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Automatic Control, IEEE Transactions on

Issue 8 • Date Aug. 2009

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Displaying Results 1 - 25 of 43
  • Table of contents

    Page(s): C1 - C4
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    Freely Available from IEEE
  • IEEE Transactions on Automatic Control publication information

    Page(s): C2
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    Freely Available from IEEE
  • Scanning the issue

    Page(s): 1737 - 1738
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  • Model Predictive Control for Stochastic Resource Allocation

    Page(s): 1739 - 1750
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (421 KB) |  | HTML iconHTML  

    In this paper, we consider a class of stochastic resource allocation problems where resources assigned to a task may fail probabilistically to complete assigned tasks. Failures to complete a task are observed before new resource allocations are selected. The resulting temporal resource allocation problem is a stochastic control problem, with a discrete state space and control space that grow in cardinality exponentially with the number of tasks. We modify this optimal control problem by expanding the admissible control space, and show that the resulting control problem can be solved exactly by efficient algorithms in time that grows nearly linear with the number of tasks. The approximate control problem also provides a bound on the achievable performance for the original control problem. The approximation is used as part of a model predictive control (MPC) algorithm to generate resource allocations over time in response to information on task completion status. We show in computational experiments that, for single resource class problems, the resulting MPC algorithm achieves nearly the same performance as the optimal dynamic programming algorithm while reducing computation time by over four orders of magnitude. In multiple resource class experiments involving 1000 tasks, the model predictive control performance is within 4% of the performance bound obtained by the solution of the expanded control space problem. View full abstract»

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  • Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots

    Page(s): 1751 - 1764
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (769 KB) |  | HTML iconHTML  

    Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation. View full abstract»

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  • Network Formation: Bilateral Contracting and Myopic Dynamics

    Page(s): 1765 - 1778
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (567 KB) |  | HTML iconHTML  

    We consider a network formation game where nodes wish to send traffic to each other. Nodes contract bilaterally with each other to form bidirectional communication links; once the network is formed, traffic is routed along shortest paths (if possible). Cost is incurred to a node from four sources: 1) routing traffic; 2) maintaining links to other nodes; 3) disconnection from destinations the node wishes to reach; and 4) payments made to other nodes. We assume that a network is stable if no single node wishes to unilaterally deviate, and no pair of nodes can profitably deviate together (a variation on the notion of pairwise stability). We study such a game under a form of myopic best response dynamics. In choosing their action, nodes optimize their single period payoff only. We characterize a simple set of assumptions under which these dynamics converge to a stable network; we also characterize an important special case, where the dynamics converge to a star centered at a node with minimum cost for routing traffic. In this sense, our dynamics naturally select an efficient equilibrium. View full abstract»

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  • The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper

    Page(s): 1779 - 1793
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (985 KB) |  | HTML iconHTML  

    A hybrid controller that induces provably stable running gaits on an asymmetric spring loaded inverted pendulum (ASLIP) is developed. The controller acts on two levels. On the first level, continuous within-stride control asymptotically imposes a (virtual) holonomic constraint corresponding to a desired torso posture, and creates an invariant surface on which the two-degree-of-freedom restriction dynamics of the closed-loop system (i.e., the hybrid zero dynamics) is diffeomorphic to the center-of-mass dynamics of a spring loaded inverted pendulum (SLIP). On the second level, event-based control stabilizes the closed-loop hybrid system along a periodic orbit of the SLIP dynamics. The controller's performance is discussed through comparison with a second control law that creates a one-degree-of-freedom non-compliant hybrid zero dynamics. Both controllers induce identical steady-state behaviors (i.e., periodic solutions). Under transient conditions, however, the controller inducing a compliant hybrid zero dynamics based on the SLIP accommodates significantly larger disturbances, with less actuator effort, and without violation of the unilateral ground force constraints. View full abstract»

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  • Global Stabilization of the Generalized MIMO Triangular Systems With Singular Input-Output Links

    Page(s): 1794 - 1806
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (502 KB) |  | HTML iconHTML  

    This work is devoted to the problem of global stabilization for a class of the general multi-input and multi-output (MIMO) triangular systems which are not feedback linearizable. To solve the problem, we develop a specific backstepping procedure and generalize some existing results. Since we deal with the global stabilization for the singular and MIMO case, the technique of the proof differs from the standard backstepping algorithms. View full abstract»

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  • Data Transmission Over Networks for Estimation and Control

    Page(s): 1807 - 1819
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (784 KB) |  | HTML iconHTML  

    We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network. View full abstract»

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  • Fault Detection Schemes for Continuous-Time Stochastic Dynamical Systems

    Page(s): 1820 - 1836
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (722 KB) |  | HTML iconHTML  

    In this paper the fault detection (FD) task in stochastic continuous-time dynamical systems is addressed. A new family of FD approaches is presented, which is based on the application of hypothesis testing on continuous-time estimators. The given FD schemes are widely analyzed in the framework of their characteristics, such as fault detectability, false alarms and missed detection. A collection of sufficient detectability conditions are given for a class of faults (referred here as generic), characterizing the faults which can be detected with certain formalized guarantee by the given FD schemes, and providing also an upper bound for the detection time in a probabilistic sense. The application and comparative performance of these FD approaches is illustrated for different faults in a simulation example. View full abstract»

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  • A Control Approach for Thrust-Propelled Underactuated Vehicles and its Application to VTOL Drones

    Page(s): 1837 - 1853
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1519 KB) |  | HTML iconHTML  

    A control approach is proposed for a class of underactuated vehicles in order to stabilize reference trajectories either in thrust direction, velocity, or position. The basic modeling assumption is that the vehicle is pro-pulsed via a thrust force along a single body-fixed direction and that it has full torque actuation for attitude control (i.e., a typical actuation structure for aircrafts, vertical take-off and landing (VTOL) vehicles, submarines, etc.). Additional assumptions on the external forces applied to the vehicle are also introduced for the sake of control design and stability analyses. They are best satisfied for vehicles which are subjected to an external force field (e.g., gravity) and whose shape induces lift forces with limited amplitude, unlike airplanes but as in the case of many VTOL drones. The interactions of the vehicle with the surrounding fluid are often difficult to model precisely whereas they may significantly influence and perturb its motion. By using a standard Lyapunov-based approach, novel nonlinear feedback control laws are proposed to compensate for modeling errors and perform robustly against such perturbations. Simulation results illustrating these properties on a realistic model of a VTOL drone subjected to wind gusts are reported. View full abstract»

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  • Trajectory Planning for Boundary Controlled Parabolic PDEs With Varying Parameters on Higher-Dimensional Spatial Domains

    Page(s): 1854 - 1868
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (953 KB) |  | HTML iconHTML  

    The flatness-based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion-convection-reaction system with spatially and temporally varying parameters defined on a 1 les m-dimensional parallelepipedon with the nonlinear input being restricted to a (m-1) -dimensional hyperplane. For this, an implicit state and input parametrization in terms of a basic output is determined via a Volterra-type integral equation with operator kernel. By recursively computing successive series coefficients, a series solution of the integral equation is obtained, whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad Gevrey class. Hence, prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization. This results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed-parameter systems defined on higher-dimensional domains. View full abstract»

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  • Analysis of Pinning-Controlled Networks: A Renormalization Approach

    Page(s): 1869 - 1875
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (556 KB) |  | HTML iconHTML  

    In this paper, a renormalization approach is introduced for analyzing pinning-controlled networks. The renormalization process consists of two operations, edge weighting and node reduction, and is built on a new concept of passivity comparison in the sense of Lyapunov V-stability. Furthermore, a cascaded model resulted from the renormalization process in a layer structure is presented for estimating the V -stability of a network. Finally, simulation studies are presented for illustration and verification of the theoretical results. View full abstract»

