Minimum-Information LQG Control - Part I: Memoryless Controllers

With the increased demand for power efficiency in feedback-control systems, communication is becoming a limiting factor, raising the need to trade off the external cost that they incur with the capacity of the controller's communication channels. With a proper design of the channels, this translates into a sequential rate-distortion problem, where we minimize the rate of information required for the controller's operation under a constraint on its external cost. Memoryless controllers are of particular interest both for the simplicity and frugality of their implementation and as a basis for studying more complex controllers. In this paper we present the optimality principle for memoryless linear controllers that utilize minimal information rates to achieve a guaranteed external-cost level. We also study the interesting and useful phenomenology of the optimal controller, such as the principled reduction of its order

Minimum Variance Control over a Gaussian Communication Channel

We consider the problem of minimizing the response of a plant output to a stochastic disturbance using a control law that relies on the output of a noisy communication channel. We discuss a lower bound on the performance achievable at a specified terminal time using nonlinear timevarying communication and control strategies, and show that this bound may be achieved using strategies that are linear

On the Minimal Average Data-Rate that Guarantees a Given Closed Loop Performance Level

This paper deals with control system design subject to average data-rate constraints. By focusing on SISO LTI plants, and a class of source coding schemes, we establish lower and upper bounds on the minimal average data-rate needed to achieve a prescribed performance level. We also provide a specific source coding scheme, within the proposed class, that is guaranteed to achieve the desired performance level at average data-rates below our upper bound. Our results are based upon a recently proposed framework to address control problems subject to average data-rate constraints.

Direct data-driven model-reference control with Lyapunov stability guarantees

In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block, which are shaped from data to reproduce the desired behavior in closed-loop. By focusing on the case where the reference model and the plant share the same order, we propose an optimal design procedure with Lyapunov stability guarantees, tailored to handle state measurements with additive noise. Two simulation examples are finally illustrated to show the potential of the proposed strategy as compared to the state of the art approaches.Comment: 8 pages, 10 figures, Preprint submitted to the 60th IEEE Conference on Decision and Control (CDC) 202