Mahbub Gani

H/sub /spl infin// control for networked systems with random communication delays

This note is concerned with a new controller design problem for networked systems with random communication delays. Two kinds of random delays are simultaneously considered: i) from the controller to the plant, and ii) from the sensor to the controller, via a limited bandwidth communication channel. The random delays are modeled as a linear function of the stochastic variable satisfying Bernoulli random binary distribution. The observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and also achieve the prescribed H/sub /spl infin// disturbance attenuation level. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality (LMI) approach. An illustrative example is provided to show the applicability of the proposed method.

Robust

In this technical note, the robust control problem is investigated for a class of stochastic uncertain discrete time-delay systems with missing measurements. The parameter uncertainties enter into the state matrices, and the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. The purpose of the problem is to design a full-order dynamic feedback controller such that, for all possible missing observations and admissible parameter uncertainties, the closed-loop system is asymptotically mean-square stable and satisfies the prescribed performance constraint. Delay-dependent conditions are derived under which the desired solution exists, and the controller parameters are designed by solving a linear matrix inequality (LMI). A numerical example is provided to illustrate the usefulness of the proposed design method.

H_{\infty }

In this technical note, the problem of designing fixed-order robust Hinfin controllers is considered for linear systems affected by polytopic uncertainty. A polynomial method is employed to design a fixed-order controller that guarantees that all the closed-loop poles reside within a given region of the complex plane. In order to utilize the freedom of the controller design, an Hinfin performance specification is also enforced by using the equivalence between robust stability and Hinfin norm constraint. The design problem is formulated as a linear matrix inequality (LMI) constraint whose decision variables are controller parameters. An illustrative example demonstrates the feasibility of the proposed design methods.

Control With Missing Measurements and Time Delays

This paper investigates the problem of designing decentralized robust Kalman filters for sensor networks observing a physical process with parametric uncertainty. A sensor network consists of distributed collection of nodes, each of which has sensing, communication and computation capabilities. We consider a heterogeneous sensor network consisting of two types of nodes (type A and type B) and central base station. Type A nodes undertake the sensing and make noisy observations of the same physical process while type B nodes play the role of cluster-heads. We derive the information form of robust Kalman filter by using the Krein space approach which proves to be useful to fuse the cluster state estimates. We obtain the decentralized robust Kalman filter for each type B node for the state estimation of uncertain stochastic system by taking into consideration the sensing model of each cluster and the information form of robust Kalman filter. The type B nodes transmit their state estimates along with the inverse of error covariance matrix to the central base station which fuses the cluster state estimates to generate the overall global state estimate. Simulation results demonstrate that the performance of the centralized state estimate is comparable to the performance of the global state estimate and this suggests that they are identical.

Fixed-Order Robust

In this paper, the robust H₂/H_∞ filtering problem is addressed for a class of uncertain discrete-time stochastic systems with missing measurement. The purpose of this paper is to design a filter, such that for all possible missing measurement and admissible uncertainty, the filtering process is exponentially mean-square quadratically stable, and simultaneously achieves the prescribed H₂ and H_∞ performance specifications. Sufficient conditions are derived, respectively, to ensure mean-square stability, the H₂ performance, and the H _∞ performance. A unified framework is established to solve the addressed robust H₂/H_∞ filtering problem by using a linear matrix inequality (LMI) approach. As a by-product, two additional optimization problems are dealt with, aiming to optimize the H₂and H_∞ filtering performances. A numerical example is provided to illustrate the usefulness of the proposed method

H_{\infty}

In this paper, we propose a novel robust H∞ optimisation approach to the design of digital filters for calibrating 2-1 cascaded sigma delta modulators. The main contribution of this paper consists of two parts. First, we develop a new filter design technique based on a linear matrix inequality (LMI) approach to model-matching problem with polytopic uncertainties in parameters. The advantage of the proposed method is that it leads to an optimal, less conservative, solution to the robust H∞ filtering problem. The second contribution involves the application of the proposed robust filter design scheme to correct for inevitable and unwelcome analog imperfections typically associated with cascaded sigma delta modulators. For numerical illustration we concentrate on the 2-1 architecture. Simulation results for a range of parameter excursions suggest that our robust H∞ filter guarantees an improved signal-to-noise ratio (SNR) performance over the nominal filter

Controller Design With Regional Pole Assignment

Variability in the analogue components of integrators in cascaded 2-1 sigma-delta modulators causes imperfect cancellation of first stage quantization noise, and reduced signal-to-noise ratio in analogue-to-digital converters. Design of robust matching filters based on low-frequency weighted convex optimization over uncertain linearized representations are mathematically very complex and computationally intensive, and offer little insight into the solution. This letter describes a design method based on formal optimization of a low-frequency uncertain linearized model of the modulator, and leads to a simple intuitive result which can shed light on the more complex models. Simulation results confirm the optimal properties of the filter.

Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks

This paper considers the problem of estimating the state of nonlinear stochastic processes observed by spatially distributed sensor nodes i.e, observations are taken by a network of sensor nodes. The measurement process of each node is assumed to be some nonlinear function of an unobservable process and is corrupted by gaussian noise. We refer to a scenario in which all nodes in the network wish to have near-optimal identical state estimate of the observed process and there is no centralized computation center. Sensor nodes do not have any global knowledge of the network topology and nodes are allowed to communicate with only their nearest neighbors. Each node applies a particle filtering algorithm to its own measurements to generate an individual state estimated signal. These nodes based estimated signals are then combined by using nonlinear distributed fusion rule to produce improved state estimated signal at each node. We demonstrate through numerical example that the performance of fused state estimated signal is superior to the performance of the state estimated signal generated by particle filtering algorithm.

Robust H 2 /H ∞ Filtering for Uncertain Systems with Missing Measurement

Uncertainty in the integrators of 2-1 sigma-delta modulators causes imperfect cancellation of first stage quantization noise, and reduces signal-to-noise ratio in analogue-to-digital converters. Design of robust matching filters based on convex optimization over uncertain linearized state-space representations gives complicated models and high-order designs. This letter describes a polynomial design method leading to simpler multilinear models and fixed-order filters. The modulators are cast as a polynomial polytope, and filters satisfying an Hinfin bound arise from solving linear matrix inequalities (LMIs). Results at low frequency show the proposed filter outperforming the nominal one, with a performance close to the estimated optimum.

An H ∞ Approach for Robust Calibration of Cascaded Sigma Delta Modulators

This paper proposes a hierarchical architecture for a heterogeneous sensor network consisting of both mobile and fixed agents. The hierarchy contains three layers. The lowest level, Layer 0, is the sensing layer and consists of fixed sensors deployed in an environment of interest according to a spatial Poisson distribution of intensity measure A. Layer 1, the next level in the hierarchy, is the aggregation layer and involves mobile agents (e.g., autonomous vehicles) gathering the sensed data from the Layer 0 nodes based on a nearest neighbour rule. The highest level of the hierarchy is the query layer, which represents requests for the data gathered by the sensors to be transmitted, via the Layer 1 agents, to a mobile base station (e.g., a flying aircraft periodically visiting the area of interest). We construct for this network a utility function which basically captures the cost associated with communication, as seen from the point of view of the mobile agents of Layer 1. Based on a gradient descent strategy we propose a motion coordination scheme to maneuver the mobile nodes from an arbitrary initial arrangement to one that minimizes the utility function. The application of the proposed algorithm in an elementary settings is illustrated via numerical simulations