We propose a novel and natural architecture for decentralized control that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the concept of Moebius inversion for posets, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Moebius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on H_2-optimal decentralized control for arbitrary posets, we prove that the H_2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture.
Poset-causal systems form a class of decentralized systems introduced by Shah and Parrilo [32] and studied mainly in the context of optimal decentralized control. In this paper we develop part of the realization theory for poset-causal systems. More specifically, we investigate several notions of controllability and observability, and their relation under duality. These new notions extend concepts of controllability and observability in the context of coordinated linear systems [16]. While for coordinated linear systems there is a clear hierarchical structure with a single (main) coordinator, …
This paper presents a new approach to distributed controller design that exploits a partial-structure representation of linear time invariant systems to characterize the structure of a system. This partial-structure representation, called the dynamical structure function, characterizes the {\em signal structure}, or open-loop causal dependencies among manifest variables, capturing a significantly richer notion of structure than the sparsity pattern of the transfer function. The design technique sequentially constructs each link in an arbitrary controller signal structure, and the main result p…
Norwegian University of Science and Technology（挪威科技大学）；Solution Seeker AS（Solution Seeker公司）
Steady-state models which have been learned from historical operational data may be unfit for model-based optimization unless correlations in the training data which are introduced by control are accounted for. Using recent results from work on structural dynamical causal models, we derive a formula for adjusting for this control confounding, enabling the estimation of a causal steady-state model from closed-loop steady-state data. The formula assumes that the available data have been gathered under some fixed control law. It works by estimating and taking into account the disturbance which th…
Inspired by online learning, data-dependent regret has recently been proposed as a criterion for controller design. In the regret-optimal control paradigm, causal controllers are designed to minimize regret against a hypothetical optimal noncausal controller, which selects the globally cost-minimizing sequence of control actions given noncausal access to the disturbance sequence. We extend regret-optimal control to the more challenging measurement-feedback setting, where the online controller must compete against the optimal noncausal controller without directly observing the state or the driv…
In this paper, we consider the optimal disturbance rejection problem for possibly infinite dimensional linear time-varying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. This approach does not assume any state space representation and views LTV systems as causal operators. After reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, which satisfy a "time-varying" allpass or flatness condition. Under mild assumptions the optimal TV contr…
We generalize the system level synthesis framework to systems defined by bounded causal linear operators, and use this parameterization to make connections between robust system level synthesis and classical results from the robust control literature. In particular, by leveraging results from L1 robust control, we show that necessary and sufficient conditions for robust performance with respect to causal bounded linear uncertainty in the system dynamics can be translated into convex constraints on the system responses. We exploit this connection to show that these conditions naturally allow fo…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which compete against a clairvoyant noncausal policy, instead of the best policy selected in hindsight from some fixed parametric class. We show that the regret-optimal estimator and regret-optimal controller can be derived in state-space form using operator-theoretic techniques from robust control and present tight,data-dependent bounds on the regret incurred by our a…
