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Automatic Control, IEEE Transactions on

Issue 11 • Date Nov. 2006

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Displaying Results 1 - 23 of 23
  • Table of contents

    Page(s): C1
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  • IEEE Transactions on Automatic Control publication information

    Page(s): C2
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  • Scannings for November 2006

    Page(s): 1733
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  • Cohesive Behaviors of Multiagent Systems With Information Flow Constraints

    Page(s): 1734 - 1748
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (794 KB) |  | HTML iconHTML  

    Bacteria, bees, and birds often work together in groups to find food. A group of mobile wheeled robots can be designed to coordinate their activities to achieve a goal. Networked cooperative uninhabited air vehicles (UAVs) are being developed for commercial and military applications. In order for such multiagent systems to succeed it is often critical that they can both maintain cohesive behaviors and appropriately respond to environmental stimuli. In this paper, we characterize cohesiveness of discrete-time multiagent systems as a boundedness or stability property of the agents' position trajectories and use a Lyapunov approach to develop conditions under which local agent actions will lead to cohesive group behaviors even in the presence of i) an interagent "sensing topology" that constrains information flow, where by "information flow," we mean the sensing of positions and velocities of agents, ii) a random but bounded delay and "noise" in sensing other agents' positions and velocities, and iii) noise in sensing a resource profile that represents an environmental stimulus and quantifies the goal of the multiagent system. Simulations are used to illustrate the ideas for multivehicle systems and to make connections to synchronization of coupled oscillators View full abstract»

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  • Controlling a Class of Nonlinear Systems on Rectangles

    Page(s): 1749 - 1759
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (577 KB) |  | HTML iconHTML  

    In this paper, we focus on a particular class of nonlinear affine control systems of the form xdot=f(x)+Bu, where the drift f is a multi-affine vector field (i.e., affine in each state component), the control distribution B is constant, and the control u is constrained to a convex set. For such a system, we first derive necessary and sufficient conditions for the existence of a multiaffine feedback control law keeping the system in a rectangular invariant. We then derive sufficient conditions for driving all initial states in a rectangle through a desired facet in finite time. If the control constraints are polyhedral, we show that all these conditions translate to checking the feasibility of systems of linear inequalities to be satisfied by the control at the vertices of the state rectangle. This work is motivated by the need to construct discrete abstractions for continuous and hybrid systems, in which analysis and control tasks specified in terms of reachability of sets of states can be reduced to searches on finite graphs. We show the application of our results to the problem of controlling the angular velocity of an aircraft with gas jet actuators View full abstract»

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  • Stabilization via Nonsmooth, Nonconvex Optimization

    Page(s): 1760 - 1769
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (819 KB) |  | HTML iconHTML  

    Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in 1994: find a stable, minimum phase, rational controller that stabilizes a specified second-order plant. Although easily stated, this particular problem remained unsolved until 2002, when a solution was found using an eleventh-order controller. Our computational methods find a stabilizing third-order controller without difficulty, suggesting explicit formulas for the controller and for the closed loop system, which has only one pole with multiplicity 5. Furthermore, our analytical techniques prove that this controller is locally optimal in the sense that there is no nearby controller with the same order for which the closed loop system has all its poles further left in the complex plane. Although the focus of the paper is stabilization, once a stabilizing controller is obtained, the same computational techniques can be used to optimize various measures of the closed loop system, including its complex stability radius or Hinfin performance View full abstract»

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  • Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions

    Page(s): 1770 - 1786
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (685 KB) |  | HTML iconHTML  

