Kunihisa Okano

Brief paper: Characterization of a complementary sensitivity property in feedback control: An information theoretic approach

This paper addresses a characterization of a complementary sensitivity property in feedback control using an information theoretic approach. We derive an integral-type constraint of the complementary sensitivity function with respect to the unstable zeros of the open-loop transfer function. It is an analogue of Bodes integral formula for the sensitivity gain. To show the constraint, we first show a conservation law of the entropy and mutual information of signals in the feedback system. Then, we clarify the relationship between the mutual information of control signals and the unstable zeros of the open-loop transfer function.

Stabilization of Uncertain Systems With Finite Data Rates and Markovian Packet Losses

This research addresses stabilization of uncertain systems over data rate constrained and lossy channels. While many of the existing works assume that the packet loss process is independent and identically distributed, we model it as a two-state Markov chain, which can deal with more practical situations including bursty dropouts. For parametrically uncertain plants, a necessary condition and a sufficient condition for mean square stability are derived. These conditions are represented by the product of the eigenvalues of the nominal plants, the data rate, the transition probabilities of the channel states, and the upper bounds of uncertainties. In particular, for scalar plants, the conditions coincide with each other.

Achievable sensitivity bounds for MIMO control systems via an information theoretic approach

Abstract This paper deals with an MIMO feedback control system that has two channels with additive noises and studies the effects of the noises on the input and output signals of the plant. We derive achievable bounds of integral type for sensitivity-like properties of the system based on an information theoretic approach. These bounds are generalizations of Bode’s integral formula for the case that the feedback system includes nonlinear elements.

Direct Controller Tuning Based on Data Matching

We consider a problem of designing a closed loop system for an unknown plant based on input/output measurements. In this paper, we propose a direct method to obtain parameters of the desired controller via controller identification from the input/output measurements and the desired response instead of model identification of the plant. A salient feature of the proposed method is to detect unexpected instability of the resulting closed-loop system by using identification error

Data rate limitations for stabilization of uncertain systems

This paper considers stabilization of parametrically uncertain systems via lossy and data-rate-constrained channels. We propose a quantization scheme which helps to reduce the required data rate for the stabilization compared with the case using the uniform quantizer; the existing works tackling the control of uncertain systems over communication channels commonly use the uniform quantizer. For systems utilizing the new quantizer, a necessary condition and a sufficient condition are derived. The conditions demonstrate limitations and tradeoffs among data rate, packet loss probability, and uncertainty bounds on plant parameters for stabilization.

Real-time control under clock offsets between sensors and controllers

This paper studies the impact of clock mismatches in spatially distributed real-time control systems. We consider a configuration in which sensor measurements are collected by one processor that transmits the measurements to another control/actuation processor through a network, but the two processors do not have a common clock. Due to the clock mismatch, there will be an offset between the actual time at which a measurement is taken and the time reported by the sensor. Our goal is to discover fundamental limitations to the ability to stabilize the control loop arising from the clocks mismatch. We consider time-varying bounded offsets and derive limitations on the offset bound for the stability of the feedback system. For the case of a scalar linear process, there exists a critical limitation, which depends on the level of instability of the plant and the nominal sampling period. In contrast, for the vector linear processes, if the process dynamics has at least two distinct real eigenvalues, then there is no fundamental limitation on the offset bound.

Stabilization of networked control systems with clock offsets

We consider the stabilization of networked control systems with time-invariant clock offsets between the sensors and the controllers. Clock offsets are modeled as parametric uncertainty and we provide necessary and sufficient conditions for the existence of a single controller that is capable of stabilizing the closed loop for every clock offset in a given range. For scalar systems, we obtain the maximum length of the offset interval for which the system can be stabilized by a single linear time-invariant controller. We compare the offset bounds that would be allowed by specific classes of controllers for scalar systems.

Data rate limitations for stabilization of uncertain systems over lossy channels

This paper considers data rate limitations for mean square stabilization of uncertain discrete-time linear systems via finite-data-rate and lossy channels. For a plant having parametric uncertainties, a necessary condition and a sufficient condition are derived, represented by the data rate, the packet loss probability, uncertainty bounds on plant parameters, and the unstable eigenvalues of the plant. The results extend those existing in the area of networked control, and in particular, the condition is exact for the scalar plant case.

Control under clock offsets and actuator saturation

This paper studies the stability analysis and the stabilization problem for systems with asynchronous sensors and controllers, and actuators subject to saturation. We consider systems with parameter uncertainties caused by clock offsets. By using a polytopic overapproximation, we investigate how large clock offsets affect stability. In addition, we employ a sector characterization approach to address actuator saturation. We see from a numerical study that the range of allowable clock offset bounds drops if the saturation limit becomes smaller than a certain value.

Sensitivity analysis of networked control systems via an information theoretic approach

This paper deals with an MIMO feedback control system that has two channels with additive noise and studies the effects of the noise on the input and output signals of the plant. We derive integral-type limitations for sensitivity-like properties of the feedback system based on an information theoretic approach. It is shown that they are generalizations of Bode¿s integral formula for the case that the feedback system includes nonlinear elements.