Resource Limited Controller Synthesis – Innovations, Quantizations, and Optimality
Present day control systems are comprised of several subsystems which are not necessarily colocated, and hence, entailing the need for a communication infrastructure to communicate sensory measurements and actuator commands. A perfect example for such systems would be a group of robots, controlled remotely, being deployed for surveillance and monitoring. Performances of such systems are easily affected by the underlying communication infrastructure that assists the dissemination of the sensory measurements accurately to the controllers. Signals are quantized (encoded) before transmission, and quantized encoded signals are decoded to reconstruct the original signal. On one hand, while it is desired to have transmissions with lower distortions, on the other hand, such transmissions are required to be fast and consuming minimal bandwidth. Therefore, based on the criticality of the task at hand, a trade-off is to be made between the acceptable amount of distortion in the transmission and the amount of communication resources used.
For a given task, we are interested in jointly selecting the best quantization scheme from a given set of available schemes and computing the control policy that would optimize the task objective. We adopt the notion of innovation quantization that encodes only the task-specific new information extracted from the sensory measurements. In this framework, we quantify the amount of new information in sensor outputs based on an innovation signal associated with the system dynamics, and hence, this quantity is dependent of the realization of the noise affecting the system. We show that the optimal quantizer selection scheme can be solved offline by solving a Linear Programming for Linear-Quadratic-Gaussian systems.
Reference: Dipankar Maity and Panagiotis Tsiotras, “Optimal Controller and Quantizer Selection for Linear-Quadratic-Gaussian Systems” Submitted to a Journal. Task: RA1.C2 Point-of-contact: Dipankar Maity and Panagiotis Tsiotras