- Learning and Adaptation
- Complex and Intelligent Systems
Traditional control theory assumes continuous or discrete-time signals, where the controller continually or periodically observes the physical subsystem, and continually or periodically provides actuation to the plant. CPS systems are closed-loop or feedback systems, where typically sensors make measurements of physical processes, the measurements are processed in the cyber subsystems, which then drive actuators that affect the physical processes. The control strategies implemented in the cyber subsystems need to be adaptive (responding to changing conditions and uncertainties in the physical system and environments) and predictive (anticipating such changes).
The principal focus of the proposed research problem is on networked adaptive systems that deal with the stability and performance of classes of systems with uncertainties and nonlinearities, when information between the compensator and the plant is passed through a wireless network, with the objective to mitigate the effects of congestion in communication paths (e.g., packet delays and packet dropout). Due to the presence of uncertainties and nonlinearities in the physical system, adaptive solutions are required. Preliminary work on networked adaptive systems with all systems assumed to be linear, time-invariant and discrete-time show good promise. There is sufficient scope to extend this to continuous-time or sampled-data systems, systems in the presence of disturbances and noise, systems with modelling uncertainties, systems that have time-varying parameters as well as nonlinear systems.
There appears two different ways in which multiple models are used. In one approach, the best amongst a set of models are chosen, and in the other, all models contribute in decision-making. The focus of this area of research is to delve into the details of the two approaches, to sort out the mathematical foundations of these approaches, or the lack of any, and put together the applications that required the use of multiple models for improved behaviour.
A preliminary question that is to be answered is the need for a model itself. Data-driven learning systems are a current topic of research worldwide which focuses on techniques that are essentially model-free. These notions are to be crystallised from a mathematical perspective, and the manner in which such methods can dovetail into the multiple model methodology is to be looked into.
In particular, there is tremendous interest in the adaptive identification and control of systems with rapidly varying parameters. These problems arise in diverse forms and disciplines including finance, sociology, and engineering. These problems are in general mathematically intractable. Adaptive methods available for identifying LTI plants are generally inadequate to deal with such time-varying problems. Preliminary work indicates that the multiple-model methodology can deal with different kinds of time-variations. In this area of research, these notions are to be placed within a mathematical framework.