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Parametric Programming and Friends


Multi-parametric programming has received a great deal of attention in the control community in the past few years since it can be used to synthesize certain constrained model predictive control (MPC) laws offline, thereby enabling significantly simpler and faster online computation. The primary tools used to perform these computations are parametric linear and quadratic programming solvers.

In the first half of this talk, we introduce the parametric linear complementarity problem (pLCP), which unifies and generalizes linear and quadratic programs and bimatrix games. We also find that virtually all fundamental algorithms of computational geometry that are of interest in various areas of constrained linear control can be posed as an equivalent parametric LCP. We then present a new and efficient computational method for solving this important class of problems.

The second half of the talk will discuss the primary limitation of all parametric algorithms in control: the complexity of the resulting controller. We will briefly introduce a new approximation algorithm based on the well established beneath/beyond technique and show that it has many advantages from a control perspective, including the ability to trade computational complexity for performance of the closed-loop system.

Type of Seminar:
IfA Seminar
Dr. Colin N. Jones
Jan 18, 2007   11am

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