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Automatic Control, IEEE Transactions on

Issue 3 • Date March 1996

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Displaying Results 1 - 22 of 22
  • Stability Theory [Book Reviews]

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    Freely Available from IEEE
  • On the robustness of receding-horizon control with terminal constraints

    Page(s): 451 - 453
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    Robustness properties of nonlinear receding-horizon controllers with zero terminal state constraints are investigated with respect to gain and additive perturbations. Some robustness margins are derived by extending to the receding-horizon case the analysis originally proposed by Geromel and da Cruz for infinite-horizon controllers. In the linear case, it is shown that the zero terminal state receding-horizon controller exhibits worse robustness margins compared to standard infinite-horizon LQ control View full abstract»

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  • Motion estimation via dynamic vision

    Page(s): 393 - 413
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    Estimating the three-dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics, such as autonomous navigation, manipulation, servo, tracking, docking, planning, and surveillance. Although “visual motion estimation” is an old problem (the first formulations date back to the beginning of the century), only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions. In this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold. Such a formulation has structural advantages over previous recursive schemes, since the estimation of motion is decoupled from the estimation of the structure of the object being viewed, and therefore it is possible to handle occlusions in a principled way View full abstract»

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  • Quadratic stability and stabilization of linear systems with Frobenius norm-bounded uncertainties

    Page(s): 453 - 456
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    In this paper, a quadratic stability condition and a quadratic stabilizer are proposed for linear systems with Frobenius norm-bounded uncertainties. The necessary and sufficient condition for the quadratic stability of the uncertain system is given by a Riccati inequality. The proposed state feedback quadratic stabilizer can be obtained by solving a Riccati equation View full abstract»

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  • Internal model control and max-algebra: controller design

    Page(s): 457 - 461
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    This note proposes an internal model control for linear discrete-event systems over max-algebra. We concentrate on the controller block of this control structure View full abstract»

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  • Multi-armed bandits with switching penalties

    Page(s): 328 - 348
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    The multi-armed bandit problem with switching penalties (switching cost and switching delays) is investigated. It is shown that under an optimal policy, decisions about the processor allocation need to be made only at stopping times that achieve an appropriate index, the well-known “Gittins index” or a “switching index” that is defined for switching cost and switching delays. An algorithm for the computation of the “switching index” is presented. Furthermore, sufficient conditions for optimality of allocation strategies, based on limited look-ahead techniques, are established. These conditions together with the above-mentioned feature of optimal scheduling policies simplify the search for an optimal allocation policy. For a special class of multi-armed bandits (scheduling of parallel queues with switching penalties and no arrivals), it is shown that the aforementioned property of optimal policies is sufficient to determine an optimal allocation strategy. In general, the determination of optimal allocation policies remains a difficult and challenging task View full abstract»

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  • A new design approach to unknown input observers

    Page(s): 464 - 468
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    This paper proposes a fundamentally new unknown input observer (UIO) which has, uniquely, r decoupled modes, provides r linearly independent combinations of plant system states, and has zero gain to all p, unknown inputs. The parameter r is adjustable. If the plant system satisfies the conditions of the existing UIO, then r=n=plant system order, and there is no difference between our UIO and the existing regular UIO. However, if the plant system satisfies either of the following two significantly more general conditions: m>p (m is the number of plant output measurements) and at least one stable transmission zero, then 1<n, and our UIO can still generate some constrained state feedback control signals. Hence, this new UIO can completely unify the regular UIO (r=n) and the static output feedback (r=m)-the two basic feedback structures of modern control theory far from being unified before View full abstract»

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  • Principle of proportional damages in a multiple criteria LQR problem

    Page(s): 461 - 464
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    A multiple criteria linear quadratic regulator (LQR) problem is considered. The principle of proportional damages is worked out to minimize a norm of a difference between ideal and optimal values of the vector-performance criteria, while the distribution of the losses (damages) of the performance criteria are under control. A multiple criteria LQR problem solution via principle of proportional damages is obtained as a linear form of state variables and is invariant to the norm which is minimized View full abstract»

