(740c) Multirate Distributed Model Predictive Control of Nonlinear Uncertain Systems

Authors: 
Heidarinejad, M., University of California, Los Angeles
Liu, J., University of California, Los Angeles
Muñoz de la Peña, D., University of California, Los Angeles
Davis, J. F., University of California - Los Angeles


Typically, model predictive control (MPC) is studied within a centralized control architecture in which all the manipulated inputs are calculated in a single MPC. Because in the evaluation of the control actions by MPC online optimization problems need to be solved, the evaluation time of the MPC strongly depends on the number of manipulated inputs. As the number of manipulated inputs increases, the evaluation time of a centralized MPC increases significantly. This may impede the ability of centralized MPC to carry out real-time calculations within the limits imposed by process dynamics and operating conditions.

Distributed MPC (DMPC) is a feasible alternative to overcome the increasing computational complexity of centralized MPC. In a DMPC architecture, the manipulated inputs are computed by solving more than one control (optimization) problems in separate processors in a coordinated fashion. With respect to available results in this direction, several DMPC methods have been proposed in the literature. In our previous works [1,2], two different DMPC architectures, namely, a sequential DMPC architecture and an iterative DMPC architecture, were designed for nonlinear systems via Lyapunov techniques. However, the results in [1,2] were obtained under the assumption that each distributed controller has access to the full system state at every sampling time. In [3], we considered the design of DMPC schemes for nonlinear systems with asynchronous and delayed measurements of the full system state.

In the present work, we consider the design of a DMPC scheme using multirate sampling for large-scale nonlinear systems composed of several coupled subsystems. Specifically, we assume that the states of each local subsystem can be divided into fast sampled states (which are available every sampling time) and slowly sampled states (which are available every several sampling times). The distributed model predictive controllers are connected through a shared communication network and cooperate in an iterative fashion to guarantee closed-loop stability when the network is closed at time instants in which full system state measurements (both fast and slow) are available. When the communication network is open, the distributed controllers operate in a decentralized fashion based only on local subsystem fast sampled state information to improve closed-loop performance. In the proposed design, the controllers are designed via Lyapunov-based MPC (LMPC). Sufficient conditions under which the state of the closed-loop system is ultimately bounded in an invariant region containing the origin are derived. The theoretical results are demonstrated through a nonlinear chemical process example.

[1] J. Liu, D. Munoz de la Pena, and P. Christofides, ?Distributed model predictive control of nonlinear process systems,? AIChE Journal, vol. 55, pp. 1171?1184, 2009.

[2] J. Liu, X. Chen, D. Munoz de la Pena, and P. Christofides, ?Sequential and iterative architectures for distributed model predictive control of nonlinear process systems,? AIChE Journal, in press.

[3] J. Liu, D. Munoz de la Pena, and P. D. Christofides, ?Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements,? Automatica, vol. 46, pp. 52?61, 2010.