Description

Model Predictive Control
1 Work out every step of the proof of Lemmas 5.2 and 5.4 in the textbook by Gru¨ne and Pannek, finding a justification for each step taken. Be prepared to discuss your reasoning during class on 11/20.
2
(MPCdlqrNoTerminal.m) to include a terminal equilibrium constraint. Simulate the constraintfree and the equilibrium terminal constraint cases under the same cost function, horizon and initial conditions. In each case, show time plots of the predicted trajectories and the closedloop trajectories. Comment on the results.
3
(CTdoubleIntMPCNoTerm.m) to include a terminal equilibrium constraint. Simulate the constraint-free case with T = 0.5 and δ = 0.05 (N = 10), with Q = I and R = 1, using the provided initial condition. Then simulate the terminal equilibrium case under the same conditions. Comment on the results.
4
It is recommended to use an initial guess based on a simulation of the plant with some arbitrary control input (such as a constant). Provide a phase plot of the predicted and actual closed-loop trajectories and show the terminal set. Experiment with α smaller than the maximum allowed for Umax.
5
Use ACADO to simulate an MPC controller according to Problem 5.8 in Gru¨ne and Pannek (N = 2). Use the supplied discrete-time example and make small modifications. Verify that the closed-loop system is asymptotically stable.
Investigate a way to use a terminal cost and a terminal set constraint for an OPC solved with ACADO. Then simulate Problem 4 above using this package. Comment on any computational speed advantages.