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No 9 (2023)
Articles
A Historical Essay on the Scientific School of V.A. Yakubovich
Abstract
The milestones of the history of the scientific school on cybernetics (the School), established in 1959 by outstanding scientist V.A. Yakubovich at Leningrad State University (LSU), are presented. The connections of the School with other Russian and foreign scientific schools in related fields are outlined.
3-36
Construction of the Time-Optimal Bounded Control for Linear Discrete-Time Systems Based on the Method of Superellipsoidal Approximation
Abstract
The speed-in-action problem for a linear discrete-time system with bounded control is considered. In the case of superellipsoidal constraints on the control, the optimal control process is constructed explicitly on the basis of the discrete maximum principle. The problem of calculating the initial conditions for an adjoint system is reduced to solving a system of algebraic equations. The algorithm for generating a guaranteeing solution based on the superellipsoidal approximation method is proposed for systems with general convex control constraints. The procedure of superellipsoidal approximation is reduced to solving a number of convex programming problems. Examples are given.
37-67
Static Feedback Design in Linear Discrete-Time Control Systems Based on Training Examples
Abstract
The problem of static feedback design in linear discrete time-invariant control systems is considered. The desired behavior of the system is defined by a set of its output variation laws (training examples) and by a requirement to the degree of its stability. Controller’s structural constraints are taken into account. Explicit relations are obtained and an iterative method based on these relations is proposed to find a good initial approximation of the desired gain matrix and to refine it sequentially. In the general case, simple-structure gain matrices are found: in such matrices, only those components are nonzero that are necessary and sufficient to give the system the desired properties. Some examples are provided to illustrate the method.
68-81
Fault Identification: An Approach Based on Optimal Control Methods
Abstract
This paper considers the problem of identifying (estimating) faults in systems described by linear models under exogenous disturbances. It is solved using optimal control methods; in comparison with sliding mode observers, they avoid high-frequency switching. The solution method proposed below involves a reduced model of the original system that is sensitive to faults and insensitive to disturbances. The corresponding theory is illustrated by an example.
82-94
Global Stability of a Second-Order Affine Switching System
Abstract
Stability of an affine switching system is studied. The system comes to existence when stabilizing a chain of two integrators by means of a feedback in the form of nested saturators. The use of such a feedback allows one to easily take into account boundedness of the control resource, to constrain the maximum velocity of approaching the equilibrium state, which is especially important in the case of large initial deviations, and to ensure desired characteristics of the transient process, such as a given exponential rate of the deviation decrease near the equilibrium state. It is proved that the closed-loop system is globally stable.
95-105
Velocity of Flow on Regular Non-Homogeneous Open One-Dimensional Net with Non-Symmetrical Arrangement of Nodes
Abstract
A system is studied such that this system belongs to the class of dynamical systems called the Buslaev nets. This class has been developed for the purpose of creating traffic models on network structures such that, for these models, analytical results can be obtained. There may be other network applications of Buslaev nets. The considered system is called an open chain of contours. Segments called clusters move along circumferences (contours) according to prescribed rules. For each contour (except the leftmost and rightmost contours) there are two adjacent contours. Each of the leftmost and rightmost contours has one adjacent contour. There is a common point (node) for any two adjacent contours. Results have been obtained on the average velocity of cluster movement, taking into account delays during the passage through nodes. These results generalize the results obtained previously for a particular case of the system under consideration.
106-119
Kosvennyy metod odnopozitsionnoy koordinatometrii s uchetom invariantov dvizheniya pri nalichii singulyarnykh oshibok izmereniy
Abstract
120-134
On the Algorithm of Cargoes Transportation Scheduling in the Transport Network
Abstract
The problem of cargoes transportation scheduling in the transport network represented by an undirected multigraph is considered. Transportations between vertices are provided at predefined time intervals. The iterative algorithm to search for a solution approximate to the optimal one by criterion value is proposed in the problem under consideration. The algorithm is constructed on the base of solutions of mixed integer linear programming problems. The applicability of the algorithm is tested by the example with more than 90 million binary variables
135-152
Minimizing the Total Weighted Duration of Courses in a Single Machine Problem with Precedence Constraints
Abstract
A single machine scheduling problem with a given partial order of jobs is considered. There are subsets of jobs called courses. It is necessary to schedule jobs in such a way that the total weighted duration of all courses is minimal. We consider the case when the initial job and the final one of each course are uniquely determined. The NP-hardness of the problem under consideration is proved. We propose an algorithm for solving the problem, the complexity of which depends polynomially on the total number of jobs, but exponentially on the number of courses, which makes it possible to use it efficiently with a fixed small number of courses and an arbitrary number of jobs.
153-168