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  • Stability Optimization of Hybrid Periodic Systems via a Smooth Criterion

    Page(s): 1875 - 1880
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (510 KB) |  | HTML iconHTML  

    We consider periodic orbits of controlled hybrid dynamic systems and want to find open-loop controls that yield maximally stable limit cycles. Instead of optimizing the spectral or pseudo-spectral radius of the monodromy matrix A, which are non-smooth criteria, we propose a new approach based on the smoothed spectral radius rhoalpha(A) , a differentiable criterion favorable for numerical optimization. Like the pseudo-spectral radius, the smoothed spectral radius rhoalpha(A) converges from above to the exact spectral radius rho(A) for alphararr 0. Its derivatives can be computed efficiently via relaxed Lyapunov equations. We show that our new smooth stability optimization program based on rhoalpha(A) has a favorable structure: it leads to a differentiable nonlinear optimal control problem with periodicity and matrix constraints, for which tailored boundary value problem methods are available. We demonstrate the numerical viability of our method using the example of a walking robot model with nonlinear dynamics and ground impacts as a complex open-loop stability optimization example. View full abstract»

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  • Switching-Driving Lyapunov Function and the Stabilization of the Ball-and-Plate System

    Page(s): 1881 - 1886
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    This note introduces the notion of switching-driving Lyapunov function which can be used to provide a sufficient stabilizability condition for general nonlinear systems. The theory is illustrated by means of the ldquoball-and-platerdquo system, for which locally stabilizing control laws are explicitly derived. View full abstract»

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  • Remarks on Dwell Time Solutions and Stability of Families of Nonlinear Vector Fields

    Page(s): 1886 - 1892
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    In this note, we discuss the problem of stability of (finite or infinite) families of continuous vector fields, all of them asymptotically stable but, in general, not exponentially stable. Under a multiple Liapunov function condition and an average dwell time constraint, we prove that the system possesses a form of stability, weaker than the standard one. The advantage of our results is that the conditions imposed on the Liapunov functions can be verified a priori, with no previous knowledge of the integral curves of the family. View full abstract»

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  • Simultaneous Stabilization and Robust Control of Polynomial Nonlinear Systems Using SOS Techniques

    Page(s): 1892 - 1897
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (596 KB) |  | HTML iconHTML  

    This technical note is concerned with the simultaneous stabilization and robust performance control for a class of polynomial nonlinear systems. Building on the tenets of state-dependent polynomial Lyapunov functions, we present sufficient conditions for simultaneous stabilization with and without Hinfin performance. These conditions can be verified by the recently developed sum of squares technique which essentially solves a linear matrix inequality feasibility problem. View full abstract»

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  • On Input-to-State Stability of Stochastic Retarded Systems With Markovian Switching

    Page(s): 1898 - 1902
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    This note develops a Razumikhin-type theorem on pth moment input-to-state stability of hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), which is an improvement of an existing result. An application to hybrid stochastic delay systems verifies the effectiveness of the improved result. View full abstract»

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  • Signal-to-Noise Ratio Fundamental Limitations in Continuous-Time Linear Output Feedback Control

    Page(s): 1902 - 1907
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (219 KB) |  | HTML iconHTML  

    In the present technical note we study the fundamental limitation on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered over either the control or measurement paths of a linear time invariant (LTI) feedback loop. By considering a linear setting we can naturally express the fundamental limitation as a lower bound on the channel signal-to-noise ratio (SNR) required for stabilisability. We start by first obtaining a closed-form expression for the squared L 2 norm of a partial fraction expansion with repeated poles in the Laplace domain. We then use the squared L 2 norm result to obtain the closed-form expression for the infimal SNR required for stabilisability. The proposed closed-form includes the case of repeated unstable plant poles and non minimum phase (NMP) zeros. View full abstract»

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  • Stability Analysis of a Max-Min Fair Rate Control Protocol (RCP) in a Small Buffer Regime

