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Automatic Control, IEEE Transactions on

Issue 6 • Date December 1967

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Displaying Results 1 - 25 of 59
  • [Front cover and table of contents]

    Publication Year: 1967 , Page(s): 0
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    Freely Available from IEEE
  • On correspondence

    Publication Year: 1967 , Page(s): 639
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    Freely Available from IEEE
  • Issue in brief

    Publication Year: 1967 , Page(s): 641 - 643
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    Freely Available from IEEE
  • Codes, automata, and continuous systems: Explicit interconnections

    Publication Year: 1967 , Page(s): 644 - 650
    Cited by:  Papers (17)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (706 KB)  

    Close relationships are established between convolutional codes and zero-state automata and between cyclic codes and zero-input automata. Furthermore, techniques of automata theory and continuous system theory are used to elaborate on the coding problem; and approaches from coding and automata are used to establish and interpret typical structural conditions in continuous systems. The investigation incorporates basic coding concepts into the currently emerging common basis for automata and continuous systems, and it gives explicit examples of the resulting benefits accruing to each of these areas from the others. View full abstract»

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  • Decoupling in the design and synthesis of multivariable control systems

    Publication Year: 1967 , Page(s): 651 - 659
    Cited by:  Papers (189)
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    Necessary and sufficient conditions for the "decoupling" of an m -input, m -output time-invariant linear system using state variable feedback are determined. Given a system which satisfies these conditions, i.e., which can be decoupled by state variable feedback, the class φ of all feedback matrices which decouple the system is characterized. The characterization of φ is used to determine the number of closed-loop poles which can be specified for the decoupled system and to develop a synthesis technique for the realization of desired closed-loop pole configurations. Transfer matrix consequences of decoupling are examined and practice implications discussed through numerical examples. View full abstract»

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  • On pole assignment in multi-input controllable linear systems

    Publication Year: 1967 , Page(s): 660 - 665
    Cited by:  Papers (175)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB)  

    It is shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed-loop system, formed by means of suitable linear feedback of the state. As an application of this result, it is shown that an open-loop system can be stabilized by linear feedback if and only if the unstable modes of its system matrix are controllable. A dual of this criterion is shown to be equivalent to the existence of an observer of Luenberger's type for asymptotic state identification. View full abstract»

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  • A second-order feedback method for optimal control computations

    Publication Year: 1967 , Page(s): 666 - 673
    Cited by:  Papers (10)
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    A second-order method for computing optimal control is described. The method computes control corrections from the state perturbations through feedback coefficients. On each successive trajectory a test is made for a conjugate point, and the algorithm automatically forms a control correction when such points occur. Unlike some earliermethods, terminal constraints of arbitrary dimensions are handled by the method. Numerical results for two cases of a non-linear example based on van der Pol's equation are included. View full abstract»

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  • On the inverse optimum control problem for a class of nonlinear autonomous systems

    Publication Year: 1967 , Page(s): 674 - 681
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (574 KB)  

    Some aspects of the inverse optimum control problem are considered for a class of nonlinear autonomous systems. A closed-loop system with a known control law is given; the problem is to determine performance criteria for which the given control law is optimum. Algebraic conditions that must be satisfied by a class of scalar performance criteria of the form V=\int\min{t}\max {\infty }[q(x)+h(u)]d_{\tau } are obtained. It is shown that if the value of the optimum V0is required to be a quadratic form V^{o} = frac{1}{2}x'Mx of the current state x , and if certain state variables cannot be measured, then M cannot be positive definite. The inverse optimum control problem corresponding to the problem of Lur'e is considered. Examples are given to illustrate the techniques and to compare the properties of a linear and nonlinear system having the same optimum performance V^{0}(x) . View full abstract»

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  • Optimal bang-bang control of linear stochastic systems with a small noise parameter

    Publication Year: 1967 , Page(s): 682 - 690
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (760 KB)  

    This study considers the problem of determining optimal feedback control laws for linear stochastic systems with amplitude-constrained control inputs. Two basic performance indices are considered, average time and average integral quadratic form. The optimization interval is random and defined as the first time a trajectory reaches the terminal region R . The plant is modeled as a stochastic differential equation with an additive Wiener noise disturbance. The variance parameter of the Wiener noise process is assumed to be suitably small. A singular perturbation technique is presented for the solution of the stochastic optimization equations (second-order partial differential equation). A method for generating switching curves for the resulting optimal bang-bang control system is then developed. The results are applied to various problems associated with a second-order purely inertial system with additive noise at the control input. This problem is typical of satellite attitude control problems. View full abstract»

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  • A direct derivation of the optimal linear filter using the maximum principle

    Publication Year: 1967 , Page(s): 690 - 698
    Cited by:  Papers (55)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (778 KB)  