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  • An alternative proof for convergence of stochastic approximation algorithms

    Page(s): 419 - 424
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    An alternative proof for convergence of stochastic approximation algorithms is provided. The proof is completely deterministic, very elementary (involving only basic notions of convergence), and direct in that it remains in a discrete setting. An alternative form of the Kushner-Clark condition is introduced and utilized and the results are the first to prove necessity for general gain sequences in a Hilbert space setting View full abstract»

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  • On the order of simultaneously stabilizing compensators

    Page(s): 430 - 433
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    In this paper, simultaneous strong stabilization problem is considered, and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator, in terms of the plant orders. A similar problem was also considered by Smith et al. (1986), where it was shown that such a bound does not exist for the strong stabilization problem of a single plant. But the examples given in the article were forcing an approximate unstable pole-zero cancellation or forcing the distance between two distinct unstable zeros to go to zero. In this paper it is shown that: 1) if approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeros are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator, and 2) for the simultaneous strong stabilization problem (even for the two plant case), such a bound cannot be found View full abstract»

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  • J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems

    Page(s): 379 - 392
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    The problem of expressing a given nonlinear state-space system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor is obtained as the solution of an associated nonlinear spectral factorization problem. As an application, one can arrive at the solution of the nonlinear H-control problem for the disturbance feedforward case View full abstract»

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  • Affine parameter-dependent Lyapunov functions and real parametric uncertainty

    Page(s): 436 - 442
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    This paper presents new tests to analyze the robust stability and/or performance of linear systems with uncertain real parameters. These tests are extensions of the notions of quadratic stability and performance where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to a linear matrix inequality (LMI) problem and hence is numerically tractable. These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations. They also avoid the frequency sweep needed in real-μ analysis, and numerical experiments indicate that they often compare favorably with μ analysis for time-invariant parameter uncertainty View full abstract»

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  • Attitude control without angular velocity measurement: a passivity approach

    Page(s): 468 - 472
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    It is well known that the linear feedback of the quaternion of the attitude error and the angular velocity globally stabilizes the attitude of a rigid body. In this note, we show that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion, thus removing the need for direct angular velocity measurement. In contrast to other approaches, this design exploits the inherent passivity of the system; a model-based observer reconstructing the velocity is not needed. An application of the proposed scheme is illustrated for the robot control problem. Simulation results are included to illustrate the theoretical results View full abstract»

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  • Sliding-mode control in discrete-state and hybrid systems

    Page(s): 414 - 419
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    The sliding-mode control approach is developed for a class of discrete-state systems in a metric space. A concept of trajectory continuity is introduced which allows the use of sliding-mode design techniques similar to that in continuous state systems. This approach is then applied to a class of hybrid systems which consists of a continuous plant, an interface, and a discrete-state controller. The introduction of the sliding-mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem View full abstract»

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  • Embedding adaptive JLQG into LQ martingale control with a completely observable stochastic control matrix

    Page(s): 424 - 430
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    With jump linear quadratic Gaussian (JLQG) control, one refers to the control under a quadratic performance criterion of a linear Gaussian system, the coefficients of which are completely observable, while they are jumping according to a finite-state Markov process. With adaptive JLQG, one refers to the more complicated situation that the finite-state process is only partially observable. Although many practically applicable results have been developed, JLQG and adaptive JLQG control are lagging behind those for linear quadratic Gaussian (LQG) and adaptive LQG. The aim of this paper is to help improve the situation by introducing an exact transformation which embeds adaptive JLQG control into LQM (linear quadratic Martingale) control with a completely observable stochastic control matrix. By LQM control, the authors mean the control of a martingale driven linear system under a quadratic performance criterion. With the LQM transformation, the adaptive JLQG control can be studied within the framework of robust or minimax control without the need for the usual approach of averaging or approximating the adaptive JLQG dynamics. To show the effectiveness of the authors' transformation, it is used to characterize the open-loop-optimal feedback (OLOF) policy for adaptive JLQG control View full abstract»

