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Automatic Control, IEEE Transactions on

Issue 3 • Date Mar 1991

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Displaying Results 1 - 17 of 17
  • Impulse control of piecewise-deterministic processes via linear programming

    Page(s): 371 - 375
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    In previous papers a state-space discretization technique in which the continuous-time discretized piecewise-deterministic Markov process (discretization on the post-jump location) approaches the original process uniformly on compact sets has been presented. Under the assumptions of continuity and boundedness of the cost function, it follows that the total discounted cost will also approach the original total cost, at least for epsilon -optimal strategies, which means that the optimal cost of the discretized process should converge to the original optimal cost. The author considers a time discretization so that the new discretized problem (state space and intervention times discretizations) will be finite-dimensional and linear programming (LP) can be used to solve it. The author presents a method that can considerably reduce the number of inequalities of the LP problem. An application to the maintenance of complex systems is given. View full abstract»

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  • Stability analysis of position and force control for robot arms

    Page(s): 365 - 371
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    Stability issues involving the control of a robot arm under the influence of external forces are discussed. Several different scenarios are considered: position control with the external force as an unmodeled disturbance, compliant control for a bounded external force in some subspace, and compliant control for a force due to the interaction with an environment whose dynamical behavior can be modeled. In each of these cases, a stability analysis using the Lyapunov method is presented. An explanation of instability is suggested in the case that the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust (in time delay) stability can be achieved via the integral force feedback. However, the integral feedback gain should be chosen sufficiently small to account for possible flexibility in the system View full abstract»

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  • Partial eigenstructure assignment and its application to large scale systems

    Page(s): 340 - 347
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    The notion of partial eigenstructure assignment (PEA) via linear state feedback control in linear multivariable systems is introduced. This notion is a natural extension of eigenstructure assignment and partial eigenvalue assignment. Some theoretical basis for PEA is provided, and a parametric expression for feedback gain matrices achieving PEA is derived. An effective numerical algorithm for PEA tailored to large-scale systems is presented. As an extension of the algorithm, a recursive algorithm for eigenstructure assignment is presented. These algorithms possess the following desired properties: (1) compared to existing methods, the presented algorithms significantly reduce the required computation time via transforming high-dimensional matrix computations into low-dimensional matrix computations; (2) they can be implemented in a parallel fashion. The proposed algorithm for PEA is applied to modal control of large flexible space structure systems View full abstract»

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  • Robust stability of discrete-time systems using delta operators

    Page(s): 377 - 380
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    The robust stability of discrete-time systems formulated in terms of the delta (δ) operator is discussed. That is, given the nominal characteristic equation P(δ) of a discrete-time system, it is of interest to know how much the coefficients can be perturbed while preserving stability. A procedure to obtain the maximum intervals for a perturbed polynomial P(δ) to still be stable is presented View full abstract»

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  • Persistent excitation in bilinear systems

    Page(s): 305 - 313
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    Discrete-time systems described by difference equations which are polynomial in the input and linear in the output are discussed. Bilinear systems are special members of this class. Two issues are examined. First, a multidimensional polynomial-based algebraic condition which is necessary and sufficient for such systems to be identifiable is given. Second, subject to an identifiability assumption, a condition on the input sequence which guarantees persistent excitation is given. The principle analytic tool used in this study involves multidimensional polynomials View full abstract»

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  • Paradigms and puzzles in the theory of dynamical systems

    Page(s): 259 - 294
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    A self-contained exposition is given of an approach to mathematical models, in particular, to the theory of dynamical systems. The basic ingredients form a triptych, with the behavior of a system in the center, and behavioral equations with latent variables as side panels. The author discusses a variety of representation and parametrization problems, in particular, questions related to input/output and state models. The proposed concept of a dynamical system leads to a new view of the notions of controllability and observability, and of the interconnection of systems, in particular, to what constitutes a feedback control law. The final issue addressed is that of system identification. It is argued that exact system identification leads to the question of computing the most powerful unfalsified model View full abstract»

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  • Feedback gains for correcting small perturbations to standing posture

    Page(s): 322 - 332
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    A dynamical model of the neuro-musculo-skeletal mechanics of a cat hindlimb is developed to investigate the feedback regulation of standing posture under small perturbations. The model is a three-joint limb, moving only in the sagittal plane, driven by 10 musculotendon actuators, each with response dynamics dependent on activation kinetics and muscle kinematics. Under small perturbations, the nonlinear postural regulation mechanism is approximately linear. Sensors exist which could provide state feedback. Thus, the linear quadratic regulator is proposed as a model for the structure of the feedback controller for regulation of small perturbations. System states are chosen to correspond to the known outputs of physiological sensors: muscle forces (sensed by tendon organs), a combination of muscle lengths and velocities (sensed by spindle organs), joint angles and velocities (sensed by joint receptors), and motoneuron activities (sensed by Renshaw cells). Thus, the feedback gain matrices computed can be related to the spinal neural circuits. Several proposals for control strategy have been tested under this formulation. It is shown that a strategy of regulating all the states leads to controllers that best mimic the externally measured behavior of real cats View full abstract»

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  • An adaptive variable structure model following control design for robot manipulators

    Page(s): 347 - 353
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    An adaptive variable structure model-following control (AVSMFC) design is proposed for trajectory tracking in a nonlinear robot system which ensures the stability of the intersection of the surfaces without necessarily stabilizing each individual one. The approach avoids the difficulties linked to the strict positive realness requirement in traditional AMFC by taking advantage of the inherent positive definiteness of the manipulator's inertia matrix, and is easily extendible to a higher number of links. The controller does not require any knowledge of a nonlinear robotic system and does not necessarily need the occurrence of a sliding mode at each individually stable discontinuity surface. It thus greatly reduces the complexity of design. In the closed loop, the joint angles asymptotically converge to the reference trajectory with a prescribed transient response. Chattering is eliminated by restricting the state of the system to slide within a boundary layer rather than along the intersection of the surfaces View full abstract»

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  • Robust stability analysis of polynomials with linearly dependent coefficient perturbations

    Page(s): 380 - 384
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    A computational tractable procedure for robust pole location analysis of uncertain linear time-invariant dynamical systems, whose characteristic polynomial coefficients depend linearly on parameter perturbations, is proposed. It is shown that, in the case of linearly dependent coefficient perturbations, the stability test with respect to any unconnected domain of the complex plane can be carried out, and the largest stability domain in parameter space can be computed by using only a quick test on a particular set of polynomials named vertex polynomials. The procedure requires only one sweeping function and simple geometrical considerations at each sweeping step. This leads to a very short execution time, as is shown in an example. A unification with Kharitonov's theory and edge theorem is also provided View full abstract»

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  • The graph topology on nth-order systems is quotient Euclidean

    Page(s): 338 - 340
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    It is shown that on the set of m-input p-output minimal nth-order state-space systems the graph topology and the induced Euclidean quotient topology are identified. The author considers the set Lnp×m of m -input p-output nth-order minimal state-space systems. The author presents three lemmas and a corollary from which a theorem is proved stating that the graph topology and the quotient Euclidean topology are identical on a quotient space Ln p×m/~. Since the graph topology is constructed to be weak, and the quotient Euclidean topology is intuitively strong, this result is unexpected View full abstract»

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  • Frequency domain synthesis of optimal inputs for online identification and adaptive control

    Page(s): 353 - 358
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    The authors formulate an input design problem for choosing proper inputs for use in single-input-single-output (SISO) online identification and model reference adaptive control algorithms. When the convergence rate divided by the adaptation gain is optimized for this adaptation gain going to zero, characterization of the optimal inputs is given in the frequency domain and is arrived at through the use of averaging theory. An expression for what is termed the average information matrix is derived and its properties are studied. To solve the input design problem, the authors recast the design problem in the form of an optimization which maximizes the smallest eigenvalue of the average information matrix over power constrained signals. A convergent numerical algorithm is provided to obtain the optimal solution View full abstract»

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  • A Levinson-type algorithm for modeling fast-sampled data

    Page(s): 314 - 321
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    The standard discrete-time autoregressive model is poorly suited for modeling series obtained by sampling continuous-time processes at fairly rapid rates. Large computational errors can occur when the Levinson algorithm is used to estimate the parameters of this model, because the Toeplitz covariance matrix is ill-suited for inversion. An alternative model is developed based on an incremental difference operator, rather than the shift operator. It is shown that, as the sampling period goes to zero, unlike the standard autoregressive parameters, the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous-time process. A Levinson-type algorithm for efficiently estimating the parameters of this model is derived. Numerical examples are given to show that when the sampling interval is small this algorithm is considerably less sensitivity to arithmetic roundoff errors than the Levinson algorithm View full abstract»

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  • Approximate noninteracting control with stability for nonlinear systems

    Page(s): 295 - 304
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    A notion of approximate noninteracting control with stability for nonlinear systems is introduced, and the design of both static and dynamic state-feedback control laws that achieve this property for a given plant is considered. This approach to the problem is based on the notion of extended linearization, and begins with an extension of the linearization approach pointwise to all constant operating points in an open neighborhood of the nominal. Under natural assumptions it is shown that obstructions to extract noninteracting control with internal stability, or input-state/output stability, can be circumvented in the context of approximate noninteraction View full abstract»

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  • Computing bifurcation points via characteristics gain loci

    Page(s): 358 - 362
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    The authors show how to check the crossing on the imaginary axis by the eigenvalues of the linearized system of differential equations depending on a real parameter μ via feedback system theory. E. Hopf's theorem (1942) refers to a system of ordinary differential equations depending on the real parameter μ in which, when a single pair of complex conjugate eigenvalues of the linearized equations cross the imaginary axis under the parameter vibration, near this critical condition periodic orbits appear. The authors present simple formulas for both static (one eigenvalue zero) and dynamic or Hopf (a single pure imaginary pair) bifurcations, and show some singular conditions (degeneracies) by continuing the bifurcation curves in the steady-state manifold. The bifurcation curves and singular sets of an interesting chemical reactor which possesses multiplicity in the equilibrium solutions and in the Hopf bifurcation points are described View full abstract»

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  • Periodic strong solution for the optimal filtering problem of linear discrete-time periodic systems

    Page(s): 333 - 338
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    The periodic Riccati difference equation (PRDE) for the optimal filtering problem of linear periodic discrete-time systems is addressed. Specifically, the author provides a number of results on the existence, uniqueness, and stability properties of symmetric periodic nonnegative-definite solutions of the periodic Riccati difference equation in the case of nonreversible and nonstabilizable periodic systems. The convergence of symmetric periodic nonnegative-definite solutions of the periodic Riccati difference equation is also analyzed. The results have been established under weaker assumptions and include both necessary and sufficient conditions. The existence and properties of symmetric periodic nonnegative-definite solutions of the PRDE are established directly from the PRDE View full abstract»

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  • Optimal root loci of flexible space structures

    Page(s): 375 - 377
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    It is shown that simple generic properties can be proved for the optimal root loci of flexible space structures (FSS). It is proved that the angles and rates at which closed-loop poles depart from the open-loop poles can be found by inspection for any FSS with sufficiently widely space natural frequencies. Similar results also apply to the angles at which certain loci approach the transmission zeros of any FSS with compatible (physically colocated and coaxial) sensors and actuators, as a consequence of the special properties of the zeros of such systems. Finally, determining the number and orders of the Butterworth configurations of such as FSS is much more straightforward than for a general state-space system: it amounts only to checking whether structural displacements or their rates are the measured outputs. These results depend on the fundamental second-order nature of such systems, and five considerably more insight than is possible a priori for general linear multivariable systems View full abstract»

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  • A root distribution criterion for interval polynomials

    Page(s): 362 - 364
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    The problem of finding the conditions under which an interval polynomial has a given number of roots in the open left-half plane and the other roots in the open right-half plane, irrespective of the values of its coefficients, is considered. A simple criterion is provided to test interval polynomials for the root distribution invariance, viewed as an extension of Kharitonov's theorem. The goal is to provide an alternative theorem and then give an efficient means of checking the root distribution invariance 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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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame