New developments in wireless technologies have generated a vast field of new applications for wireless networked control systems like wireless sensor networks [1] and cooperative control of multi-agent systems [2]. Wireless networked control systems can also improve the closed-loop performance and fault-tolerance of chemical processes [3]. From a control theory point of view, networks introduce new dynamics in the closed-loop system which have to be taken into account at the controller design stage. For example, wireless sensors/actuators may be characterized by a significant, from a feedback control point of view, data loss rate.

The stability and robustness properties of nonlinear systems under state feedback control in the presence of data losses have been studied; however, these results are based on the assumption that full state measurements are available [3]. In many applications, this assumption does not hold and an output feedback control scheme has to be used. Recently, output feedback control of nonlinear systems subject to data losses has been studied; although, when data losses occur, the control actuator output is fixed at the last available input [5].

In the present work, we adopt a different strategy based on using an estimate of the state computed via the nominal model of the plant to decide the control actuator output over the period of time in which feedback is lost between consecutively received measurements, see for example [6]. In particular, we use Lyapunov-based model predictive controller (LMPC) with a high-gain observer [7]. LMPC is based on uniting receding horizon control with control Lyapunov functions and computes the manipulated input trajectory solving a finite-horizon constrained optimal control problem. When data losses occur, we update the input taking advantage of the predictions obtained from the solution of the optimization problem. It can be seen that even though both LMPC and controllers in previous works enforce practical stability in the closed-loop system, the performance of the proposed output feedback LMPC approach is better than the performance of the “last available input” strategy.

The application of the theoretical results is demonstrated using a chemical reactor example and a high-recovery reverse-osmosis desalination process. The proposed method is shown to provide a guaranteed stability region through LMPC for the closed-loop system in the presence of sensor-to-controller and actuator-to-controller connectivity failures or data loss in a wireless system. In the context of the desalination process, we also demonstrate that the proposed techniques provide improved closed-loop system performance and the ability to keep the permeate salinity below a critical value when full-state feedback is not available.

[1] C. Y. Chong and S. P. Kumar. Sensor networks: Evolution, opportunities, and challenges. Proceedings of the IEEE, 91:1247-1256, 2003.

[2] P. Wilke and T. Braunl. Flexible wireless communication network for mobile robot agents. Industrial Robot-An International Journal, 28:220-232, 2001.

[3] P. Mhaskar, A. Gani, C. McFall, P. D. Christofides, and J. F. Davis. Fault-tolerant control of nonlinear process systems subject to sensor faults. AIChE J., 53:654-668, 2007.

[4] W. Zhang, M. S. Branicky, and S. M. Phillips. Stability of networked control systems. IEEE Control Systems Magazine, 21(1):84-89, 2001.

[5] D. Munoz de la Pena and P. D. Christofides. Output feedback control of nonlinear systems subject to sensor data losses. In Proceedings of the American Control Conference, accepted, New York City, New York, 2007.

[6] L. A. Montestruque and P. J. Antsaklis. On the model-based control of networked systems. Automatica, 39:1837-1843, 2003.

[7] P. Mhaskar, N. H. El-Farra, and P. D. Christofides. Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control. Systems and Control Letters, 55:650-659, 2006.

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