(473f) Lyapunov-Based Economic Model Predictive Control of Nonlinear Systems: Handling Asynchronous, Delayed Measurements and Distributed Implementation

Economic model predictive control (EMPC) refers to a class of model predictive control formulations in which the cost functional expresses directly economic optimization considerations of the plant under consideration, rather than penalizing the deviations of the plant states and of the manipulated inputs from desired steady-state values. As a result, EMPC may lead to the computation of time-varying optimal operating policies for the plant in contrast to MPC with traditional cost functionals which typically leads to stabilization of the plant at the desired steady state.

While there have been several calls, particularly within process control, for the integration of model predictive control (MPC) and economic optimization of processes as early as two decades ago, the subject of EMPC has received relatively little attention. Recently, in [1], MPC schemes using an economics-based cost function were proposed and the
stability properties were established using a suitable Lyapunov function. In a recent paper [2], the approach in [1] was extended to deal with cyclic process operation.
In a recent work [3], we presented an EMPC scheme for nonlinear systems that utilizes suitable Lyapunov-based stability constraints. The proposed EMPC is designed via Lyapunov-based techniques and has two different operation modes. 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 within the closed-loop system stability region.

In this work, we extend the results in [3] into two directions. First, we present an EMPC algorithm for nonlinear systems that efficiently handles asynchronous and delayed measurements using suitable Lyapunov-based constraints to ensure stability for a well-defined set of initial conditions, and demonstrate its application to a chemical process example. Second, we present a distributed EMPC (DEMPC) architecture for nonlinear systems. In this architecture, the distributed controllers communicate in a sequential fashion, optimize their inputs through maximizing a plant-wide (global) economic objective function and guarantee practical stability of the closed-loop system.

[1] M. Diehl, R. Amrit, and J. B. Rawlings, “A Lyapunov function for economic optimizing model predictive control,” IEEE Transactions on Automatic Control, in press.
[2] R. Huang, E. Harinath, and L. T. Biegler, “Lyapunov stability of economically-oriented NMPC for cyclic processes,” Journal of Process Control, in press.
[3] M. Heidarinejad, J. Liu, and P. D. Christofides, “Lyapunov-based economic model predictive control of nonlinear systems,” in Proceedings of the American Control Conference, in press, 2011