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We consider the optimal control of linear systems over wireless MIMO fading channels, where the MIMO wireless fading and random access of the remote controller may cause intermittent controllability or uncontrollability of the closed-loop control system. We formulate the optimal control design over random access MIMO fading channels as an infinite horizon average cost Markov decision process (MDP), and we propose a novel state reduction technique such that the optimality condition is transformed into a time-invariant reduced-state Bellman optimality equation. We provide the closed-form characterizations on the existence and uniqueness of the optimal control solution via analyzing the reduced-state Bellman optimality equation. Specifically, in the case that the closed-loop system is almost surely controllable, we show that the optimal control solution always exists and is unique. In the case that MIMO fading channels and the random access of the remote controller destroy the closed-loop controllability, we propose a novel controllable and uncontrollable positive semidefinite (PSD) cone decomposition induced by the singular value decomposition (SVD) of the MIMO fading channel contaminated control input matrix. Based on the decomposed fine-grained reduced-state Bellman optimality equation, we further propose a closed-form sufficient condition for both the existence and the uniqueness of the optimal control solution. The closed-form sufficient condition reveals the fact that the optimal control action may still exist even if the closed-loop system suffers from intermittent controllability or almost sure uncontrollability.
In this paper, we consider a networked control system (NCS) in which an dynamic plant system is connected to a controller via a temporally correlated wireless fading channel. We focus on communication power design at the sensor to minimize a weighted
Stochastic stability for centralized time-varying Kalman filtering over a wireles ssensor network with correlated fading channels is studied. On their route to the gateway, sensor packets, possibly aggregated with measurements from several nodes, may
Jointly optimal transmission power control and remote estimation over an infinite horizon is studied. A sensor observes a dynamic process and sends its observations to a remote estimator over a wireless fading channel characterized by a time-homogene
This note studies the use of relays to improve the performance of Kalman filtering over packet dropping links. Packet reception probabilities are governed by time-varying fading channel gains, and the sensor and relay transmit powers. We consider sit
Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing app