# (412c) On Closed-Loop Performance of Lyapunov-Based Economic Model Predictive Control of Nonlinear Systems

- Conference: AIChE Annual Meeting
- Year: 2012
- Proceeding: 2012 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Wednesday, October 31, 2012 - 9:10am-9:30am

The development of optimal operation and control policies for chemical process systems aiming at optimizing process economics has always been an important research subject with major practical implications. Generally, economic considerations are addressed via a two layer approach in which the upper layer carries steady-state process optimization to obtain economically optimal process operating set points (steady-states) while the lower layer employs appropriate feedback control laws to steer the process state to an economically optimal steady-state operating point. Model predictive control (MPC) is widely utilized in the process control layer to provide optimal manipulated input values by minimizing a (typically) quadratic cost function which usually penalizes the deviation of the system state and manipulated inputs from their economically-optimal steady-state values subject to input and state constraints. This two-layer approach restricts process operation to seek a solution within the neighborhood of steady-state operation. In order to account for general economic optimization considerations, the quadratic cost function used in standard MPC should be replaced by an economics-based cost function which may result in a time-varying operation. Consequently, the standard MPC should be re-formulated in an appropriate way to guarantee closed-loop stability. At this point, there is limited work to ensure improvement of closed-loop performance through time-varying operation via economic MPC with respect to operation under conventional MPC in the context of finite time operation. In [1], we demonstrated through closed-loop simulations that there is improvement in economic closed-loop performance when we apply time-varying solution of economic MPC instead of steady-state solution of Lyapunov-based MPC.

Motivated by the lack of available methodologies to guarantee performance of economic MPC, the present work focuses on a Lyapunov-based economic model predictive control (LEMPC) scheme for nonlinear systems which is capable of optimizing closed-loop performance with respect to a general objective function that may directly address economic considerations. Unlike steady-state operation of conventional Lyapunov-based model predictive control (LMPC), LEMPC design through time varying operation guarantees to improve economic cost function value with respect to conventional LMPC by incorporating appropriate constraints in its formulation and solving an auxiliary LMPC problem at each sampling time. The proposed scheme takes advantage of a predefined Lyapunov-based feedback law through a two mode operation to characterize its stability region while maintaining the closed-loop system state in an invariant set. The first operation mode corresponds to the periods in which the cost function should be optimized (e.g., normal production periods); and in this operation mode, the MPC maintains the closed-loop system state within a pre-defined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the MPC to an appropriate steady-state. Theoretical results are demonstrated through a nonlinear chemical process example.

[1] M. Heidarinejad, J. Liu, and P. D. Christofides. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal, 58:855-870, 2012.

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