On Relaxations Applicable to Model Predictive Control for Systems with Binary Control Signals

• In this work, different relaxations applicable to an MPC problem with binary control signals are compared. The relaxations considered are the QP relaxation, the standard SDP relaxation and an equality constrained SDP relaxation. The relaxations are related theoretically and both the tightness of the bounds and the computational complexities are compared in numerical experiments.The result is that the standard SDP relaxation is the one that usually gives the best bound and is most computationally demanding, while the QP relaxation is the one that gives the worst bound and is least computationally demanding. The equality constrained relaxation presented in this paper often gives a better bound than the QP relaxation and is much less computationally demanding compared to the standard SDP relaxation. Furthermore, for a special case, it is shown that the equality constrained SDP relaxation can be cast in the form of a QP. This makes it possible to replace the ordinary QP relaxation usually used in branch and bound for these problems witha tighter SDP relaxation. Numerical experiments indicate that this relaxation can decrease the overall computational time spent in branch and bound.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

Predictive control

Hybrid systems

Binary control

Integer programming

Semidefinite programming

TECHNOLOGY

TEKNIKVETENSKAP

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