(654g) Quasi-Decentralized Model Predictive Control of Process Systems Using Adaptive Sampling

As one of the few systematic methods suited for handling constraints, multivariable interactions and optimization requirements, Model Predictive Control (MPC) has been the subject of considerable interest in process control research. Numerous MPC formulations and methods have already been developed over the past few decades to address different kinds of problems arising from process control practice. Despite this progress, a close examination of the literature shows that the majority of existing MPC formulations are often developed on the basis of the conventional feedback control paradigm where the sensors are assumed to collect the measurements and transmit them to the controller at a fixed sampling/communication rate. With the increasing complexity of the process/controller interface brought about by, for example, the incorporation of wireless sensor networks in control systems, constraints on the information collection, processing and transmission are encountered more frequently. In some applications, it is also advantageous for the control system to have the ability to respond to changes in operating conditions by adaptively changing the rate of measurement collection and transmission so that the control system performance can be optimized under limited resources. These considerations require re-examination of the applicability of existing MPC methods developed within the conventional feedback control paradigm.

In this work, we focus on predictive control of large-scale dynamical systems consisting of interconnected subsystems, and develop a quasi-decentralized MPC framework using an adaptive sampling strategy. The framework aims to enforce closed-loop stability and achieve the desired performance specifications in each subsystem with minimal measurement sampling and communication between the constituent subsystems. Specifically, a Lyapunov-based model predictive controller is initially synthesized for each subsystem to enforce closed-loop stability within a well-characterized stability region for a fixed measurement sampling rate. The controller minimizes a local performance index over a finite horizon subject to constraints on the dynamics of the prediction models, bounds on the states and inputs, as well as a stability constraint that essentially enforces a prescribed decay rate for the local Lyapunov function over a sampling interval. The Lyapunov stability constraint is used to characterize the minimum time required for the local state to escape from the stability region (starting from a given initial state), and this characterization is then used as the basis for devising a sampling strategy that can adaptively adjust the sampling and communication rates based on the evolution of the local Lyapunov functions. The key idea is to implement the control sequence generated when the optimization problem is solved for as long as possible until a new measurement is sampled when either the minimum escape time or the end of the prediction horizon is reached. The new measurement is then used to update the states of the locally embedded prediction models, re-solve the optimization problem and assess whether the sampling rate should be maintained or changed based on a comparison with the last available measurement. The implementation of this strategy requires only local monitoring of the state within each subsystem to determine when the flow of information between the constituent subsystems can be suspended or restored. Switched system techniques are used to analyze closed-loop stability and derive precise conditions for the implementation of the proposed adaptive sampling policy. Finally, the theoretical results are illustrated using a reactor-separator process example.