Showing papers in "International Journal of Systems Science in 1986"
TL;DR: In this paper, a modification of the theory of sliding variable structure control systems is used to design a control law that is a continuous arbitrarily close approximation, within a predefined subspace, to the discontinuous variable structural control law.
Abstract: A straightforward modification of the theory of ‘sliding’ variable structure control systems is used to design a control law that is a continuous arbitrarily close approximation, within a predefined subspace, to the discontinuous variable structure control law. Linear combinations of eigenvectors, and certain null spaces, are used to analyse the state trajectory under the influence of the continuous control law. Comparisons are drawn and the inherent robustness properties of variable structure control systems are retained, while the undesirable chatter motion of the sliding mode is eliminated. The accuracy of the approximation to the idealized case can easily be calculated. The general results are illustrated by the simulation of a time-invariant fourth-order multivariable system with two controls
324 citations
TL;DR: A new class of hierarchical structures is proposed involving iterative procedures which utilize available process mathematical models and feedback information and are adaptive where the process model contains parameters which are updated at each iteration.
Abstract: Novel structures are developed and discussed for the steady-state optimizing control of large-scale industrial processes. A new class of hierarchical structures is proposed involving iterative procedures which utilize available process mathematical models and feedback information. In contrast to the majority of existing structures, the new techniques are optimal in the sense that the control produced by each structure satisfies the Kuhn-Tucker necessary optimality conditions. The structures are adaptive where the process model, which is assumed to be point-parametric, contains parameters which are updated at each iteration. Depending on the real process measurement capabilities, some of the structures incorporate output information feedback only, while others utilize both input and output measurements. These measurements are used in different ways leading to structures with local and global feedback, together with alternative coordination strategies.
48 citations
TL;DR: In this article, a memoryless feedback controller is developed for a model reference control system which is linear, uncertain and has retarded arguments, under certain assumptions guarantees that all solutions are uniformly bounded and also that the system trajectories are always attracted towards some stable hypersurface in the space, no matter what the uncertainties and initial conditions are.
Abstract: A memoryless feedback controller is developed for a model reference control system which is linear, uncertain and has retarded arguments. The controller under certain assumptions guarantees that all solutions are uniformly bounded and also that the system trajectories are always attracted towards some stable hypersurface in the space, no matter what the uncertainties and initial conditions are. Along the hypersurface the motion of the trajectories are insensitive to system parameter variations.
42 citations
TL;DR: In this paper, reduced-order modelling and control analysis of linear, discrete-time systems with dominant and non-dominant modes is presented, and a matrix norm condition is derived, which enables approximate expressions for the block-diagonalizing matrices, eigenvalue distribution and state trajectories to be obtained.
Abstract: In this paper reduced-order modelling and control analysis of linear, discrete-time systems having dominant and non-dominant modes are presented. Decoupling of modes is achieved using an explicitly invertible linear transformation. A matrix norm condition is derived, the satisfaction of which enables approximate expressions for the block-diagonalizing matrices, eigenvalue distribution and state trajectories to be obtained. Design of stabilizing feedback controllers is developed and it is shown that two gain matrices are needed for separate assignment of dominant and non-dominant eigenvalues. The theoretical analysis is illustrated by control system examples.
40 citations
TL;DR: In this paper, the controllability of a positive dynamic system with linear structure was studied, i.e., if the initial state is non-negative, then the state variable is not negative for all future time.
Abstract: A positive dynamic system has the property that if the initial state is non-negative, then the state variable is non-negative for all future time. In this article, we study controllability of one such system with linear structure.
37 citations
TL;DR: In this article, a solution of the generalized LQG stochastic optimal multi variable control problem is obtained using a polynomial-matrix-systems approach using a dual performance index including the usual error and control weighting terms and also sensitivity and complementary sensitivity weighting matrices.
Abstract: A solution of the generalized LQG stochastic optimal multi variable control problem is obtained using a polynomial-matrix-systems approach. The generalized problem involves a dual performance index including the usual error and control weighting terms and also sensitivity and complementary sensitivity weighting matrices. The system model includes input disturbance, reference and coloured measurement noise signals. The cost-function weighting operators can also represent dynamical systems. The problem description was motivated by the need to construct multi-variable explicit self-tuning controllers for marine applications.
32 citations
TL;DR: In this paper, a stability test for large-scale systems with delays by employing both the aggregation technique and solutions of the complex Lyapunov equation is proposed, and an example is given to illustrate the application of the results.
Abstract: A stability test is proposed for large-scale systems with delays by employing both the aggregation technique and solutions of the complex Lyapunov equation. An example is given to illustrate the application of the results
30 citations
TL;DR: This paper presents an extension to the modified two-step algorithm for determining the optimum steady-state operating condition of a system that gives a faster convergent rate and ensures that the optimal condition is achieved in more general cases where system inequality constraints involving system outputs occur.
