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Online QP Benchmark Collection

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This page offers a collection of challenging benchmark QP series for download. Each benchmark problem is provided as a zip-archive containing several files which are explained here.

 

No.:

Filename:

Dimensions:

Description:

01

chain80.tar.gz
chain80.zip

101 QPs,
240 variables (bounded),
0 constraints,
0 equality constraints

This test problem aims at regulating a chain of nine masses connected by springs into a certain steady-state. One end of the chain is fixed on a wall while the three velocity components of the other end are used as control input with fixed lower and upper bounds. The prediction horizon of 16 seconds is divided into 80 control intervals. The model equations are derived from linearisation of the nonlinear ODE model (with 57 states) at the steady-state. Deviation from the steady-state, the velocities of all masses and the control action are penalised via the objective function.

In order to obtain the QP series we simulated in a closed-loop manner integrating the nonlinear ODE system to obtain the movements of the chain. Starting at the steady-state, a strong perturbation was exerted to the chain by moving the free end with a given constant velocity for 3 seconds. Then the MPC controller took over and tried to return the chain into its original steady-state.

02

chain80w.tar.gz
chain80w.zip

101 QPs,
240 variables (bounded),
709 constraints,
0 equality constraints

This test problem aims at regulating a chain of nine masses connected by springs into a certain steady-state. One end of the chain is fixed on a wall while the three velocity components of the other end are used as control input. Besides fixed lower and upper input bounds, also state constraints are included into the optimisation problem in order to ensure that the chain does not hit a vertical wall close to the steady-state. The prediction horizon of 16 seconds is divided into 80 control intervals. The model equations are derived from linearisation of the nonlinear ODE model (with 57 states) at the steady-state. Deviation from the steady-state, the velocities of all masses and the control action are penalised via the objective function.

In order to obtain the QP series we simulated in a closed-loop manner integrating the nonlinear ODE system to obtain the movements of the chain. Starting at the steady-state, a strong perturbation was exerted to the chain by moving the free end with a given constant velocity for 3 seconds. Then the MPC controller took over and tried to return the chain into its original steady-state while not hitting against the wall.

03

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Last Modified By: Hans Joachim Ferreau
Last Update:2010-12-03
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