    The purpose of this paper is to present an alternate derivation of optimal linear filters. The basic technique is the use of a matrix version of the maximum principle of Pontryagin coupled with the use of gradient matrices to derive the optimal values of the filter coefficients for minimum variance estimation under the requirement that the estimates be unbiased. The optimal filter which is derived turns out to be identical to the well-known Kalman-Bucy filter. View full abstract»

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  • Identification of linear discrete time systems using the instrumental variable method

    Publication Year: 1967 , Page(s): 707 - 718
    Cited by:  Papers (61)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (965 KB)  

    This paper explores the possibility of using the instrumental variable method to estimate the parameters of linear time-invariant discrete-time systems. The existence of optimal estimates is established, methods for their approximate computation are given, and an on-line identification scheme based on recursive computation is proposed. Experimental results are included. View full abstract»

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  • A frequency-time domain stability criterion for sampled-data systems

    Publication Year: 1967 , Page(s): 719 - 724
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (568 KB)  

    An improved sufficient condition developed for the asymptotic stability of a sampled-data system having a single monotonic nonlinearity, with a slope in the sector (0, k_{2}) and a pulse transfer function G^{\ast }(z) , is \Re [(1+X^{\ast }(z)+Y^{\ast }(z))(G^{\ast }(z)+I/k_{2})]\geq 0 for z on the unit circle, where x(i) \leq 0 for i< 0 and x(i)=0 for i> 0, y(i) \leq 0 for i\geq 0 and y(i)=0 for i< 0 , and \Sigma \min{i=-\infty }\max {+\infty } |x(i) + y(i)| < 1 . An improved frequency domain condition is also presented for the case of the nonlinearity being odd as well as monotonic. View full abstract»

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  • An improved frequency time domain stability criterion for autonomous continuous systems

    Publication Year: 1967 , Page(s): 725 - 731
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (577 KB)  

    A sufficient condtion given for the asymptotic stability of a system having a single monotonic nonlinearity with slope confined to [0, k_{2}] and a transfer function G(j\omega ) , is \Re (1 + X(j\omega ) + Y(j\omega ) + \alpha j\omega )(G(j\omega ) + 1/k_{2}) \geq 0 where \alpha > 0 , x(t)\leq 0 for t \leq 0 and x(t)=0 for t> 0 , y(t)\leq0 for t> 0 and y(t) = 0 for t < 0 , and \int\min{-\infty }\max {\infty }(| x(t)| + | y(t) | )dt < 1 . The improvement consists of the addition of the X(j\omega ) term which corresponds to a nonzero time function for t< 0 , resulting in Z(j\omega ) multipliers whose phase angle is capable of varying from +90° to -90° any desired number of times. As is shown by examples, the new criterion gives better results than existing criteria. Also developed is an improved criterion for an odd monotonic nonlinearity. View full abstract»

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  • On a modified Lur'e problem

    Publication Year: 1967 , Page(s): 731 - 740
    Cited by:  Papers (10)
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    This paper considers the problem of asymptotic stability in the large of an autonomous system containing a single nonlinearity. The nonlinear function is assumed to belong to several subclasses of monotonically increasing functions in the sector (0, K) , and the stability criterion is shown to be of the form \Re Z(j\omega ) [G(j\omega ) +frac{1}{K}] -frac{\delta '}{K} \geq 0 where the constant \delta ' is equal to Z(\infty ) - Z_{p}(\infty ) and Z_{p}(s) is a Popov multiplier. The multiplier Z(s) can, in general, have complex conjugate poles and zeros and is thus more general than the type of multipliers obtained in previous results. The nonlinear functions considered are odd monotonic functions, functions with a power law restriction, and a new class of functions with restricted asymmetry having the property |{f(\theta)\over f(-\theta)}|\leq c for all \theta . Unlike in certain earlier publications, no upper bound is placed on the derivative of the nonlinearity here. The results obtained can be used to establish stability in some cases even when the Nyquist plot of the linear part transfer function lies in all four quadrants and the nonlinearity is not necessarily odd. Furthermore, it is shown that the conditions on the multiplier and, consequently, those on the linear part can be relaxed as the feedback function approaches linearity. View full abstract»

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  • A frequency-domain stability chart for nonlinear feedback systems

    Publication Year: 1967 , Page(s): 740 - 743
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (474 KB)  

    A modification of the Popov criterion for absolute stability is presented. A new chart, designed to facilitate the application in practice of the new criterion, is introduced and its use is discussed. The range of use of the chart is then extended to encompass a previously published generalization of the Popov criterion. Then a procedure for use of the chart in conjunction with a Nichols chart in a simple and straightforward engineering procedure for designing absolutely stable single-loop nonlinear feedback systems is presented. An example is included to illustrate the procedure described. View full abstract»

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  • Simplified algebraic characterization of optimal singular control for autonomous linear plants