Abstract: This paper presents an extension to the modified two-step algorithm for determining the optimum steady-state operating condition of a system. The new version of the algorithm gives a faster convergent rate and ensures that the optimal condition is achieved in more general cases where system inequality constraints involving system outputs occur. The performance of the algorithm under noisy measurements is examined by simulation. Simple filter techniques are employed to attenuate errors in process measurements.
30 citations
TL;DR: Simulation results of an optimal adaptive algorithm (Brdyś and Roberts 1984) and a double iterative alternative are presented and it is shown that the former does not increase the total number of information exchanges during the iteration procedure and may even reduce it.
Abstract: This paper presents computer simulation results of an optimal adaptive algorithm (Brdyś and Roberts 1984) and develops a double iterative alternative. Both algorithms are optimal in the sense that Kuhn-Tucker necessary optimality conditions are satisfied. The aim of the latter is to reduce the number of times that information is required from the real system. Simulation results also show that it does not increase the total number of information exchanges during the iteration procedure and may even reduce it.
29 citations
TL;DR: A computationally efficient pole-zero placement self-tuning control algorithm for multi-input-multi-output servo systems that is applicable to non-minimum-phase plants and can also handle unknown but bounded pure time delays.
Abstract: A computationally efficient pole-zero placement self-tuning control algorithm for multi-input-multi-output servo systems is developed. It is effectively an implicit algorithm in the sense that the controller design step is trivial. Moreover, the controller is obtained as a left matrix-fraction and so can be immediately implemented. Although the algorithm is restricted to stable plants, it is applicable to non-minimum-phase plants and can also handle unknown but bounded pure time delays. Results obtained from computer simulations of the algorithm, as well as by trials on an actual stirred-tank process, are presented.
27 citations
TL;DR: In this paper, the authors present sufficient conditions for feedback stabilizability of controlled stochastic systems and apply them to three examples applied to electrically suspended gyros, showing that they are sufficient for stabilisation.
Abstract: In this paper, we present certain sufficient conditions for (feedback) stabilizability of controlled stochastic systems. Theoretical results are illustrated by three examples applied to electrically suspended gyros.
TL;DR: In this article, a necessary and sufficient condition for the existence of an output feedback with closed-loop regularity is presented, where the condition is that there should not be an infinity of solutions for any initial condition.
Abstract: For feedback control of linear systems in descriptor form it is essential that the closed-loop system be regular; that is, there should not be an infinity of solutions of the closed-loop differential equations for any initial condition. Closed-loop regularity cannot be taken for granted. In this paper a necessary and sufficient condition for the existence of an output feedback giving closed-loop regularity is presented
TL;DR: In this article, the necessary conditions of structural classification are developed by the Volterra and Wiener theories and correlation analysis, and some formulae for discriminating the feedback non-linear system's structure are newly developed.
Abstract: It is desirable to know the internal structure of a non-linear system that is regarded as a 'black box'. The structural classification of the 'black box' is made from input and output relations. In this paper, the necessary conditions of structural classification are developed by the Volterra and Wiener theories and correlation analysis. A class of non-linear models in cascade is described by cross-correlation functions and Volterra and Wiener kernels. These conditions are first discussed in the frequency domain. Then the formulae of the conditions for structural identification in the time domain are obtained. Further, relations between structural information and the kernels are developed. Simulations are carried out that verify the authors' methods of structural testing. Next, some formulae for discriminating the feedback non-linear system's structure are newly developed. Furthermore, it is shown that the linear subsystem transfer functions and the non-linear subsystem parameters for these feedback non-l...
TL;DR: In this article, a simple division method in conjunction with the method owing to Wolovich and Antsaklis (1984) is presented for obtaining the observability and controllability indices, the irreducible right (left) matrix fraction descriptions from reducible or irredUCF descriptions, the greatest common divisors of two polynomial matrices and the solution of a Diophantine equation without utilizing the state-space realization of the matrix Traction description.
Abstract: Based on the transfer function matrices or the matrix fraction descriptions of multivariable systems, a simple division method in conjunction with the method owing to Wolovich and Antsaklis (1984) is presented in this paper for obtaining the observability and controllability indices, the irreducible right (left) matrix fraction descriptions from reducible or irreducible left (right) matrix fraction descriptions, the greatest common divisors of two polynomial matrices and the solution of a Diophantine equation, without utilizing the state-space realization of the matrix Traction description.
TL;DR: In this article, the canonical decomposition of discrete-time linear systems based on reachability, controllability, observability, and reconstructibility is studied and a sufficient condition for the existence of such a decomposition is worked out.