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  • Control of linear systems with saturating actuators

    Page(s): 368 - 378
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    This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design. The authors take a semiglobal approach to solve some of the central control problems for such systems. These problems include stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties. The authors develop further the semiglobal design technology which was initiated in their earlier work (Lin and Saberi, 1995) and utilize it to deal with these control problems View full abstract»

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  • H design with pole placement constraints: an LMI approach

    Page(s): 358 - 367
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    This paper addresses the design of state- or output-feedback H controllers that satisfy additional constraints on the closed-loop pole location. Sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane. These conditions are expressed in terms of linear matrix inequalities (LMIs), and the authors' formulation is therefore numerically tractable via LMI optimization. In the state-feedback case, mixed H2/H synthesis with regional pole placement is also discussed. Finally, the validity and applicability of this approach are illustrated by a benchmark example View full abstract»

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  • Global output regulation and disturbance attenuation with global stability via measurement feedback for a class of nonlinear systems

    Page(s): 315 - 327
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    Considers the problem of global stabilization via output feedback for a class of nonlinear systems which have been previously considered by many authors and are characterized by having nonlinear terms depending only on the output y. The author's result incorporates many previous results. When static output feedback is considered, it is shown that the existence of an output control Lyapunov function, satisfying a suitable continuity property, is sufficient for constructing a continuous output feedback law u=k(y) which globally (or semiglobally) stabilizes the above class of systems. When dynamic output feedback is allowed, it is shown that the stabilization problem can be split into two independent stabilization subproblems: one is the corresponding problem via state feedback, and the other is the problem via output injection. From solving the two subproblems, one obtains two Lyapunov functions which, combined, give a candidate Lyapunov function for solving the output feedback stabilization problem. The proofs of the author's results give systematic procedures for constructing output feedback controllers, once two such Lyapunov functions are known. One can also consider the problem of output regulation and disturbance attenuation with global stability via measurement feedback and show that a similar “separation” condition holds View full abstract»

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  • String stability of interconnected systems

    Page(s): 349 - 357
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    Introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input-output stable. The authors derive sufficient (“weak coupling”) conditions which guarantee the asymptotic string stability of a class of interconnected systems. Under the same “weak coupling” conditions, string-stable interconnected systems remain string stable in the presence of small structural/singular perturbations. In the presence of parameter mismatch, these “weak coupling” conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient-based parameter adaptation law is used and that the states of all the systems go to zero asymptotically View full abstract»

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  • Stable adaptive neural control scheme for nonlinear systems

    Page(s): 447 - 451
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    Based on the Lyapunov synthesis approach, several adaptive neural control schemes have been developed during the last few years. So far, these schemes have been applied only to simple classes of nonlinear systems. This paper develops a design methodology that expands the class of nonlinear systems that adaptive neural control schemes can be applied to and relaxes some of the restrictive assumptions that are usually made. One such assumption is the requirement of a known bound on the network reconstruction error. The overall adaptive scheme is shown to guarantee semiglobal uniform ultimate boundedness. The proposed feedback control law is a smooth function of the state View full abstract»

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  • Robustness of exponential stability of stochastic differential delay equations

    Page(s): 442 - 447
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    Regard the stochastic differential delay equation dx(t)=[(A+A¯(t))+(B+B¯(t-τ))x(t-τ)] dt+g(t, x(t), x(t-τ))dw(t) as the result of the effects of uncertainty, stochastic perturbation, and time lag to a linear ordinary differential equation x˙(t)=(A+B)x(t). Assume the linear system is exponentially stable. In this paper we characterize how much the uncertainty, stochastic perturbation, and time lag the linear system can bear such that the stochastic delay system remains exponentially stable. The result can also be extended to nonlinear systems View full abstract»

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  • An observability criterion for dynamic systems governed by Riccati differential equations

    Page(s): 434 - 436
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    In this paper, we present an observability criterion for systems whose state is governed by a matrix Riccati differential equation and whose output is given by a affine transformation View full abstract»

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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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P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame