Minimum-information LQG control part I: Memoryless controllers

Abstract

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.

Computing Complexity-aware Plans Using Kolmogorov Complexity

“…Combining equation ( 13) and ( 14) yields (12). We now show that K φ (0 T ) ≤ log 2 (T )+c 0 , for some constant c 0 independent of T , where 0 T is the string consisting of T zeros.…”

“…In the second category, a low-complexity policy is instead obtained directly. Here, notable methods include policy distillation [30], VC-dimension constraints [16], concise finitestate machine plans [23], [24], low-memory policies through sparsity constraints [7], and information-theoretic approaches such as KL-regularisation [27], [35], mutual information regularisation with variations [33], [12], [34], and minimal specification complexity [11], [10]. Our work belongs to this second category and resembles [23], [24], [11], [10] the most, but differ since we consider Kolmogorov complexity.…”

On Kalman-Bucy filters, linear quadratic control and active inference

“…In information theory, Shannon [82] also introduced a different notion of a separation principle, to explain coding via two (separate) phases of source compression and channel coding [45]. The connections between Shannon's work and the separation principle in control theory have become more clear in recent years, thanks to a growing literature showing how Shannon's definition captures and potentially generalises the results from control theory, see for instance [89,88,30]. Here however, the focus will be on the principle traditionally described in control theory for LQG in continuous systems [54,105], under the following standard assumptions [105,5,14,3,85]:…”

Task-Driven Estimation and Control via Information Bottlenecks

“…Our work differs in that we provide analytic (i.e., model-based) methods for finding such representations and policies and we explicitly characterize the resulting robustness. Another branch of work considers the construction of LQG policies that achieve a performance goal while minimizing an information-theoretic quantity such as the mutual information between inputs and outputs [26], [27] or Massey's directed information [28], [29]. In contrast to these works, our derivation handles nonlinear systems and also presents robustness results for the resulting controllers, which have not been discussed to our knowledge in existing literature.…”