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Model Predictive Control Based on Linear Programming - The Explicit Solution

Author(s):

A. Bemporad, F. Borrelli, M. Morari
Conference/Journal:

vol. AUT01-06
Abstract:

For discrete-time linear time-invariant systems with constraints on inputs and states, we describe a method to determine explicitly, as a function of the initial state, the solution to optimal control problems that can be formulated using a linear program (LP). In particular, we focus our attention on performance criteria based on a mixed $1$/$infty$-norm, namely $1$-norm with respect to time and $infty$-norm with respect to space. We show that the optimal control profile is a piecewise affine and continuous function of the initial state. Thus, when optimal control profiles are computed at each time step as in model predictive control (MPC) schemes, the explicit piecewise affine form allows to eliminate on-line LP, as the computation associated with MPC becomes a simple function evaluation. Therefore the proposed technique is attractive for a wide range of applications where simple on-line computation is a crucial requirement. Besides practical advantages, the availability of the explicit structure of the MPC controller provides an insight into the type of control action in different regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.

Further Information
Year:

2001
Type of Publication:

(04)Technical Report
Supervisor:



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% Autogenerated BibTeX entry
@TechReport { BemBor:2001:IFA_7,
    author={A. Bemporad and F. Borrelli and M. Morari},
    title={{Model Predictive Control Based on Linear Programming - The
	  Explicit Solution}},
    institution={},
    year={2001},
    number={},
    address={},
    month=jan,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=7}
}
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