(266c) Lyapunov-Based Model Predictive Control of Nonlinear Systems Subject to Time-Varying Measurement Delays

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


The problem of designing feedback control systems for nonlinear systems subject to time-varying measurement delays is a fundamental one and its solution can find significant application in a number of control engineering problems including, for example, design of networked control systems (NCS). NCS are control systems which operate over a communication network (wired or wireless) and can lead to significant improvements in the efficiency, flexibility, robustness and fault-tolerance of industrial control systems as well as to reduction of the installation, reconfiguration and maintenance costs. However, the design of NCS has to account for the dynamics introduced by the communication network which may include time-varying delays, data quantization or data losses. In addition to NCS, another source of time-varying delays in the feedback loop is measurement sensor delays, which are particularly important during the measurement of species concentrations and particle size distributions in process control applications.

Motivated by the above, this work deals with the design of predictive controllers for nonlinear system subject to time-varying measurement delay in the feedback loop. In particular, we modify the Lyapunov-based MPC schemes developed previously by our group to take into account time-varying measurement delays, both in the optimization problem formulation and in the controller implementation. In the LMPC scheme proposed in the present work, when measurement delays occur, the nominal model of the system is used together with the delayed measurement to estimate the current state, and the resulting estimate is used to evaluate the LMPC controller; at sampling times where no measurements are available due to the delay, instead of setting the control input to zero or to the last available value, the actuator implements the last optimal input trajectory evaluated by the controller (this requires that the controller must store in memory the last evaluated optimal control input trajectory). The proposed LMPC scheme inherits the stability and robustness properties in the presence of uncertainty and time-varying delay of the Lyapunov-based controller, while taking into account optimality considerations. Specifically, the proposed LMPC scheme allows for an explicit characterization of the stability region and guarantees that the closed-loop system in the presence of time-varying measurement delays is ultimately bounded in a region that contains the origin if the maximum delay is smaller than a constant that depends on the parameters of the system and the Lyapunov-based controller that is used to formulate the optimization problem. The application of the proposed Lyapunov-based model predictive control method is illustrated using a nonlinear chemical process example with asynchronous, delayed measurements and its stability and performance properties are demonstrated to be superior to the ones of two existing Lyapunov-based model predictive controllers.

1. Liu, J., D. Munoz de la Pena, P. D. Christofides and J. F. Davis, "Lyapunov-Based Model Predictive Control of Nonlinear Systems Subject to Time-Varying Measurement Delays," Int. J. Adapt. Contr. & Sign. Process., in press.