Abstract: The paper deals with the canonical decomposition of discrete-time linear systems based on the classical properties of reachability, controllability, observability and reconstructibility. First, a set of relationships between the structural subspaces is established and used to derive a general form of the discrete-lime duality principle. By means of these results, a sufficient condition for the existence of a canonical decomposition is worked out. Such a condition is also necessary if the attention is focused on decompositions based on the classical structural properties. Depending on the pair of properties considered, four different decompositions can be achieved. Finally, by making reference to controllability and reconstructibility a canonical decomposition is shown to exist for periodic systems. In general, non-reversible periodic systems admit no other decomposition but this one.
TL;DR: In this paper, the authors considered a production and inventory problem in which the utility or potential of an item gradually reduces with the passage of time, such as grain, photographic film and electronic component.
Abstract: This paper considers a production and inventory problem in which the utility or potential of an item gradually reduces with the passage of time, such as grain, photographic film and electronic component. The aim of this paper is to determine the production rate of the decaying item in a way that minimizes the current value of total cost using optimal control theory. For the model developed, a computational procedure of finding an optimal solution is developed. The steady-state solution and the properties of the optimal solution for the case of constant rate of decay are discussed.
TL;DR: In this article, the problem of finding the optimal processing time multiple k* for the total work content due-date assignment method, and the optimal sequence π* to minimize the expected total amount of missed due-dates was studied.
Abstract: Given a set of n jobs with independent random processing times and the same start times, the problem is to find the optimal processing time multiple k* for the total work content due-date assignment method, and the optimal sequence π* to minimize the expected total amount of missed due-dates It is shown that k* is a constant for a given job set Although in general π* cannot be determined analytically, it is shown that, under certain circumstances, π* should be in shortest-expected-processing-time sequence to minimize the objective function
TL;DR: In this paper, a single-product parallel-facilities production-planning model, in which known demands must be satisfied, is analyzed, and an optimal solution is characterized, upon which only one facility in each period is shown optimal to supply exact requirements.
Abstract: A single-product parallel-facilities production-planning model, in which known demands must be satisfied, is analysed. Concave production and inventory costs are considered. No backlogging is assumed. The structure of an optimal solution is characterized, upon which only one facility in each period is shown optimal to supply exact requirements. This is then used in a simple dynamic-programming algorithm. A numerical example for the algorithm is discussed
TL;DR: In this paper, the singular value decomposition of the extended reachability and observability matrices is used to define a balanced system, and two methods for determining the balanced representation are presented, the properties of the balanced systems are derived and the usefulness of the balancing method to system reduction is demonstrated.
Abstract: The definition is introduced of a balanced system through the singular value decomposition of the extended reachability and observability matrices. On this basis, two methods for determining the balanced representation are presented, the properties of the balanced systems are derived and the usefulness of the balancing method to system reduction is demonstrated.
TL;DR: In this paper, generalized orthogonal polynomials that represent all types of orthogonality functions are introduced and the operational matrix for integration of a generalized polynomial is derived and then applied to solve the equations of linear dynamic systems.
Abstract: Generalized orthogonal polynomials that represent all types of orthogonal polynomial are introduced in this paper. Using the idea of orthogonal polynomial functions that can be expressed by power series, and vice versa, the operational matrix for integration of a generalized orthogonal polynomial is first derived and then applied to solve the equations of linear dynamic systems. The characteristics of each kind of orthogonal polynomial in relation to solving linear dynamic systems is demonstrated. The computational strategy for finding the expansion coefficients of the state variables is very simple, straightforward and easy. The operational matrix is simpler than those of conventional orthogonal polynomials. Hence the expansion coefficients are more easily calculated from the proposed recursive formula when compared with those obtained from conventional orthogonal polynomial approximations.
TL;DR: In this article, a state feedback control law for uncertain robotic systems such that the error between the generalized coordinates and the trajectory of a reference model is uniformly ultimately bounded with respect to any arbitrarily small set of ultimate boundedness is presented.
Abstract: We present a state feedback control law for uncertain robotic systems such that the error between the generalized coordinates and the trajectory of a reference model is uniformly ultimately bounded with respect to any arbitrarily small set of ultimate boundedness
TL;DR: In this article, the Luenberger observer is used for state estimation of linear systems using continuous orthogonal functions, which has the distinct advantage that the smoothing effect of integration reduces the effect of noise.
Abstract: A new approach is presented to facilitate research in the state estimation of linear systems using continuous orthogonal functions. The principle of the Luenberger observer is utilized in developing simple algebraic expressions for the estimates of states. This approach has the distinct advantage that the smoothing effect of integration reduces the effect of noise. Hence, this observer gives acceptable estimates of the states in the presence of zero-mean observation noise, even without a filter. Results of simulation indicate that the proposed method works quite well. In addition, the algorithms are recursive and suitable for on-line implementation.
