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Economic Model Predictive Control with Extended Horizon Open Access


Other title
Nonlinear Systems
Optimization Horizon
Economic Performance
Model Predictive Control
Type of item
Degree grantor
University of Alberta
Author or creator
Liu, Su
Supervisor and department
Liu, Jinfeng (Chemical and Materials Engineering)
Examining committee member and department
Zhao, Qing (Electrical and Computer Engineering)
Huang, Biao (Chemical and Materials Engineering)
Prasad, Vinay (Chemical and Materials Engineering)
Ricardez-Sandoval, Luis (Chemical Engineering, University of Waterloo)
Department of Chemical and Materials Engineering
Process Control
Date accepted
Graduation date
2017-11:Fall 2017
Doctor of Philosophy
Degree level
In this thesis, we propose a computationally efficient economic model predictive control (EMPC) design which is based on a well-known methodology --- the separation of the control and prediction horizon. The extension of the prediction horizon of EMPC is realized by employing an auxiliary control law which asymptotically stabilizes the optimal steady state. The contributions of this thesis are to systematically analyze the stability and performance of the general EMPC scheme with extended horizon, and to explore its extensions and applications to several specific scenarios. Specifically, we establish stabilizing conditions of the proposed EMPC in a progressive manner. First, we establish practical stability of the EMPC with respect to the extended horizon for strictly dissipative systems satisfying mild assumptions. Then, under stronger conditions involving Lipschitz continuities and exponential stability of the auxiliary controller, the shrinkage of the practical stability region is shown to be exponential. Further, we characterize a general condition on the storage function under which exponential stability of the optimal steady state can be established. Conventional set-point tracking MPC with quadratic cost falls into the latter category. The achievable performance of the proposed EMPC design is also discussed in a similar manner under different stabilizing conditions. It is revealed that the performance of the proposed EMPC is approximately upper-bounded by the auxiliary controller. Our theoretical results provide valuable insights into the intrinsic properties of EMPC as the discussions are laid out in a very general setting and the results are compatible with the analysis of existing MPC / EMPC designs. With a deepened theoretical understanding of EMPC with extended horizon, we further explored the extension of the proposed EMPC design in several scenarios: (1) We consider the case where a locally optimal LQR control law can be found. A terminal cost is constructed as the value function of the LQR controller plus a linear term characterized by the Lagrange multiplier associated with the steady-state constraint. This design results in an EMPC this is locally optimal. (2) We take advantage of EMPC with extended horizon to handle systems with scheduled switching operations. The EMPC operations are divided into two phases --- an infinite-time operation phase and a mode transition phase. The proposed EMPC schemes are much more efficient and achieves improved mode transition performance than existing EMPC designs. (3) We consider systems with zone tracking objectives which can be viewed as a special case of economic objective. The proposed zone MPC penalizes the distance of the predicted state and input trajectories to a desired target zone which is not necessarily positive invariant. We resort to LaSalle's invariance principle and develop invariance-like theorem which is suitable for stability analysis of zone control. Auxiliary controllers which asymptotically stabilize an invariant subset of the target zone are employed to enlarge the region of attraction. (4) We apply the proposed EMPC algorithm to the control of oilsand primary separation vessel (PSV) to maximize the bitumen recovery rate.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Su Liu and Jinfeng Liu, Economic model predictive control with extended horizon. Automatica, 73:180-192, 2016.Su Liu and Jinfeng Liu. A terminal cost for economic model predictive control with local optimality. In Proceedings of the American Control Conference, pages 1954-1959, Seattle, WA, 2017.Su Liu and Jinfeng Liu. Economic model predictive control for scheduled switching operations. In Proceedings of the American Control Conference, pages 1784-1789, Boston, MA, 2016.Su Liu, Jing Zhang and Jinfeng Liu. Economic MPC with terminal cost and application to an oilsand primary separation vessel. Chemical Engineering Science, 136:27-37, 2015.

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