Some properties of cyclic codes†

This paper will investigate the properties of cyclic codes under the transformation,$ It is discovered that for all the non-shortened cyclic codes (binary or (/-nary), if (g(x), (x?1)) =1 then the set of all the codewords is invariant under the transformation f_b. If (g(x), Lx?1)) = (x; ? 1), then the set of all the code words is generated by g(x)/(x ? 1). Next this paper shows a systematic method for the construction of orthogonal cyclic codes in which all the code vectors are orthogonal to each other even to itself     

Some applications of matrices to location of zeros of polynomials†

In previous papers classical theorems on location of zeros of a polynomial with respect to the left half plane Γ₁ or the unit circle Γ₂ have been reformulated more simply in terms of appropriate companion matrices. It is shown how this work can be extended to the problem of zero location with respect to more general regions Γ of the complex plane. The first approach is to apply the bilinear transformation to the given polynomial, so that for example Γ₁ can be mapped into Γ₂ and a matrix representation of this is derived. An alternative method is discussed which relies on transformation of Γ into Γ₂. Some examples illustrate how any theorem involving Hurwitz-typc minors can be expressed in companion matrix terms, with a consequent halving of the orders of the determinants involved.     

Solution of non-linear optimization problems in power systems†

The application of differential dynamic programming or hybrid quasilinearization technique to the solution of non-linear optimization problems in power systems has encountered the problem of computational instability, particularly in higher order systems. This paper describes the application of a continuation procedure to alleviate this difficulty. Sixth order non-linear systems have been optimized with and without constraints on control variables. Both open-loop and, for the first time, closed-loop systems including both exciter and governor dynamics, are analysed. The studies presented show that this technique is quite effective in obtaining accurate solutions for non-linear boundary-value-problems in power systems.     

Sub-optimal solutions of linear control and eigenvalue pattern problems†

The present paper deals with sub-optimal solutions for problems of minimizing integral cost fimetioiuils which consider the state variables alone for stationary linear processes. The control vector and its time derivative are assumed to be bounded. The resulting control policies are linear with respect to the state vector. The performance of the proposed sub-optimal policies is compared with that of classical control systems and a procedure for sub-optimal eigenvalue patterns is presented for systems of any order.     

Solution of discrete regulation problems using linear algebraic equations†

The solution of linear algebraic equations are used as a method of synthesizing linear, deterministic, multivariable, discrete systems for either stable or unstable open loop plants, Well-defined relationships are established between weights of a quadratic performance index and plant dynamics via the optimal system determinant.

The discrete calculus of variations provides the necessary conditions for minimizing a quadratic cost functional. This gives closed form expressions for U°(z) and Y°(z) and generates the optimal system.     

Similarity in DTOL and related problems†

Deterministic Informationless Lindenmayer Sytems with Tables (DTOL) aro systems introduced for the mathematical modelling of the development of Filainontoita organisms under changing environmental conditions. The sequence equivalence problem for DTOL, i.e. the problem of determining whether the sequences of organisms produced by two given DTOL are equal, is open in the general case. We introduce hero a weaker notion of equivalence between DTOL, to be called similarity, and prove its decidability. We also prove the decidability of the original sequence-equivalence problem for some particular cases.     

Some Studies on Two and Three-level Simplified Expressions of Boolean Functions†

A method of directly testing whether the AND-OR or the OR-AND form of a switching function is more economic for some simple cases is presented. Simplified expressions leading to economic three-level synthesis have also been derived.     

On the estimation of stochastic sensitivity for non-linear dynamical systems in state estimation problems†

This paper consists of two main parts. Recognizing the existence of identification errors due to variations of system parameters, the first part is devoted to the verification of the existence of a unique continuous solution of a non-linear vector stochastic differential equation with a random parameter and to the establishment of the stochastic sensitivity equation. Both the a and β-stochastic sensitivity equations are established through the precise definition of stochastic sensitivity.

The remainder of this paper deals with evaluation of quantitative aspects of the sensitivity in the state estimation by using the stochastic sensitivity equation.     

The application of Kolmogorov–Rényi statistics to problems of parameter uncertainty in systems design†

This paper presents a method for dealing with parameter uncertainty in system design which is based on the study of the statistical properties of an ensemble of systems defined by a given structure and by a priori parameter distributions rather than point parameter estimates. It is assumed that the model of the actual system is a random member of the ensemble. The object of the analysis is to design or modify the properties of the ensemble to ensure a high probability of adequate performance of the actual system. The primary statistical function employed is the sample distribution function. This function is used to estimate the true population distribution of a scalar variable chosen to measure the system property of interest. The sample distribution function is constructed from random samples of this figure of merit generated by a suitable digital computer programme. The accuracy of the estimation of the population distribution by the sample distribution is determined by application of statistical results of Kolmogorov and Rényi.     

An integral-equation function-space method for solving inequality-constrained optimal control problems†

A function-space method using an integral equation representation of the second variation is applied to inequality-constrained optimal control problems. Numerical solutions for a bang-bang control problem and a singular control problem are solved using the computational algorithm.     

A computational method for parameter optimization problems arising in control†

A parameter optimization procedure is presented for large-scale problems arising in linear control system design that include equality and inequality constraints. The procedure is based on a novel min—max algorithm for locating a constrained relative minimum without the use of penalty functions or slack variables. This algorithm is constructed from an auxiliary minimization problem with equality constraints. Inequality constraints then are introduced using the notion of an effective constraint. Typical problem formulations are discussed, and an extensive design example is presented.     

