Julio H. Braslavsky

Fundamental Limitations in Filtering and Control

The issue of fundamental limitations in filtering and control lies at the very heart of any feedback system design, since it reveals what is and is not achievable on the basis of that systems structural and dynamic characteristics. Alongside new succinct treatments of Bodes original results from the 1940s, this book presents a comprehensive analysis of modern results, featuring contemporary developments in multivariable systems, sampled-data, periodic and nonlinear problems. The text gives particular prominence to sensitivity functions which measure the fundamental qualities of the system, including performance and robustness. With extensive appendices covering the necessary background on complex variable theory, this book is an ideal self-contained resource for researchers and practitioners in this field.

Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels

There has recently been significant interest in feedback stabilization problems over communication channels, including several with bit rate limited feedback. Motivated by considering one source of such bit rate limits, we study the problem of stabilization over a signal-to-noise ratio (SNR) constrained channel. We discuss both continuous and discrete time cases, and show that for either state feedback, or for output feedback delay-free, minimum phase plants, there are limitations on the ability to stabilize an unstable plant over an SNR constrained channel. These limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity bit rate over the same channel.

String Instability in Classes of Linear Time Invariant Formation Control With Limited Communication Range

This paper gives sufficient conditions for string instability in an array of linear time-invariant autonomous vehicles with communication constraints. The vehicles are controlled autonomously and are subject to a rigid or semi-rigid formation policy. The individual controllers are assumed to have a limited range of forward and backward communication with other vehicles. Sufficient conditions are given that imply a lower bound on the peak of the frequency response magnitude of the transfer function mapping a disturbance to the leading vehicle to a vehicle in the chain. This lower bound quantifies the effect of spacing separation policy, intervehicle communication policy, and vehicle settling response performance. These results extend earlier works to give a unified treatment of heterogeneous, non-nearest neighbor communication and semi-rigid one-dimensional formation control.

Level Crossing Sampling in Feedback Stabilization under Data-Rate Constraints

This paper introduces a novel event-driven sampled-data feedback scheme where the plant output samples are triggered by the crossings - with hysteresis - of the signal through its quantization levels. The plant and controller communicate over binary channels that operate asynchronously and are assumed to be error and delay-free. The paper proposes two systematic output feedback control design strategies. The first strategy consists in the digital emulation of a previously designed analog controller. The second strategy is a simple direct design that drives the plant state to the origin in finite time after a total transmission of 2n + 2 bits, where n is the order of the plant

Inherent design limitations for linear sampled-data feedback systems

There is a well-developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller. This theory describes limitations on achievable performance present when the plant has non-minimum phase zeros, unstable poles, and/or time delays. The parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants. This paper develops a theory of design limitations for sampled-data feedback systems wherein the response of the analogue system output is considered. This is done using the fact that the steady-state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental. This fact allows fundamental sensitivity and complementary sensitivity functions that re...

Minimum Variance Control Over a Gaussian Communication Channel

We consider the problem of minimizing the response of a plant output to a stochastic disturbance using a control law that relies on the output of a noisy communication channel. We discuss a lower bound on the performance achievable at a specified terminal time using nonlinear time-varying communication and control strategies and show that this bound may be achieved using strategies that are linear. We also consider strategies that are defined over an infinite horizon that may achieve better transient response that those that are optimal for the terminal time problem.

Output feedback stabilisation over bandwidth limited, signal to noise ratio constrained communication channels

Stabilisability of an open loop unstable plant is studied under the presence of a bandwidth limited additive coloured noise communication channel with constrained signal to noise ratio. The problem is addressed through the use of an LTI filter explicitly modelling the bandwidth limitation, and another LTI filter to model the additive coloured noise. Results in this paper show that a bandwidth limitation increases the minimum value of signal to noise ratio required for stabilisability, in comparison to the infinite bandwidth, white noise case. Examples are used to illustrate the results in the continuous and discrete framework

Limiting performance of optimal linear filters

We study the lowest achievable mean-square estimation error in two limiting optimal linear filtering problems. First, when the intensity of the process noise tends to zero, the lowest achievable mean-square estimation error is a function of the unstable poles of the system. Second, when the intensity of the measurement noise tends to zero, the lowest achievable mean-square estimation error is a function of the nonminimum phase zeros of the system. We link these results with Bode integral characterisations of performance limitations in linear filtering.

Undershoot and settling time tradeoffs for nonminimum phase systems

It has been known for some time that real nonminimum phase zeros imply undershoot in the step response of linear systems. Bounds on such undershoot depend on the settling time demanded and the zero locations. In this note, we review such constraints for linear time invariant systems and provide new stronger bounds that consider simultaneously the effect of two real nonminimum phase zeros. Using the concept of zero dynamics, we extend these results to a class of nonlinear systems.

Stabilization with disturbance attenuation over a Gaussian channel

We propose a linear control and communication scheme for the purposes of stabilization and disturbance attenuation when a discrete Gaussian channel is present in the feedback loop. Specifically, the channel input is amplified by a constant gain before transmission and the channel output is processed through a linear time invariant filter to produce the control signal. We show how the gain and filter may be chosen to minimize the variance of the plant output. For an order one plant, our scheme achieves the theoretical minimum taken over a much broader class of compensators.