    Publication Year: 1967 , Page(s): 743 - 746
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    In an earlier publication[1] the authors extended the results of Wonham and Johnson[2] by characterizing the nature of the (stable) singular strip for a given performance index without recourse to a special transformation to phase coordinates. The solution presented there[1] required solving a (quadratic) matrix Riccati equation; whereas here the singular strip and the corresponding stable optimal feedback control law are found by factoring a polynomial which is computationally much easier to accomplish. The final result is illustrated by a numerical example. View full abstract»

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  • On the matrix Riccati equation

    Publication Year: 1967 , Page(s): 746 - 749
    Cited by:  Papers (4)
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    The matrix Riccati equation and its relation to optimization, sensitivity, and stability problems in linear systems is noted. Explicit solutions are summarized for several particular cases with emphasis on direct and unified proofs. In the stationary case, a direct proof is given for the well-known relation between solutions of the Riccati differential and algebraic equations. View full abstract»

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  • Optimal control trajectories with minimax objective functions by linear programming

    Publication Year: 1967 , Page(s): 749 - 752
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (369 KB)  

    A standard linear programming code may be used to compute optimal trajectories for a linear discrete-time system with respect to a minimax criterion on either state or control trajectories. Arbitrary linear constraints, equality or inequality, constant or time-varying, may be placed on linear combinations of the state or control variables along their trajectories or at a fixed terminal time. An important feature of the method is that the dimension of the linear programming problem is independent of the dimension of the state space but depends entirely on the numbers of control variables, constraints, and time intervals. Optimal trajectories for a 21st- order system have been calculated in a few minutes of computer time. View full abstract»

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  • On a class of pursuit-evasion problems

    Publication Year: 1967 , Page(s): 752 - 755
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    This paper shows that a pursuit-evasion problem can be made amenable to solution with nonlinear programming algorithms by operating the pursuer and evader systems in a "discrete" mode of control and by choosing the cost function judiciously. View full abstract»

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  • A learning technique for Volterra series representation

    Publication Year: 1967 , Page(s): 761 - 764
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (333 KB)  

    This paper presents a method of system identification based upon the techniques of pattern recognition. The method developed is an on-line error-correcting procedure which provides the coefficients of the Volterra series representation of the system. The systems considered are those with finite settling time and piecewise constant inputs. The method is extremely general, identifying both linear and nonlinear systems in the presence of noise, without the requirement of special test signals. The theoretical basis for this method lies in the observation that system identification is a special case of the general theory of pattern recognition. A system is treated as a transformation from the set of past inputs to the real line, the system output. The Volterra expansion treats this transformation as a hypersurface, the shape of which is determined by the Volterra kernels. However, the techniques of pattern recognition produce this type of surface as the discriminant function between pattern classes. Furthermore, these surfaces are iteratively obtained as more data are available. Consequently, the computational difficulties, which are encountered in obtaining the Volterra kernels, are circumvented by this iterative learning procedure. View full abstract»

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  • Deterministic aspects of the identification of linear discrete dynamic systems

    Publication Year: 1967 , Page(s): 764 - 766
    Cited by:  Papers (1)
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    Ho[2]has shown that problems of identification of state of noisy discrete dynamic systems are closely related to deterministic minimum norm. solutions of a set of overdetermined equations. This paper further applies this philosophy to the recursive identification of the transition matrix of a discrete n th-order linear system, as the number of measurements of the state vector increases from one to N > n . View full abstract»

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  • A survey of dynamic programming computational procedures

    Publication Year: 1967 , Page(s): 767 - 774
    Cited by:  Papers (13)
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    Although dynamic programming has long provided a powerful approach to optimization problems, its applicability has been somewhat limited because of the large computational requirements of the standard computational algorithm. In recent years a number of new procedures with greatly reduced computational requirements have been developed. The purpose of this paper is to survey a number of the more promising of those techniques. A review of the theory of dynamic programming and the standard computational algorithm is included. Several applications of the new techniques are discussed. View full abstract»

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  • Conjugate gradient search in the initial costate space

    Publication Year: 1967 , Page(s): 776 - 777
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (208 KB)  

    The conjugate gradient algorithm of Fletcher and Reeves (1964) has recently been fruitfully incorporated in the numerical solution of optimal control problems. Unlike others who apply the algorithm as a searching mechanism in function space, this correspondence demonstrates the effectiveness of the algorithm as a tool for searching in the initial costate space. The technique presented herein is the penalty function approach suggested by Knapp and Frosts (ibid., voL AC-IO. pp. 189-193. April 1965) coupled with a conjugate gradient search. View full abstract»

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  • Comment on the linear optimal control problem

    Publication Year: 1967 , Page(s): 777 - 778
    Cited by:  Papers (1)
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    First Page of the Article
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  • On the existence and synthesis of optimal singular control with quadratic performance index

    Publication Year: 1967 , Page(s): 778 - 779
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    The objective of this correspondence is to study the singular solutions of the optimal control which minimizes the performance index subject to s et of given conditions. 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
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University of Notre Dame