Minyue Fu

The sector bound approach to quantized feedback control

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback

The article concerns linear systems which are subject to both time-varying norm-bounded parameter uncertainty and exogenous disturbance. It addresses the robust H/sub infinity / control problem of designing a linear dynamic output feedback controller such that the closed-loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties. It is shown that such a problem is equivalent to a scaled H/sub infinity / control problem. >

Distributed Consensus With Limited Communication Data Rate

Communication data rate and energy constraints are important factors which have to be considered when investigating distributed coordination of multi-agent networks. Although many proposed average-consensus protocols are available, a fundamental theoretic problem remains open, namely, how many bits of information are necessary for each pair of adjacent agents to exchange at each time step to ensure average consensus? In this paper, we consider average-consensus control of undirected networks of discrete-time first-order agents under communication constraints. Each agent has a real-valued state but can only exchange symbolic data with its neighbors. A distributed protocol is proposed based on dynamic encoding and decoding. It is proved that under the protocol designed, for a connected network, average consensus can be achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. An explicit form of the asymptotic convergence rate is given. It is shown that as the number of agents increases, the asymptotic convergence rate is related to the scale of the network, the number of quantization levels and the ratio of the second smallest eigenvalue to the largest eigenvalue of the Laplacian of the communication graph. We also give a performance index to characterize the total communication energy to achieve average consensus and show that the minimization of the communication energy leads to a tradeoff between the convergence rate and the number of quantization levels.

Robust stability for time-delay systems: the edge theorem and graphical tests

The robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable). Given a set D in the complex plane, the goal is to find a constructive technique to verify whether all roots of every quasi-polynomial in P belong to D (that is, to verify the D-stability of P). First it is demonstrated by counterexample that Kharitonovs theorem does not hold for general delay systems. Next it is shown that under a mild assumption on the set D a polytope of quasi-polynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem for the D-stability of a polytope of polynomials. The third result gives a constructive graphical test for checking the D-stability of a polytope of quasi-polynomials which is especially simple when the set D is the open left-half plane. An application is given to demonstrate the power of the results. >

Generalized S-procedure and finite frequency KYP lemma

The contribution of this paper is twofold. First we give a generalization of the S-procedure which has been proven useful for robustness analysis of control systems. We then apply the generalized S-procedure to derive an extension of the Kalman – Yakubovich – Popov lemma that converts a frequency domain condition within a finite interval to a linear matrix inequality condition suitable for numerical computations.

Passivity analysis and passification for uncertain signal processing systems

The problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers, decision feedback equalizers, and digital and analog filters. Equally important is the problem of passification, where a compensator needs to be designed for a given system to become passive. This paper considers these two problems for a large class of systems that involve uncertain parameters, time delays, quantization errors, and unmodeled high-order dynamics. By characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints (IQCs), we present solutions to the problems of robust passivity analysis and robust passification. More specifically, for the analysis problem, we determine if a given uncertain system is passive for all admissible uncertainty satisfying the IQCs. Similarly, for the problem of robust passification, we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty. The solutions are given in terms of the feasibility of one or more linear matrix inequalities (LMIs), which can be solved efficiently.

H/sub infinity / analysis and synthesis of discrete-time systems with time-varying uncertainty

The problems of H/sub infinity / analysis and synthesis of discrete-time systems with block-diagonal real time-varying uncertainty are considered. It is shown that these problems can be converted into scaled H/sub infinity / analysis and synthesis problems. The problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case. The results on synthesis are established for general linear dynamic output feedback control. >

Mean square stability for Kalman filtering with Markovian packet losses

This paper studies the stability of Kalman filtering over a network subject to random packet losses, which are modeled by a time-homogeneous ergodic Markov process. For second-order systems, necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure. While for certain classes of higher-order systems, necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices. All stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the Markov process. Their implications and relationships with related results in the literature are discussed.

Brief paper: State estimation for linear discrete-time systems using quantized measurements

In this paper, we consider the problem of state estimation for linear discrete-time dynamic systems using quantized measurements. This problem arises when state estimation needs to be done using information transmitted over a digital communication channel. We investigate how to design the quantizer and the estimator jointly. We consider the use of a logarithmic quantizer, which is motivated by the fact that the resulting quantization error acts as a multiplicative noise, an important feature in many applications. Both static and dynamic quantization schemes are studied. The results in the paper allow us to understand the tradeoff between performance degradation due to quantization and quantization density (in the infinite-level quantization case) or number of quantization levels (in the finite-level quantization case).

Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian

The paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape. A new technique based on complex Laplacian is introduced to address the problems of which formation shapes specified by inter-agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability. Concerning the first question, we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex Laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter-agent specification of the formation shape is 2-rooted. Concerning the second question, a distributed and linear control law is developed based on the complex Laplacian specifying the target formation shape, and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed-loop system at desired locations are given. Moreover, we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re-design and change their control laws.