Robustness of absolute stability†

The stability of a class of single-input, single-output singularly perturbed systems formed by a linear time-invariant feedforward block with a sector bounded time varying feedback is considered. It is shown that if the reduced order ‘ slow ’ subsystem is absolutely stable and the parasitics are asymptotically stable and sufficiently fast then the full system is absolutely stable. Bounds on the singular perturbation parameter for uniform asymptotic stability and absolute stability are obtained.     

Stabilization of non-linear systems†

The problem of stabilizing a discrete-time non-linear system is considered. For a rather large class of common stabilizable non-linear systems, a procedure leading to the stabilization of a given non-linear system Σ belonging to that class is derived. In this procedure, a pair of compensators is constructed, consisting of a precompensator and an output feedback compensator, which, when connected in closed loop around the system Σ, yield a closed-loop system that is internally stable for bounded input sequences. The procedure allows the construction of infinitely many different pairs of such compensators, thus facilitating the choice of a convenient one.     

Vulnerability of dynamic systems†

The purpose of this paper is to formulate and partially resolve the problem of vulnerability of dynamic systems in the context of the theory of directed graphs. A system is considered vulnerable if its structural properties such as input (output) reachability or structural controllability (observability) is destroyed by a perturbation characterized as removal of a line, or set of lines, from the corresponding graph. Graph-theoretic procedures are developed to identify the minimal sets of lines which are essential for preserving the structural properties of the system.     

Hierarchies of recursive computations†

A recursive version of the Turing machine model is used to analyze the time and storage complexity of recursive algorithms. Hierarchy theorems are proven for time and for width of recursion (the amount of storage used at a level). A particular language is shown to be the “hardest” language to recognize without recursion. Previous results relating recursive and non-recursive time bounded computations are sharpened.     

Optimization of linear systems of constrained configuration†

For the sake of simplicity it is often desirable to restrict the number of feedbacks in a controller. In this case the optimal feedbacks depend on the disturbance to which the system is subjected. Using a quadratic error integral as a measure of the response, three criteria of optimization are considered :

1. The response to a given initial disturbance.

2. The worst response to an initial disturbance of given magnitude.

3. The worst comparison with the unconstrained optimal system.

It is shown that for each of these criteria the gradient with respect to the feedbacks can be calculated by a uniform method. The solution may then be found either directly or by a descent procedure. The method is illustrated by an example.     

Radar backscattering of forest stands†

Research on the potential applications of microwave remote sensing in agriculture is conducted in the Netherlands by the ROVE team. Since active microwave remote sensing, featuring its all-weather capability, also seems to be a promising tool for forest classification, especially on a global scale, the Wageningen Agricultural University started a new working group in co-operation with the ROVE team in order to explore this field of application.

Results of four X-band SLAR flights have been analysed. The digital radar images obtained are accurately corrected both geometrically and radiometrically and indicate gamma values instead of arbitrary grey tones.

Radar signatures, showing seasonal and angular effects, of 16 classes of forest stands have been derived from the images. Special attention has been paid to the statistical properties of the radar signatures and their impact on classification accuracy. Several interesting phenomena have been observed indicating effects of vegetation structure on radar backscattering.

One of the test areas is a young forest in the Oost-Flevoland polder featuring a substantial variety of species; parcels are relatively large, rectangular in shape, homogeneous in structure and age and with pure species stands making this an ideal test site. Another test area is an old forest located at the Veluwe. Much variation in age is present here, which made it possible to determine relationships between tree age and radar backscatter for several coniferous tree species.

The initial work as presented here clearly demonstrates the appropriateness of X-band ability in the classification of (Dutch) forests. Theoretical considerations suggest that a multitemporal approach is likely to give the most accurate results of tree-type classification. A classification simulation yielded overall error fractions ranging from 10 to 16 per cent at the Oost-Flevoland polder test area and 14 to 28 per cent at the Veluwe test area. This can be demonstrated in multitemporal radar images as well as in actual classified images.     

Constrained controllability of discrete-time systems†

The constrained controllability of the discrete-time system x_k+1=A(k)x_k+B(k)u,_k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints. Constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state

Conditions for checking constrained controllability to a given target set from a specified initial state are presented. These conditions involve solving finite-dimensional optimization problems and can be checked via numerical computation. In addition, conditions for checking global constrained controllability to a given target set are presented. A system is globally constrained controllable if for every initial state, there exists an admissible control that steers the system to the target.

If a given discrete-time system is constrained controllable, it may be desirable to obtain an admissible control that steers the system to the target from a specified initial state. Such a control is called a steering control. Results for computing steering controls are also presented

This paper is concluded with a numerical example. In this example, it is shown that the constrained controllability of a continuous-time system which has been discretized is dependent on the discretization time. The set of states which can be steered to the target changes as the discretization time changes. Furthermore, the example shows that a discrete-time steering control cannot always be obtained by discretizing a continuous-time steering control; the steering control for the discrete-time system must be obtained directly from the discrete-time model.     

Fuzzy control of steam turbines†

A feasibility study of a fuzzy logic speed control of a steam turbine is reported. The efficiency of the fuzzy control is compared with conventional PID control. As a basis for this comparison, we use a mathematical model of the turbine which has been well validated at a real turbine in connection with the design of the PID control. For this model, a simple fuzzy controller is designed. To assess the resulting fuzzy control, we study by simulation the step response of the speed at a full load reduction, as well as the robustness with respect to parameter variations of the turbine.