    In this paper, we develop a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration. The only assumptions we make about the system are well-posedness of the algebraic loop and local stability. Problems to be considered include the estimation of the domain of attraction, the reachable set under a class of bounded energy disturbances and the nonlinear L2 gain. The regional analysis is established through an effective treatment of the algebraic loop and the saturation/deadzone function. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a norm-bounded differential inclusion (NDI) that contain the original system. Adjustable parameters are incorporated into the differential inclusions to reflect the regional property. The main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain Lyapunov function where the PDI or the NDI is valid. With quadratic Lyapunov functions, conditions for stability and performances are derived as linear matrix inequalities (LMIs). To obtain less conservative conditions, we use a pair of conjugate non-quadratic Lyapunov functions, the convex hull quadratic function and the max quadratic function. These functions yield bilinear matrix inequalities (BMIs) as conditions for stability and guaranteed performance level. The BMI conditions cover the corresponding LMI conditions as special cases, hence the BMI results are guaranteed to be as good as the LMI results. In most examples, the BMI results are significantly better than the LMI results View full abstract»

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  • A Behavioral Approach to Estimation and Dead-Beat Observer Design With Applications to State–Space Models

    Page(s): 1787 - 1797
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (516 KB) |  | HTML iconHTML  

    The observer design problem is investigated in the context of linear left shift invariant discrete behaviors, whose trajectories have supports on Z+. Necessary and sufficient conditions for the existence of a dead-beat observer of some relevant variables from some measured ones, in the presence of some unmeasured (and irrelevant) variables, are introduced, and a complete parametrization of all dead-beat observers is given. Equivalent conditions for the existence of causal dead-beat observers are then derived. Finally, several classical problems addressed for state-space models, like state estimation, the design of unknown input observers or the design of fault detectors and identifiers (possibly in the presence of disturbances), are cast in this general framework, and the aforementioned equivalent conditions and parametrizations are specialized to these cases View full abstract»

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  • Frequency Domain Input–Output Analysis of Sliding-Mode Observers

    Page(s): 1798 - 1803
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (214 KB) |  | HTML iconHTML  

    The sliding-mode (SM) observer dynamics are analyzed in the frequency domain. It is shown that the SM observer is essentially a relay feedback-feedforward system. It is feedback with respect to the measured variable of the system being observed, and the feedforward with respect to the control applied to the system being observed. Having noted this, the input-output properties of observer dynamics are analyzed with the use of the locus of a perturbed relay system (LPRS) method. The performance of the observer is assessed via the use of the frequency response techniques. An example of performance analysis of the observer dynamics in the frequency domain is given View full abstract»

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  • A Block Triangular Form for Nonlinear Observer Design

    Page(s): 1803 - 1808
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    This note reconsiders existence conditions for an established block triangular form (BTF) for a broad class of multi-output nonlinear systems. Systems transformable into BTF coordinates allow for decentralized observer design performed subsystem-at-a-time effectively treating upper subsystem states as measurements. Sufficient conditions are given to ensure that the output is linear in BTF coordinates. An example illustrates the BTF construction and a typical observer design View full abstract»

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  • Partial-State Observers for Nonlinear Systems

    Page(s): 1808 - 1812
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (198 KB) |  | HTML iconHTML  

    This note deals with the design of reduced-order observers for a class of nonlinear systems. The order reduction of the observer is achieved by only estimating a required partial set of the state vector. Necessary and sufficient conditions are derived for the existence of reduced-order observers. An observer design procedure based on linear matrix inequalities is given. A numerical example is given to illustrate the design method View full abstract»

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  • Stabilizing Model Predictive Control of Hybrid Systems

    Page(s): 1813 - 1818
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (454 KB) |  | HTML iconHTML  

    In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory View full abstract»

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  • Generalization of Linear Cyclic Pursuit With Application to Rendezvous of Multiple Autonomous Agents

    Page(s): 1819 - 1824
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    Cyclic pursuit is a simple distributed control law in which agent i pursues agent i+1 modulo n. We generalize existing results and show that by selecting the gains of the agents, the point of convergence of these agents can be controlled. The condition for convergence, the range of controller gains and the reachable set where convergence can occur are studied. It is also shown that the sequence in which an agent pursues another does not affect the point of convergence View full abstract»

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  • Robust Stability of a Class of Uncertain Markov Jump Nonlinear Systems

    Page(s): 1825 - 1831
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (295 KB) |  | HTML iconHTML  

