(146f) Output Feedback Control of Nonlinear Systems Subject to Constraints and Asynchronous Measurements

Sensors (along with actuators) are integral to the operation and control of chemical processes. The importance of sensors is well recognized and several researchers have focused on the problem of efficient sensing and measurement for well-functioning sensors and networks of sensors [1]. Given the complexity of process operation and normal wear and tear, sensor malfunctions often occur and manifest themselves in incorrect process information being available to the control algorithm. The common occurrence of sensor malfunctions motivate quantifying the robustness of control algorithms to such errors. In [2] sensor faults arising due to communication losses were modeled as delays in implementing the control action while [3] considers the problem of availability of sensor measurements at different (known) rates. In practical applications, the knowledge of precise times at which sensor information will be available may not be known; instead it may only be possible to establish an average rate of measurement availability (owing to the variability associated with sampling times, measurements and communication delays).

When explicitly considered, this problem of intermittent availability of measurements (asynchronous measurements) can be analyzed as a robustness property. Specifically, for a given stabilizing control law, a bound on the sensor data loss rate is computed such that if the sensor data loss rate is within this bound, closed-loop stability is preserved. For unconstrained systems, such a bound for the data loss rate can be defined over an infinite time interval (e.g., see [4,5] and the references therein). For constrained systems, however, a data loss rate defined over an infinite time interval does not allow for the computation of such a bound. The robustness characterization is further complicated when not all the states are measured. Even with continuous measurements, the unavailability of some of the states as measurements necessitates the design of appropriate state estimators and analyzing the closed-loop system comprising the system, the state estimates and the controller to establish closed-loop stability. The intermittent loss of measurements necessitates redesigning the state estimation scheme and accounting for the asynchronous nature of the measurements in analyzing the closed-loop system.

Motivated by the above, in this work we consider the problem of output-feedback control of constrained nonlinear systems under asynchronous measurements. To clearly elucidate our approach, we first consider the state-feedback problem and characterize the robustness property of the closed-loop system under asynchronous measurements. Then, we devise an estimation scheme under asynchronous measurements and characterize the stability properties of the closed-loop system, quantifying the relationship between the controller and the estimation parameters and the maximum allowable data-loss rate that the closed-loop system can tolerate for the time over which the data-loss rate is defined. The proposed approach is illustrated using a chemical process example and then demonstrated on a polyethylene reactor.

References

[1] M. Bagajewicz and E. Cabrera. A new MILP formulation for instrumentation network design and upgrade. AIChE J., 48:2271-2282, 2002.

[2] N. H. El-Farra, A. Gani, and P. D. Christofides. Fault-tolerant control of process systems using communication networks. AIChE J., 51:1665-1682, 2005.

[3] S. Tatiraju, M. Soroush, and B. A. Ogunnaike. Multirate nonlinear state estimation with application to a polymerization reactor. AIChE J.], 45:769-780, 1999.

[4] A. Hassibi, S. P. Boyd, and J. P. How. Control of asynchronous dynamical systems with rate constraints on events. In Proceedings of 38th IEEE Conference on Decision and Control, pages 1345-1351, Phoenix, AZ, 1999.

[5] W. Zhang, M. S. Branicky, and S. M. Phillips. Stability of networked control systems. IEEE Contr. Sys. Mag., 21:84-99, 2001.