期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 56, 期 3, 页码 703-707出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2010.2101291
关键词
Asymptotic stability; economic cost function; model predictive control (MPC); unreachable setpoint
资金
- Research Council KUL (Center of Excellence on Optimization in Engineering (OPTEC) [EF/05/006, GOA AMBioRICS, IOF-SCORES4CHEM]
- Flemish Government via FWO [G.0452.04, G.0499.04, G.0211.05, G.0226.06, G.0321.06, G.0302.07, G.0320.08, G.0558.08]
- IWT
- EU via ERNSI [FP7-HDMPC, FP7-EM-BOCON]
- Belgian Federal Science Policy Office [IUAP P6/04]
- Texas-Wisconsin-California Control Consortium (TWCCC)
- NSF [CTS-0825306]
- [ERNSI]
- Directorate For Engineering
- Div Of Chem, Bioeng, Env, & Transp Sys [0825306] Funding Source: National Science Foundation
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 [1] 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.
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