DocumentCode :
1408823
Title :
A Lyapunov Function for Economic Optimizing Model Predictive Control
Author :
Diehl, Moritz ; Amrit, Rishi ; Rawlings, James B.
Author_Institution :
OPTEC/ESAT-SCD, K.U. Leuven, Leuven, Belgium
Volume :
56
Issue :
3
fYear :
2011
fDate :
3/1/2011 12:00:00 AM
Firstpage :
703
Lastpage :
707
Abstract :
Standard model predictive control (MPC) yields an asymptotically stable steady-state solution using the following procedure. Given a dynamic model, a steady state of interest is selected, a stage cost is defined that measures deviation from this selected steady state, the controller cost function is a summation of this stage cost over a time horizon, and the optimal cost is shown to be a Lyapunov function for the closed-loop system. In this technical note, the stage cost is an arbitrary economic objective, which may not depend on a steady state, and the optimal cost is not a Lyapunov function for the closed-loop system. For a class of nonlinear systems and economic stage costs, this technical note constructs a suitable Lyapunov function, and the optimal steady-state solution of the economic stage cost is an asymptotically stable solution of the closed-loop system under economic MPC. Both finite and infinite horizons are treated. The class of nonlinear systems is defined by satisfaction of a strong duality property of the steady-state problem. This class includes linear systems with convex stage costs, generalizing previous stability results and providing a Lyapunov function for economic MPC or MPC with an unreachable setpoint and a linear model. A nonlinear chemical reactor example is provided illustrating these points.
Keywords :
Lyapunov methods; asymptotic stability; closed loop systems; cost optimal control; linear systems; nonlinear control systems; optimisation; Lyapunov function; asymptotic stability; closed loop system; duality; economic cost function; economic optimization; linear system; model predictive control; nonlinear system; steady state problem; Asymptotic stability; economic cost function; model predictive control (MPC); unreachable setpoint;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2010.2101291
Filename :
5672577
Link To Document :
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