Quadratic Invariance for Distributed Control System with Intermittent Observations

Unified Approach to Convex Robust Distributed Control Given Arbitrary Information Structures

“…Second, we characterize convexity given any arbitrary information structure as per above, in terms of a test on finitely many binary matrices. The test we propose generalizes those proposed in [8,13,24,25] for particular information structures, in the sense that they can all be alternatively proved as direct corollaries of our main result. To show generality of our approach, we provide an example of a quadratically invariant information structure which was not captured in the previous works.…”

“…This work can be extended in several directions. First, it would be interesting to use the tools developed in this paper to address the case of time-varying system dynamics and study their interaction with event-dependent information structures such as those considered in [25]. Second, Example 1 suggests that forgetting mechanisms can also be included in the information structure without necessarily compromising convexity.…”

“…We remark that the convexity tests proposed in [8,13] cannot be applied in this case, as the information structure cannot be described by a time-invariant sparsity pattern with delays. The cases of time-varying delays considered in [20] and that of intermittent observations recently considered in [25] assume that controllers never forget the information they have either observed or received over time. Hence, to the best of the authors' knowledge, the QI information structure considered here is not captured by other work.…”

“…Starting from the results of this technical note, the work [25] has recently characterized convexity for the case of scheduled intermittent observations. See [25,Lemma 1] for the appropriate choice of matrices S k,j in terms of time-varying sensing and communication topologies. [26] can be encoded by letting S k,j be taken at random from a pre-specified set of possible sparsities.…”

Optimal power‐constrained control of distributed systems with information constraints

“…A more general result is given in Rotkowitz and Lall [8], where the quadratically invariant information structures are characterized which allow for the convex formulation of the problem. Lastly, the design of quadratically invariant information structures for distributed systems with intermittent observations is presented in Abara et al [9]. The latter two results concern the computational tractability of the optimal information-constrained control problem.…”