On the design of output feedback controllers for continuous-time LTI systems over fading channels

GS13 Control Technology: article no. GS13-1ICISIP2016 is organized by the Institute of Industrial Applications Engineers (IIAE)This paper considers continuous-time linear time-invariant (LTI) systems over fading channels, and addresses the design of output feedback controllers that stabilize the closed-loop system in the mean square sense. It is shown that a sufficient and necessary condition for the existence of such controllers can be obtained by solving a convex optimization problem in the form of a semidefinite program (SDP). This condition is obtained by introducing a modified Hurwitz stability criterion and by exploiting polynomials that can be written as sums of squares of polynomials.published_or_final_versio

Distributed Kalman Filters over Wireless Sensor Networks: Data Fusion, Consensus, and Time-Varying Topologies

Kalman filtering is a widely used recursive algorithm for optimal state estimation of linear stochastic dynamic systems. The recent advances of wireless sensor networks (WSNs) provide the technology to monitor and control physical processes with a high degree of temporal and spatial granularity. Several important problems concerning Kalman filtering over WSNs are addressed in this dissertation. First we study data fusion Kalman filtering for discrete-time linear time-invariant (LTI) systems over WSNs, assuming the existence of a data fusion center that receives observations from distributed sensor nodes and estimates the state of the target system in the presence of data packet drops. We focus on the single sensor node case and show that the critical data arrival rate of the Bernoulli channel can be computed by solving a simple linear matrix inequality problem. Then a more general scenario is considered where multiple sensor nodes are employed. We derive the stationary Kalman filter that minimizes the average error variance under a TCP-like protocol. The stability margin is adopted to tackle the stability issue. Second we study distributed Kalman filtering for LTI systems over WSNs, where each sensor node is required to locally estimate the state in a collaborative manner with its neighbors in the presence of data packet drops. The stationary distributed Kalman filter (DKF) that minimizes the local average error variance is derived. Building on the stationary DKF, we propose Kalman consensus filter for the consensus of different local estimates. The upper bound for the consensus coefficient is computed to ensure the mean square stability of the error dynamics. Finally we focus on time-varying topology. The solution to state consensus control for discrete-time homogeneous multi-agent systems over deterministic time-varying feedback topology is provided, generalizing the existing results. Then we study distributed state estimation over WSNs with time-varying communication topology. Under the uniform observability, each sensor node can closely track the dynamic state by using only its own observation, plus information exchanged with its neighbors, and carrying out local computation

Stabilization of Networked Multi-Input Systems With Channel Resource Allocation

In this paper, we study the problem of state feedback stabilization of a linear time-invariant (LTI) discrete-time multi-input system with imperfect input channels. Each input channel is modeled in three different ways. First it is modeled as an ideal transmission system together with an additive norm bounded uncertainty, introducing a multiplicative uncertainty to the plant. Then it is modeled as an ideal transmission system together with a feedback norm bounded uncertainty, introducing a relative uncertainty to the plant. Finally it is modeled as an additive white Gaussian noise channel. For each of these models, we properly define the capacity of each channel whose sum yields the total capacity of all input channels. We aim at finding the least total channel capacity for stabilization. Different from the single-input case that is available in the literature and boils down to a typical H∞ or H 2 optimal control problem, the multi-input case involves allocation of the total capacity among the input channels in addition to the design of the feedback controller. The overall process of channel resource allocation and the controller design can be considered as a case of channel-controller co-design which gives rise to modified nonconvex optimization problems. Surprisingly, the modified nonconvex optimization problems, though appear more complicated, can be solved analytically. The main results of this paper can be summarized into a universal theorem: The state feedback stabilization can be accomplished by the channel-controller co-design, if and only if the total input channel capacity is greater than the topological entropy of the open-loop system. © 1963-2012 IEEE

Stabilization of networked multi-input systems with channel resource allocation

In this paper, we study the problem of state feedback stabilization of a linear time-invariant (LTI) discrete-time multi-input system with imperfect input channels. Each input channel is modeled in three different ways. First it is modeled as an ideal transmission system together with an additive norm bounded uncertainty, introducing a multiplicative uncertainty to the plant. Then it is modeled as an ideal transmission system together with a feedback norm bounded uncertainty, introducing a relative uncertainty to the plant. Finally it is modeled as an additive white Gaussian noise channel. For each of these models, we properly define the capacity of each channel whose sum yields the total capacity of all input channels. We aim at finding the least total channel capacity for stabilization. Different from the single-input case that is available in the literature and boils down to a typical H∞ or H 2 optimal control problem, the multi-input case involves allocation of the total capacity among the input channels in addition to the design of the feedback controller. The overall process of channel resource allocation and the controller design can be considered as a case of channel-controller co-design which gives rise to modified nonconvex optimization problems. Surprisingly, the modified nonconvex optimization problems, though appear more complicated, can be solved analytically. The main results of this paper can be summarized into a universal theorem: The state feedback stabilization can be accomplished by the channel-controller co-design, if and only if the total input channel capacity is greater than the topological entropy of the open-loop system. © 1963-2012 IEEE

Stabilization of Networked Multi-Input Systems with Channel Resource Allocation

In this paper, we study the problem of stabilizing a linear time-invariant discrete-time system with information constraints in the input channels. The information constraint in each input channel is modeled as a sector uncertainty. Equivalently, the transmission error of an input channel is modeled as an additive system uncertainty with a bound in the induced norm. We attempt to find the least information required, or equivalently the largest allowable uncertainty bound, in each input channel which renders the stabilization possible. The solution for the single-input case, which gives a typical H(infinity) optimal control problem, is available in the literature and is given analytically in terms of the Mahler measure or topological entropy of the plant. The main purpose of this paper is to address the multi-input case. In the multi-input case, if the information constraint in each input channel is given a priori, then our stabilization problem turns out to be a so-called mu synthesis problem, a notoriously hard problem. In this paper, we assume that the information constraints in the input channels are determined by the network resources assigned to the channels and they can be allocated subject to a total recourse constraint. With this assumption, the resource allocation becomes part of the design problem and a modified mu synthesis problem arises. Surprisingly, this modified mu-synthesis problem can be solved analytically and the solution is also given in terms of the Mahler measure or topological entropy as in the single-input case