**1998 (Volume 7)**Number 1/2

**An evolutionary method of trajectory planning in collision situations at sea**Roman Śmierzchalski
*(Gdynia Maritime Academy, Poland )* |

In a collision situation at sea, the decision support system should help the operator to choose a proper manoeuvre in given circumstances, teach him good practices, and enhance his general intuition on how to behave in similar situations in future. An accepted approach in those cases is a multiple criterion decision problem. In this paper, a modified version of the EP/N (Evolutionary Planner/Navigator) algorithm - has been used as a major component of such a decision support system for computing the near optimum trajectory of a ship in given environment. By taking into account certain boundaries of the manoeuvring region, along with navigation obstacles and other moving ships, the problem of avoiding collisions at sea was reduced to a dynamic optimisation task with static and dynamic constrains. The introduction of a time parameter and moving constrains representing the passing ships is the main distinction of the new system. Sample results, having the form of ship trajectories obtained using the program for typical navigation situations are given.

**keywords:** evolutionary algorithms, trajectory planing, avoiding collisions at sea, decision support system.

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**Some remarks on pole assignability of distributed parameter systems**Toshihiro Kobayashi
*(Kyushu Institute of Technology, Japan )* |

The pole assignment problem of distributed parameter systems with unbounded feedback is discussed. The problem can be solved under a weaker restriction between the open-loop poles {βn} and the closed-loop poles {λn}. Two types of the expression of a characteristic equation whose roots are the closed-loop poles are first given. Next a feedback element is given which realizes the desired pole assignment of the closed-loop system. An interesting result is shown that an infinite number of the open-loop poles can be shifted such that: |λn - βn |=O(|λn|^((1 - ε)/2)) (ε sufficiently small positive number) for all *n*.

**keywords:** pole assignment problem; distributed parameter systems, unbounded feedback.

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**Controllability of a generalized linear control system**Hubert Wysocki
*(Naval Academy, Poland)* |

In this paper, a definition of controllability of a generalized linear differential control system is introduced using the Bittner operational calculus. Controllability criteria are also discussed. Adequate examples in various models of the operational calculus are given.

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**On reducing the order of the stabilizing compensator for a linear multivariable plant**Radosław Ładziński
*(Warsaw University of Technology, Poland )* |

The text covers an in-depth study on the order of the compensator applied in a feedback system for stabilization of the linear, time-invariant, n-th order, multivariable plant. It is shown that all such compensators evolve from the n-th order structure depicted in two forms in Fig. 2 (dotted lines). Presentation includes the so-called reduced and subreduced order compensators and the case of a static output feedback, i.e. the compensator of order zero. All theoretical considerations are supported by examples, in which various types of compensators are synthesized.

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**Parametric minimization of influence of stochastic disturbation in linear systems**Tadeusz Banek
*(Technical University of Lublin, Poland)* |

A structure optimization problem in linear systems is considered. It is shown that parametric minimization (in the mean square sense) of influence of stochastic disturbation can be reduced to some nonlinear programming problem. Sufficient condition for equivalence of these problems and existence of their solutions are given. It is also shown how to apply the results to controlled systems.

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**Discrete-averaged mathematical models of neutral delay systems**Wojciech Kozera
*(Maritime University of Szczecin, Poland)* |

This article presents a method of determining discrete-averaged mathematical models of multi-input multi-output (MIMO) linear time-invariant systems with constant commensurate delays characterized by a finite-dimensional subspace of antistable states. The proposed method generalizes the, presented in works [10 - 13], methods of determining models for retarded-delay systems to include systems of neutral type. The finite-dimensional approximation substantially facilitates analysis and enables designing the physically implemented control laws of the systems in question. To illustrate these problems, included are simple examples of determining unstable eigenvalues and of stabilization of the plant with a digital-analog (hybrid) compensator.

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**A neuro-fuzzy approach to system modelling, Part I. Methodology**Marian B. Gorzałczany
*(Kielce University of Technology, Poland)* |

Description of behaviour of complex and ill-defined systems and processes is usually based on a combination of two types of knowledge and data: a qualitative, fuzzy knowledge which contains elements of uncertainty and vagueness, and often is expressed in the form of linguistic rules usually provided by a domain expert, and quantitative, nonfuzzy information which appears in the form of measurements and other numerical data. Part I of this paper presents a methodology for modelling of complex systems which can effectively represent, process and generalize both above-mentioned types of system's knowledge. The proposed methodology combines artificial neural networks with some elements of the theory of fuzzy sets and fuzzy logic, yielding a structure that can be called a fuzzy neural network or a neuro-fuzzy system. Two examples of application of our approach in the area of system modelling are presented in Part II of the paper (ACS No. 3/4 1998).

**keywords:** Fuzzy sets, artificial neural networks, neuro-fuzzy systems, fuzzy neural networks, fuzzy models, identification methods, fuzzy controllers.

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