    Page(s): 1908 - 1913
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    In this note we analyse various stability properties of a max-min fair rate control protocol (RCP) operating with small buffers. We first tackle the issue of stability for networks with arbitrary topologies. We prove that the max-min fair RCP fluid model is globally stable in the absence of propagation delays, and also derive a set of conditions for local stability when arbitrary heterogeneous propagation delays are present. The network delay stability result assumes that, at equilibrium, there is only one bottleneck link along each route. Lastly, in the simpler setting of a single link, single delay model, we investigate the impact of the loss of local stability via a Hopf bifurcation. View full abstract»

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  • Monotone Piecewise Affine Systems

    Page(s): 1913 - 1918
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    Piecewise affine (PWA) systems are autonomous systems with discontinuous vector fields which are affine ordinary differential equations at the points of continuity. These systems have applications to many fields of engineering, including systems biology and traffic engineering. We define what it means for a PWA system to be monotone, and we provide a set of sufficient conditions for monotonicity of PWA systems with hyperrectangular invariants. Such sufficient conditions are useful for understanding the dynamics of such PWA systems and for designing controllers for qualitative, reference tracking. We apply these results towards the drug-discovery problem for the cancer-related p53 pathway. View full abstract»

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  • Certainty Equivalence Adaptive Control of Plants With Unmatched Uncertainty Using State Feedback

    Page(s): 1918 - 1924
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (342 KB) |  | HTML iconHTML  

    A systematic design procedure using state-feedback certainty equivalence adaptive control (CEAC) technique is developed for linear plants and a class of nonlinear plants with unmatched uncertainty. It is shown that a reduced order observer and adaptive laws with normalization in conjunction with the CEAC law result in a stable overall system in the case of linear plants of any relative degree, and a class of nonlinear plants of relative degree two. In the case of higher relative degrees a CEAC approach based on multiple observers is proposed. The proposed schemes guarantee overall system stability and asymptotic tracking. View full abstract»

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  • On the “Uniform” Observability of Discrete-Time Nonlinear Systems

    Page(s): 1925 - 1928
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    In constructing an observer for a discrete-time nonlinear system, the system is commonly required to satisfy a certain kind of "uniform" observability condition, that is, the state should always be reconstructible from observation windows of a specific length, irrespective of the values of the state and inputs. In this technical note, it is proved that this "uniform" requirement is unnecessary in the sense that if the initial state and inputs are on a compact set, then the "uniform" observability is derived from its non-uniform counterpart. View full abstract»

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  • Globally Optimal Distributed Kalman Fusion With Local Out-of-Sequence-Measurement Updates

    Page(s): 1928 - 1934
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (237 KB) |  | HTML iconHTML  

    In a distributed multisensor fusion systems, observations produced by sensors can arrive at local processors out of sequence. The resulting problem at the central processor/fusion center-how to update current estimate using multiple local out-of-sequence-measurement (OOSM) updates - is a nonstandard distributed estimation problem. In this note, based on the centralized update algorithm with multiple asynchronous (1-step-lag) OOSMs see we firstly deduce the optimal distributed fusion update algorithm with multiple local asynchronous (1-step-lag) OOSM updates, which is proved, under some regularity conditions, to be equivalent to the corresponding optimal centralized update algorithm with all-sensor 1-step-lag OOSMs. Then, we propose an optimal distributed fusion update algorithm with multiple local arbitrary-step-lag OOSM updates. View full abstract»

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  • Modified Anti-Windup Compensators for Stable Plants

    Page(s): 1934 - 1939
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (314 KB) |  | HTML iconHTML  

    We investigate the effects of deferring the activation of anti-windup by allowing actuators to remain in the saturated regime longer, without any assistance. The basic idea is to apply anti-windup when the performance of the saturated system faces substantial degradation. For this, we present a modified anti-windup scheme along with the appropriate LMIs to obtain the gains. For two examples, we show that the modified anti-windup scheme renders better performance than the immediate application of anti-windup. View full abstract»

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Aims & Scope

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

Full Aims & Scope

Meet Our Editors

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