Francisco J. Vargas

Stabilization of two-input two-output systems over SNR-constrained channels

Abstract This paper concerns the stabilization of discrete-time two-input two-output (TITO) linear time-invariant (LTI) systems over communication channels. We consider parallel additive white noise (AWN) channels, in which each individual channel is independently constrained in the signal-to-noise ratio (SNR). Necessary and sufficient conditions for stabilizability are obtained on the SNRs of the channels for both state and output feedback architectures. Our main results are derived assuming that the channel is located between the controller and the plant. We also consider stabilizability when the channel is between the plant and the controller, showing that there exists a duality between the results for both architectures.

Necessary and sufficient conditions for mean square stabilization over MIMO SNR-constrained channels

This paper studies mean square stabilization of MIMO discrete-time linear time-invariant systems over a parallel MIMO additive white noise (AWN) channel. Such channel consists of multiple independent SISO AWN channels subject to independent input power constraints. We derive dynamic output feedback stabilization conditions subject to such constraints, for minimum phase plants that have relative degree one. Consequently, these conditions are also valid for general plants provided that state feedback is employed. Our results show that necessary and sufficient condition for stabilization can be determined by studying the feasibility of a constrained algebraic Riccati equation. These results are also extended to stabilization problems subject to channel capacity constraints.

Optimal ripple-free deadbeat control using an integral of time squared error (ITSE) index

This paper describes an optimal ripple-free deadbeat control strategy for single-input-single-output (SISO) linear sampled data plants. The cost function to be minimized is a linear combination of a time-weighted cumulative term that penalizes the tracking error, that is, an integral of time squared error (ITSE) cost term, and a cumulative term which penalizes the control signal deviations from its steady-state value. The optimization problem turns out to be convex, and closed-form solutions are obtained. An example is included to illustrate our results.

Optimal control over multiple erasure channels using a data dropout compensation scheme

In this paper we focus on networked control systems subject to data dropouts. We consider that the controller communicates with the plant through multiple independent erasure channels, and that each actuator sends acknowledgement packages to the controller. We restrict our attention to the optimal design of a class of controllers that embeds a data dropout compensator and where, besides this compensation mechanism, all processing is an affine function of the available data. Our first result shows that the optimal design consists in solving, separately, an estimation problem and a control problem. The optimal controller is a linear function of the estimated state, which is obtained exploiting the information given by the acknowledgement packages and the data dropout compensator. Since we focus on a specific class of controllers, our proposal is suboptimal, however, unlike the optimal LQG controller found in the literature, our proposal is easier to implement, and its steady state behaviour can be simply determined. We also show that, under standard conditions, the affine part of the optimal controller converges to an LTI filter, which can be used as a simple alternative to the time varying controller.

Analysis and design of partly networked architectures for two-input two-output LTI systems

Abstract This article deals with the control of a two-input two-output (TITO) discrete time LTI plant, where one control signal is to be sent through a transparent channel, and the remaining control signal has to be sent through a channel that presents signal-to-noise ratio (SNR) constraints. For this situation, we study three different control architectures: state feedback, output feedback, and output feedback enriched with feedback around the constrained channel. We explore how the stability, and the best achievable performance, depend on the location of the SNR constrained channel for each architecture. An interesting conclusion of this work is that the best channel choice, when stability is the only concern, may be inadequate when the focus is on performance. A numerical example is included to illustrate our results.

On stabilizability of MIMO systems over parallel noisy channels

In this paper we study the mean square stabilizability of MIMO discrete-time linear time-invariant plants over parallel additive white noise channels. We also consider a basic linear encoder-decoder scheme based on the design of a diagonal scaling matrix. We analyse the case of non minimum phase plants in an output feedback control setting. We obtain necessary and sufficient conditions for mean square stabilization when each SISO branch of the channel is subject to an individual signal-to-noise ratio constraint. We characterize a region where the set of constraints are compatible with mean square stability.

Optimal design of a class of controllers and data-dropout compensators for LTI plants controlled over erasure channels

We consider the control of linear time-invariant (LTI) systems over erasure channels. We propose a class of controllers where, besides memoryless dependency on the plant to controller channel state, all processing is affine (and possibly time-varying). For such controller class, we show that optimal designs separate into an estimation problem and a linear quadratic regulator problem. The structure of the optimal controller is such that its affine part converges, as the horizon length tends to infinity, to an LTI filter under the same conditions which guarantee mean-square stability in the now well-known LQG control problem over erasure channels. Our infinite horizon proposal is computationally inexpensive and its steady-state behavior is easily characterized.

Stabilization of TITO Systems over Parallel SNR-Constrained AWN channels

Abstract This paper concerns the stabilization of two-input two-output (TITO) discrete-time linear time-invariant (LTI) systems over parallel additive white noise (AWN) channels, in which each individual channel is independently constrained in SNR. Necessary and sufficient conditions for stabilizability are obtained on the SNRs of the channels, in terms of the unstable poles and non minimum phase zeros of the plant, for both state and output feedback control.

Optimal design of remote controllers for LTI plants over erasure channels

Abstract In this paper we consider the remote control of a noisy linear time-invariant (LTI) plant over erasure channels located in both the plant-to-controller and controller-to-plant links. We restrict our attention to a class of controllers where all processing is affine, except for some elementary use of sensor-to-controller channel state information. For such controller class, we show that optimal designs separate into an estimation and a state feedback design problem when perfect packet acknowledgements are available at the controller. Interestingly, our results also show that the affine part of the controller converges, as the time goes to infinity, to an LTI filter under the same conditions which guarantee mean-square stability in the well-known LQG control problem over erasure channels. However, our infinite horizon proposal is computationally inexpensive and its steady-state behaviour can be characterized straightforwardly.

Explicit conditions for stabilization over noisy channels subject to SNR constraints

In this paper, we analyze the stability of networked control systems when parallel additive white noise (AWN) channels are considered. We assume that the parallel AWN channels are individually constrained in its signal to noise ratio (SNR). We obtain explicit conditions on the minimum requirements on the channel SNRs necessary for stability for a set of particular plant structures. Our results show explicitly the role played by the unstable plant pole directions in the stability of NCSs. We also show that, when state feedback control is used, a simple characterization on the channel SNRs for stability can be given.