exact penalty functions for MPC using mixed integer programming

Cited by 15 publications

References 24 publications

A linear MPC algorithm for embedded systems with computational complexity guarantees

A linear MPC algorithm for embedded systems with computational complexity guarantees

An exact penalty-function approach to proactive fault-tolerant economic MPC

A new speed optimization algorithm with application in pickling and rolling line

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