Erik Johannesson

Brief paper: Sporadic event-based control of first-order linear stochastic systems

The standard approach in computer-controlled systems is to sample and control periodically. In certain applications, such as networked control systems or energy-constrained systems, it could be advantageous to instead use event-based control schemes. Aperiodic event-based control of first-order stochastic systems has been investigated in previous work. In any real implementation, however, it is necessary to have a well-defined minimum inter-event time. In this paper, we explore two such sporadic control schemes for first-order linear stochastic systems and compare the achievable performance to both periodic and aperiodic control. The results show that sporadic control can give better performance than periodic control in terms of both reduced process state variance and reduced control action frequency.

Sporadic control of first-order linear stochastic systems

The standard approach in feedback control systems is to sample and control periodically. For some applications, such as networked control systems or severely energy-constrained systems, it could be advantageous to instead use event-based control schemes. Aperiodic control (that is, event-based control with no specified minimum inter-event time) of first-order stochastic systems has been investigated in previous work. In any real implementation, however, it is necessary to have a well-defined minimum inter-event time. In this paper, we explore two such sporadic control schemes for first-order linear stochastic systems and compare the achievable performance to both periodic and aperiodic control. The results indicate that sporadic control can give better performance than periodic control in terms of reduced process state variance and control action frequency.

Encoder and decoder design for signal estimation

In this paper, we study the joint design of optimal linear encoders and decoders for filtering and transmission of a signal over an additive Gaussian noise channel subject to a real-time constraint. The objective is to minimize the variance of the estimation error at the receiving end. The design problem is nonconvex, but it is shown that a global optimum can be found by solving a related two-stage problem. The first stage consists of a mixed H2 and H1 norm minimization problem, where the H2 norm corresponds to the error variance in a corresponding Wiener-Kolmogorov filtering problem and the H1 norm is induced by the channel noise. The second stage consists of a spectral factorization. The results are illustrated by a numerical example.

Optimal linear control for channels with signal-to-noise ratio constraints

We consider the problem of stabilizing and minimizing the disturbance response of a SISO LTI plant, subject to a stochastic disturbance, over an analog communication channel with additive white noise and a signal-to-noise ratio (SNR) constraint. The controller is linear, based on output feedback and has a structure with two degrees of freedom: One part represents sensing and encoding operations and the other part represents decoding and issuing the control signal. It is shown that the problem of simultaneously designing the two optimal controller parts can be solved in two stages: First a functional depending both on the 1- and 2-norms of the Youla parameter is minimized. This minimization can be arbitrarily well approximated by a quasiconvex program. The second stage consists of a spectral factorization.

A framework for linear control over channels with signal-to-noise ratio constraints

We present a framework for the solution of control and estimation problems under a signal-to-noise (SNR) ratio constraint. The framework can be used to design optimal linear controllers, based on output feedback, with two degrees of freedom: One part of the controller is placed before the communication channel and represents sensing and encoding operations. The other part represents decoding and issuing of the control signal. The framework includes a generalized plant model that can be used to represent problem instances covered in previous papers [12], [11] as special cases. It is shown that the design problem can be solved by minimization of a convex functional depending on the 1- and 2-norms of the Youla parameter, followed by a spectral factorization.

Signal Estimation Over Channels with SNR Constraints and Feedback

We consider the problem of designing optimal linear encoders and decoders for estimation and transmission of a signal over an analog communication channel with additive noise and a signal-to-noise ratio (SNR) constraint. The objective is to minimize the variance of the estimation error at the receiving end, subject to a real-time constraint. It has been previously shown that, for channels without feedback, a solution can be obtained by solving a mixed norm minimization problem and performing a spectral factorization, see Johannesson et al. (2010b). In this paper, these results are extended to the case when the encoder has access to feedback from the channel output. This results in improved performance, which is demonstrated by a numerical example. (Less)