TL;DR: On these bases, all the existing block pulse operational matrices can be derived in a mathematically rigorous way without having to use graphical demonstrations.
Abstract: It is pointed out that the mathematical bases for block pulse operational methods to various dynamic system problems are to represent the delay operator exp(— hs)approximately by and to represent exp ( — αhs) approximately by (1 — α) + α exp ( — hs), where 0 ≤ α ≤ 1. On these bases, all the existing block pulse operational matrices—the integration matrix, the convolution matrix, the correlation matrix, the delay matrix, and the stretch matrix—can be derived in a mathematically rigorous way without having to use graphical demonstrations.
TL;DR: Brownian matrices arise in certain models used in digital signal processing as discussed by the authors and can be used to solve linear systems of linear equations, where any brownian matrix is congruent to a tridiagonal matrix.
Abstract: Brownian matrices arise in certain models used in digital signal processing. Fast algorithms for solving brownian systems of linear equations can be derived because any brownian matrix is congruent to a tridiagonal matrix. This, and related properties, are developed and extended to matrices having a more general patterned structure.
TL;DR: In this paper, it is shown that a recently proposed approach to linear aggregation, when properly generalized using a differential-geometric language, provides a natural framework for the aggregation of non-linear dynamics.
Abstract: The aggregation method in linear-system theory is extended to a class of non-linear system. It is shown that a recently-proposed approach to linear aggregation, when properly generalized using a differential-geometric language, provides a natural framework for the aggregation of non-linear dynamics.
TL;DR: In this article, the controllability result for the discrete-time linear system xk+1 = Axk + uk (k = 0, 1), for which the input uk belongs to an arbitrary bounded and convex set Ω, is considered.
Abstract: The discrete-time linear system xk+1 = Axk + uk (k = 0, 1,[tdot]), for which the input uk belongs to an arbitrary bounded and convex set Ω, is considered. The error in the sufficiency proof of the controllability result when 0 ∊ ri (Ω) owing to Wing and Desoer is avoided by using convexity arguments, and the result is extended to encompass the case 0 ∉ ri (Ω)
TL;DR: Numerical results have shown that for either linear or non-linear discrete models with interference, the new algorithm performs very well and in the absence of interference, it performs better than the extended Kalman filter algorithm for some non- linear discrete models.
Abstract: A suboptimum smoothing algorithm is presented for dynamic systems with or without an arbitrary random interference. For the disturbance noise, observation noise and interference, only independency is assumed. The model functions are any defined functions. This algorithm estimates the states by first representing the state model by a trellis diagram and then using a suboptimum decoding algorithm. It requires a constant memory for its implementation. Numerical results have shown that for either linear or non-linear discrete models with interference, the new algorithm performs very well. Further, in the absence of interference, it performs better than the extended Kalman filter algorithm for some non-linear discrete models.
TL;DR: A double Chebyshev series is introduced to approximate functions of two independent variables and then applied to analyse and identify linear distributed systems and the solution for the coefficient matrices can be obtained directly from a Kronecker product formula.
Abstract: A double Chebyshev series is introduced to approximate functions of two independent variables and then applied to analyse and identify linear distributed systems. The solution for the coefficient matrices can be obtained directly from a Kronecker product formula. In addition, the algorithm for formulating the algebraic equations to estimate unknown parameters is derived, with the method used being algebraic and computer-oriented. Two illustrative examples are given and excellent results are obtained owing to the rapid convergence property of the Chebyshev series
TL;DR: In this paper, shifted Chebyshev polynomials of the second kind have been used to analyze linear time-varying systems and bilinear systems using the least square method.
Abstract: Linear time-varying systems and bilinear systems are analysed via shifted Chebyshev polynomials of the second kind. Using the operational matrix for integration and the product operational matrix, the dynamical equation of a linear time-varying system (or bilinear system) is reduced to a set of simultaneous linear algebraic equations. The coefficient vectors of shifted Chebyshev polynomials of the second kind can be determined by using the least-squares method. Illustrative examples show that shifted Chebyshev polynomials of the second kind having a finite number of terms are more accurate than either the Legendre or Laguerre methods.
TL;DR: In this paper, the sensitivity of the discrete-time Kalman filter to errors in the state transition matrix is examined and the approach makes use of the matrix Taylor expansion and estimates the deviation from the "nominal" computed performance.
Abstract: The sensitivity of the discrete-time Kalman filter to errors in the state transition matrix is examined. The approach makes use of the matrix Taylor expansion and estimates the deviation from the ‘nominal’ computed performance. Although only the first term of the expansion is retained, satisfactory accuracy is achieved. The method is considerably simple and constitutes a quick way to diagnose or establish limits for divergence. Direct application to stochastic observers is also possible