    This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result View full abstract»

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  • Control Effort Reduction in Tracking Feedback Laws

    Page(s): 1831 - 1837
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (611 KB) |  | HTML iconHTML  

    We develop a path-following algorithm for redesign of tracking feedback laws to reduce the control effort. Our algorithm provides a tradeoff between the control effort and the dynamic performance along the path, while maintaining the desired convergence to the path. We illustrate it on a realistic hovercraft model, and compare the resulting control effort with control efforts of other path-following and tracking algorithms View full abstract»

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  • Mode-Independent {cal H}_{\infty } Filters for Markovian Jump Linear Systems

    Page(s): 1837 - 1841
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (251 KB) |  | HTML iconHTML  

    This note addresses the problem of Hinfin filtering for continuous-time linear systems with Markovian jumping parameters. The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant Hinfin filter for systems where the jumping parameter is not accessible. The cases where the transition rate matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust Hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed filter designs are given in terms of linear matrix inequalities View full abstract»

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  • On Repetitive Learning Control for Periodic Tracking Tasks

    Page(s): 1842 - 1848
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB) |  | HTML iconHTML  

    In this note, a repetitive learning control (RLC) approach is proposed to deal with periodic tracking tasks for nonlinear dynamical systems with nonparametric uncertainties. We address two fundamental issues associated with the learning control methodology: The existence of the solution, and learning convergence property. Applying the existence theorem of the neutral differential difference equation, and using Lyapunov-Krasovskii functional, the existence of the solution and learning convergence can be proven rigorously. A further extension of the RLC to cascade systems is also explored View full abstract»

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  • Asymptotic Evaluation of Delay in the SRPT Scheduler

    Page(s): 1848 - 1854
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (310 KB) |  | HTML iconHTML  

    In this note, the shortest remaining processing time (SRPT) scheduler is considered. We focus on the SRPT scheduling policy for a discrete-time queueing system that is accessed by a large number of flows (a many flows regime). In such an asymptotic regime (large capacity and large number of flows), we derive the expression for the delay rate function, which describes the complete delay distribution, for batch arrival processes, and with bounded job sizes. Based on these results, we compare the delay rate function (i.e., for any finite delay, and asymptotic in the number of flows) of the SRPT scheduler with that of a first-in-first-out (FIFO) scheduler, when there is a mix of job sizes. Our analysis holds for any finite mix of job sizes and for truncated heavy-tailed arrival processes. We apply the result to a system accessed by jobs which are one of two sizes: 1 or M. We investigate the unfairness of SRPT by comparing the delay rate function of size M jobs for SRPT and FIFO. We show that the difference in the delay rate function between SRPT and FIFO for size M jobs decay as O(1/M gamma) for some gamma that satisfies 0<gamma<1 and for M sufficiently large. In other words, the delay distributions under FIFO and SRPT becomes increasingly similar for increasingly larger jobs. On the other hand, for size 1 jobs, the delay rate function under SRPT is invariant with M. However, for FIFO, the delay rate function decays as O(1/Mgamma) for some 0<gamma<1 and M large. Thus, for size 1 jobs, SRPT performs increasingly better compared to FIFO as the range in job size increases. These results indicate that SRPT is a good policy to implement for web-servers, where empirical evidence suggests a large variability in job sizes View full abstract»

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  • Observers for a Special Class of Bilinear Systems: Design and Application

    Page(s): 1854 - 1858
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    This note presents full- and reduced-order observation strategies for a subclass of systems that are bilinear in the immeasurable states. Lyapunov analysis is carried out to derive the conditions for convergence of the observed states for all strategies. The full order observer is then utilized in the problem of bus voltage regulation effected by a static compensator (STATCOM) acting as a controlled reactive current source View full abstract»

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  • Convex Optimization

    Page(s): 1859
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    Page(s): 1860
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  • IEEE Control Systems Society Information

    Page(s): C3
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  • Blank page [back cover]

    Page(s): C4
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In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame