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Automatic Control, IEEE Transactions on

Issue 8 • Date Aug. 1997

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Displaying Results 1 - 19 of 19
  • Optimal Sampled-data Control Systems [Book Reviews]

    Publication Year: 1997 , Page(s): 1190 - 1191
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    Freely Available from IEEE
  • On the partial stochastic realization problem

    Publication Year: 1997 , Page(s): 1049 - 1070
    Cited by:  Papers (26)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (952 KB)  

    We describe a complete parameterization of the solutions to the partial stochastic realization problem in terms of a nonstandard matrix Riccati equation. Our analysis of this covariance extension equation (CEE) is based on a complete parameterization of all strictly positive real solutions to the rational covariance extension problem, answering a conjecture due to Georgiou (1987) in the affirmative. We also compute the dimension of partial stochastic realizations in terms of the rank of the unique positive semidefinite solution to the CEE, yielding some insights into the structure of solutions to the minimal partial stochastic realization problem. By combining this parameterization with some of the classical approaches in partial realization theory, we are able to derive new existence and robustness results concerning the degrees of minimal stochastic partial realizations. As a corollary to these results, we note that, in sharp contrast with the deterministic case, there is no generic value of the degree of a minimal stochastic realization of partial covariance sequences of fixed length View full abstract»

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  • State feedback ℋ-suboptimal control of a rigid spacecraft

    Publication Year: 1997 , Page(s): 1186 - 1191
    Cited by:  Papers (26)
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    A state feedback ℋ-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback ℋ-suboptimal control problem on TS3 is solved globally. The ℋ-suboptimal state feedback on TS3 involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen View full abstract»

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  • Globally valid adaptive controllers of mechanical systems

    Publication Year: 1997 , Page(s): 1149 - 1154
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    The adaptive controller design of a large class of mechanical systems is addressed in this paper. The configuration space for the attitude of a vehicle is modelled as SO(3), namely the rotation matrix group. To avoid singularity problems, some studies adopt the representation of unit quaternions for modeling system dynamics and for the design of controllers. However, the complicated formulation of quatrains makes the application of this method limited to simple mechanical systems. Here, the strategy is to carry out the modeling and analysis in terms of the global representations of jet bundles of SO(3), while the unit quaternion is chosen to implement the controller for its least number of parameters (four) to represent SO(3) globally. Based on the transformation between the rotation matrix and the quaternion, the method explored in this paper gives rise to an adaptive controller in a clean and efficient way View full abstract»

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  • Robust, fragile, or optimal?

    Publication Year: 1997 , Page(s): 1098 - 1105
    Cited by:  Papers (251)
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    We show by examples that optimum and robust controllers, designed by using the H2, H, l1, and μ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. The examples show that this fragility usually manifests itself as extremely poor gain and phase margins of the closed-loop system. The calculations given here should raise a cautionary note and draw attention to the larger issue of controller sensitivity which may be important in other nonoptimal design techniques as well View full abstract»

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  • A study of the gap between the structured singular value and its convex upper bound for low-rank matrices

    Publication Year: 1997 , Page(s): 1176 - 1179
    Cited by:  Papers (1)
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    The size of the smallest structured destabilizing perturbation for a linear time-invariant system can be calculated via the structured singular value (μ). The function μ can be bounded above by the solution of a convex optimization problem, and in general there is a gap between μ and the convex bound. This paper gives an alternative characterization of μ which is used to study this gap for low-rank matrices. The low-rank characterization provides an easily computed bound which can potentially be significantly better than the standard convex bound. This is used to find new examples with larger gaps than previously known View full abstract»

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  • H-controller synthesis with time-domain constraints

    Publication Year: 1997 , Page(s): 1179 - 1186
    Cited by:  Papers (5)
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    For a class of discrete-time linear time-invariant (LTI) plants, we present necessary and sufficient conditions for the existence of a discrete-time LTI controller which ensures that the H norm of a closed-loop map of interest is less than a prespecified level, subject to time-domain constraints on this closed-loop map. In cases when such an LTI controller does not exist, we show that the problem of finding an LTI controller that satisfies the input-output constraints with the smallest error can be posed as a convex optimization problem based on linear matrix inequalities. We also consider, briefly, other related problems that can be solved completely using a similar approach, namely controller synthesis to minimize the optimally scaled H norm and controller synthesis to maximize the guaranteed dissipation View full abstract»

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  • Improving stability margins via dynamic-state feedback for systems with constant uncertainty

    Publication Year: 1997 , Page(s): 1161 - 1163
    Cited by:  Papers (1)
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    It is well known that if a linear system with time-varying uncertainty in the system matrix and/or the input connection matrix is quadratically stabilizable by linear dynamic state feedback, then it is also quadratically stabilizable by linear static state feedback. In this paper, we provide an example of a system with unknown constant real uncertainty which is stabilizable by a linear, dynamic-state feedback controller but not by a static-state feedback controller View full abstract»

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  • γ-δ Routh approximation for interval systems

    Publication Year: 1997 , Page(s): 1127 - 1130
    Cited by:  Papers (12)
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    The paper presents the γ-δ Routh approximation for interval systems. The interval γs and δs are evaluated for the higher order interval systems, and then an rth-order approximant is obtained by retaining the first r, interval δs, and γs. A numerical example illustrates the procedure View full abstract»

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  • A Jacobi-like method for solving algebraic Riccati equations on parallel computers

    Publication Year: 1997 , Page(s): 1071 - 1084
    Cited by:  Papers (11)
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    An algorithm to solve continuous-time algebraic Riccati equations through the Hamiltonian Schur form is developed. It is an adaption for Hamiltonian matrices of an asymmetric Jacobi method of Eberlein (1987). It uses unitary symplectic similarity transformations and preserves the Hamiltonian structure of the matrix. Each iteration step needs only local information about the current matrix, thus admitting efficient parallel implementations on certain parallel architectures. Convergence performance of the algorithm is compared with the Hamiltonian-Jacobi algorithm of Byers (1990). The numerical experiments suggest that the method presented here converges considerably faster for non-Hermitian Hamiltonian matrices than Byers' Hamiltonian-Jacobi algorithm. Besides that, numerical experiments suggest that for the method presented here, the number of iterations needed for convergence can be predicted by a simple function of the matrix size View full abstract»

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  • A cone complementarity linearization algorithm for static output-feedback and related problems

    Publication Year: 1997 , Page(s): 1171 - 1176
    Cited by:  Papers (705)  |  Patents (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with nu (respectively, ny) independent inputs (respectively, outputs). The algorithm is based on a “cone complementarity” formulation of the problem and is guaranteed to produce a stabilizing controller of order m⩽n-max(nu,ny), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura's generic stabilizability result (m⩽n-nu-ny+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis View full abstract»

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  • Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach

    Publication Year: 1997 , Page(s): 1144 - 1148
    Cited by:  Papers (201)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (188 KB)  

    This paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time-delay. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state-space model. We develop methods for robust stability analysis and robust stabilization. The proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities View full abstract»

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  • General matrix pencil techniques for the solution of algebraic Riccati equations: a unified approach

    Publication Year: 1997 , Page(s): 1085 - 1097
    Cited by:  Papers (36)
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    We present a unified theory of matrix pencil techniques for solving both continuous and discrete-time algebraic Riccati equations (AREs) under fairly general conditions on the coefficient matrices. The theory applies to a large class of AREs and Riccati-like equations arising from the singular H- and H2-control problems, singular linear quadratic control, the 4-block Nehari problem, or from singular J-spectral factorizations. The underlying concept is the so-called proper deflating subspace of a (possibly singular) matrix pencil in terms of which necessary and sufficient conditions for the solvability of Riccati equations are given. It is shown that these conditions can be checked and the solutions computed by a numerically sound algorithm View full abstract»

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  • Polynomial filtering of discrete-time stochastic linear systems with multiplicative state noise

    Publication Year: 1997 , Page(s): 1106 - 1126
    Cited by:  Papers (47)
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    The problem of finding an optimal polynomial state estimate for the class of stochastic linear models with a multiplicative state noise term is studied. For such models, a technique of state augmentation is used, leading to the definition of a general polynomial filter. The theory is developed for time-varying systems with nonstationary and non-Gaussian noises. Moreover, the steady-state polynomial filter for stationary systems is also studied. Numerical simulations show the high performances of the proposed method with respect to the classical linear filtering techniques View full abstract»

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  • On global output feedback regulation of Euler-Lagrange systems with bounded inputs

    Publication Year: 1997 , Page(s): 1138 - 1143
    Cited by:  Papers (51)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    We identify a class of Euler-Lagrange systems with bounded inputs that can be globally asymptotically stabilized via dynamic output feedback. In particular, we prove that if the system is fully actuated and the forces due to the potential field can be “dominated” by the constrained control signals, then global output feedback regulation is still possible, incorporating some suitable saturation functions in the controller View full abstract»

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  • The role of information state and adjoint in relating nonlinear output feedback risk-sensitive control and dynamic games

    Publication Year: 1997 , Page(s): 1163 - 1170
    Cited by:  Papers (24)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (412 KB)  

    This paper employs logarithmic transformations to establish relations between continuous-time nonlinear partially observable risk-sensitive control problems and analogous output feedback dynamic games. The first logarithmic transformation is introduced to relate the stochastic information state to a deterministic information state. The second logarithmic transformation is applied to the risk-sensitive cost function using the Laplace-Varadhan lemma. In the small noise limit, this cost function is shown to be logarithmically equivalent to the cost function of an analogous dynamic game View full abstract»

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  • Necessary and sufficient conditions for existence of decoupling controllers

    Publication Year: 1997 , Page(s): 1157 - 1161
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (224 KB)  

    It is well known that if a linear time-invariant plant is free from coincidences of poles and zeros in the right half-plane, then it can be decoupled with internal stability under unity-feedback configuration. We consider plants for which such coincidences do occur and give necessary and sufficient conditions under which stabilizing decoupling controllers exist. The conditions derived, based on transfer matrices and residues, are simple and straightforward View full abstract»

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  • Partially observable nonlinear risk-sensitive control problems: dynamic programming and verification theorems

    Publication Year: 1997 , Page(s): 1130 - 1138
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    In this paper, we consider continuous-time partially observable optimal control problems with exponential-of-integral cost criteria. We derive a rigorous verification theorem when the state and control enter nonlinear in the dynamics. In addition, we show that the quadratic sensor problem is estimation-solvable with respect to a certain cost criterion. The framework relies on dynamic programming and the Hamilton-Jacobi theory View full abstract»

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  • Synthesis of positive real feedback systems: a simple derivation via Parrott's theorem

    Publication Year: 1997 , Page(s): 1154 - 1157
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (156 KB)  

    A simple derivation of the formulas for controller rendering a closed-loop system strongly positive real is presented. The derivation is based on Parrott's theorem and the positive real lemma. When the positive real lemma is applied to the closed loop system, a bilinear matrix inequality results. The significance of Parrott's theorem in the context of a strongly positive real synthesis problem is that it allows one to convert this bilinear matrix inequality into two linear matrix inequalities 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