(186f) State Estimation-Based Economic Model Predictive Control of Nonlinear Systems

Authors: 
Heidarinejad, M., University of California, Los Angeles
Liu, J., University of California, Los Angeles


Traditionally, optimal operation and control policies for chemical
process systems are addressed via a two layer

approach in which the upper layer carries steady-state process
optimization to obtain economically optimal
process operating points (steady-states) while the lower layer utilizes
appropriate feedback control systems to steer the process state to an
economically optimal steady-state.
Model predictive control (MPC) is widely used in the lower layer to obtain
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 [1]; however, this
two-layer approach usually limits process operation around a steady-state.
Economic model predictive control (EMPC) framework deals with a
reformulation of the conventional MPC quadratic cost function in which an
economic (not necessarily quadratic) cost function is used directly as the
cost in MPC, and thus, it may, in general, lead to  time-varying process
operation policies (instead of steady-state operation), which directly optimize process economics.
In a previous work [2], we presented a
two-mode Lyapunov-based economic MPC (LEMPC) design for nonlinear systems which is also capable of handling asynchronous and delayed measurements and extended
it in the context of distributed MPC [3]. Currently, all  economic MPC schemes have been developed under the assumption of state
feedback. 
State estimation in  certain classes
of nonlinear systems can be carried out within the framework of high-gain
observers, however,
at this stage these estimation techniques have not been used in
conjunction with economic MPC schemes. Motivated by this, in this work, we focus on a class of nonlinear
systems and design an estimator-based EMPC system.
Working with the class of full-state feedback linearizable nonlinear systems, we use
a high-gain observer to estimate the nonlinear system state using output
measurements and a Lyapunov-based approach to
design an EMPC system that uses the observer state estimates. We prove,
using singular perturbation arguments, that the closed-loop system is
practically stable provided the observer gain is sufficiently large. We
use a chemical process example to demonstrate the ability of the
state-estimation based
EMPC to achieve process time-varying operation that leads to a superior
cost performance metric compared to steady-state operation. In the
example,
the high-gain observer is used to obtain estimates of the reactant
concentration from temperature measurements; a meaningful case in process control practice.
[1] P. D. Christofides, J. Liu, and D. Munoz de la Pena. "Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications", Advances in Induatrial Control Series. Springer-Verlag, London, England, 2011.
[2] 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.
[3] X. Chen, M. Heidarinejad, J. Liu and P. D. Christofides, "Distributed Economic MPC: Application to a Nonlinear Chemical Process Network'', Journal of Process Control, 22, 689-699, 2012.
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