The study of hybrid systems has emerged as an active research area in process control. Hybrid processes are characterized by inherent and strong interactions between continuous dynamics and discrete events. The continuous dynamics, which are typically modeled by differential equations, usually originate from the underlying physical laws such as mass, momentum, and energy conservation; while the discrete events can be the result of physico-chemical discontinuities in the continuous dynamics, transitions between different operating regimes, the use of discrete actuators and sensors in the control system, or the use of logic-based switching for supervisory and safety control. The theoretical challenges posed by hybrid dynamics, together with the abundance of practical applications where such interactions arise, have motivated significant research work on the design of supervisory and control schemes for hybrid systems. While the focus of much of the earlier studies has been on linear hybrid systems, more recent efforts have focused on nonlinear systems where the fusion of advances in nonlinear process control with hybrid system tools has led to the formulation and solution of several practical control problems (see  for some results and references in this area).
This progress notwithstanding, a careful examination of existing hybrid control methods shows that the hybrid control problem is typically formulated and addressed within the classical feedback control paradigm where the process outputs are assumed to be transmitted directly and flawlessly to the controller where the control actions are generated and fed back to the process. In practice, this paradigm needs to be re-examined; partly due to the increasing complexity of the interface between the controller and the process which features additional information-processing steps and devices that should be accounted for in the design of the control system. For instance, with the increased reliance in recent years on networked control systems as well as the emergence of applications where large numbers of networked sensors and actuators are deployed, the example of digitally-interconnected subsystems controlled over finite communication channels (i.e., channels with discrete and lossy information transmission) is becoming commonplace. In such systems, inherent limitations on the information collection and processing capabilities of the measurement system and on the transmission capacity of the communication medium can undermine the overall process performance if not taken explicitly into account in the control system design. Issues such as resource (e.g., power) utilization, data losses, measurement quantization, processing and communication delays, and real-time scheduling constraints ultimately impose constraints on the sensor-controller communication link. One approach to deal with this problem in order to mitigate the impact of such constraints is to design the control system in a way that requires only minimal sensor-controller information transfer to meet the desired closed-loop stability and performance objectives. Beyond reducing the susceptibility of the control system to sensor-controller communication disruptions, such a resource-aware control approach also helps identify the fundamental limits on the stabilizability of a given process subject to limitations on measurement availability.
Motivated by these considerations, we present in this work a methodology for model-based control of nonlinear hybrid process systems using an adaptive predictor corrector strategy. The approach aims to stabilize the process with minimal sensor-controller information transfer. The hybrid control structure consists of a bank of dedicated mode observers that run in parallel to the process and identify which mode is active at any given time, a family of Lyapunov-based feedback controllers that enforce closed-loop stability under continuous sensor-controller communication, and a supervisor that monitors the evolution of each Lyapunov function and switches synchronously between the different controllers. The mode observers are co-located with the sensors and thus receive continuous measurements from the sensors to evaluate the residuals which are defined as the differences between the outputs of the mode observers and the states of the process. Unknown input observer design techniques are used to decouple the effects of uncertainties on the residuals and ensure that the mode observers are able to identify the active mode at any given time and detect mode transitions reliably. A transition to a certain mode is signified by the convergence of the residual of the corresponding mode observer to zero. Once the active mode is identified, the corresponding controller is activated by the supervisor to stabilize the process.
To keep the transfer of information from the sensors to the controller to a minimum, a model of each mode is embedded within the corresponding controller to generate estimates of the process state variables when the mode is active and measurements are not transmitted. The model predictions are used to generate the necessary control action and are corrected by updating the model state when senor-controller communication is re-established. The logic for suspending and resuming the communication is dictated by the supervisor which monitors the evolution of the Lyapunov function of the active mode and compares it against a pre-specified stability threshold. When the value of the Lyapunov function begins to breach this threshold, the sensors are prompted to send their data to update the state of the model and correct its predictions. Communication is then suspended for as long as the Lyapunov function obeys the prescribed stability threshold. The key idea of this approach is to use the model as a predictor and to use the Lyapunov stability constraint for each mode as a criterion for adaptively correcting the model predictions. This naturally leads to a state-dependent time-varying communication logic which allows the plant to respond adaptively to changes in operating conditions by increasing or decreasing the sensor-controller information transfer. Another advantage of this approach is that it ultimately leads to an efficient utilization of the sensor-controller link in the sense that data are acquired and transmitted only when necessary to maintain closed-loop stability. Finally, the design and implementation of the developed hybrid control structure are illustrated using a chemical process example.
 Christofides, P. D. and N. H. El-Farra, Control of Nonlinear and Hybrid Process Systems: Designs for Uncertainty, Constraints and Time-Delays, Springer-Verlag, Berlin, Germany, 2005.