scholarly journals The Optimization of Solutions of the Dynamic Systems with Random Structure

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Miroslava Růžičková ◽  
Irada Dzhalladova

The paper deals with the class of jump control systems with semi-Markov coefficients. The control system is described as the system of linear differential equations. Every jump of the random process implies the random transformation of solutions of the considered system. Relations determining the optimal control to minimize the functional are derived using Lyapunov functions. Necessary conditions of optimization which enables the synthesis of the optimal control are established as well.

2021 ◽  
Vol 26 (3-4) ◽  
pp. 302-313
Author(s):  
L.G. Gagarina ◽  
◽  
A.A. Doronina ◽  
R.A. Fomin ◽  
D.A. Chukhlyaev ◽  
...  

Optimal control is closely related to the choice of the most advantageous control modes for complex objects, which are described using ordinary differential systems. The problem of optimal control consists in calculating the optimal control program and synthesizing the optimal control system. This problem arises in the applied field of the optimal control theory, in the case when control is based on the principle of feedback and in automatic control systems. Optimal control problems, as a rule, are calculated by numerical methods to find the extremum of a functional or to solve a boundary value problem for a differential equation system. From a mathematical standpoint, the synthesis of optimal control systems is a nonlinear programming problem in functional spaces. In this study the problem of complete controllability of a bilinear control system on the plane was considered. The controllability of bilinear systems with both unlimited and limited control was studied. The evidences of closed trajectory systems controllability theorems were produced. The authors have defined multiple criteria of complete controllability for bilinear system with limited control. The complete controllability conditions of bilinear control system have been proposed with their algebraic reasoning. In the contemporary context of universal robotization of production, completely controllable systems matter in navigation, as well as in modeling of a number of economic and social processes.


Author(s):  
A.M. Krasnov

Based on the analysis of the general patterns of development of automated control systems, the main patterns of the development of aviation aiming and navigation systems (AANS) in the directions of their integration, automation, optimization and unification are considered. The prospects for the development of AANS in the indicated directions are determined. The aim of the article is to develop a concept for the construction of advanced integrated interactive aviation sighting and navigation systems. Integrated interactive AANS operate under conditions of a priori uncertainty and in the process of functioning automatically adapt to unforeseen changes in the structure and properties of AANS and the external environment. The integrated interactive AANS provides for operational adaptation to changing the composition of information sources, as well as ensuring the unification of algorithmic support for both various tasks solved by the AANS, and different classes of AANS installed on various types of aircraft (AC). This is a fertile ground for building highly reliable AANS that provide the required aiming accuracy. A holistic concept has been developed for the construction of advanced integrated interactive aviation sighting and navigation systems. The proposed concept is a set of interrelated principles based on the methodology of system analysis and synthesis, modern achievements in the field of aviation science, engineering, technology, including: new principles of AANS integration, based on integration not only at the level of onboard equipment and algorithms, but also at the level control tasks for aircraft and weapons as a single purposeful multi-stage dynamic system with a variable structure; new principles of building integrated interactive AANS, implementing the concept of optimal automation; new principles for organizing the use of AANS, based on the optimal choice of weapons in an attack and the distribution of combat functions between the aircraft and weapons; new principles for constructing a unified algorithmic support for AANS, based on the use of methods of the theory of multistage dynamical systems, the theory of systems with a random structure, observation control methods, methods of statistical analysis and synthesis of algorithms for optimal control and filtering, taking into account the errors of their implementation in the BCVS; new principles for determining the structure of the computing system and organizing the solution of problems based on the optimal planning of the computing process in multiprocessor BCVS; new principles of building a human-machine interface based on a rational combination of natural and artificial intelligence; new principles of ensuring the reliability and survivability of systems based on methods for constructing fault-tolerant algorithms, optimal control of the state of the system and its dynamic reconfiguration; new principles of forming the appearance of the AANS, based on the optimization of its structure and parameters within the generalized system «object − environment», and on this basis the presentation of requirements for information, executive and computing subsystems. The title of the concept contains key words that reflect two fundamental concepts that underlie the formation of the appearance of the AANS of promising aircraft − integration and interactivity (mutual activity of a person and the «aircraft − weapon» system). Integration is manifested in the integration of tasks, in the complex receipt and processing of information, in the integration of algorithms and aircraft onboard equipment. The active inclusion of human intelligence in the aircraft and weapons control system, the optimal distribution of functions between the crew and the AANS, the creation of a new man-machine interface − this is the second main direction in the development of promising AANS. The central place in the considered concept is occupied by the principle of system analysis and synthesis of AANS application processes. The implementation of this principle provides a methodologically correct choice of a system of performance criteria for the analysis and synthesis of the AANS, an agreed system of mathematical models for describing the processes of its functioning, a reasonable justification of tactical and technical requirements. The use of modern AANS is carried out in intensive fire, information and maneuvering enemy countermeasures. In these conditions, the effective execution of tasks will be possible if their algorithmic support is built taking into account the principle of adaptation and resistance to resistance. The theoretical basis for the implementation of the above principles and the concept as a whole are fundamental and applied results obtained in recent years. First of all, these should include: the theory of multistage dynamic systems and methods for controlling the final state of the «aircraft − weapons» system; theory of systems with a random structure and methods of algorithmic protection of AANS from functional disorders; methods of optimization of the computational process in multiprocessor BCVS and numerical methods for accelerated solution of combat missions; theory and methods of optimization of the structure of information management systems; methods of optimal automation of information and control systems; mathematical methods and models for evaluating the effectiveness and optimization of conditions for the combat use of aircraft weapons systems. The practical significance lies in the fact that the implementation of the concept of building integrated interactive AANS makes it possible to successfully solve many problems of creating and mastering new generations of aviation equipment at all stages of the life cycle, since these AANS allow: to significantly expand the range of conditions for using aircraft; provide a comprehensive optimization of estimates of the phase coordinates of the aircraft and the attacked target; significantly reduce the time, material and labor costs for the operation of the AANS (docking, tuning, adjustment); significantly increase the survivability of the AANS in conditions of possible combat damage due to functional redundancy. The proposed concept of building integrated interactive AANS is focused on the creation of so-called open architecture systems that are well adapted to all stages of the life cycle. At the same time, the most important property is laid in the created system already at the initial stages of development − the possibility of modernization during operation.


2014 ◽  
Vol 602-605 ◽  
pp. 937-941
Author(s):  
Hua Tao ◽  
Li Wei Zhu

Previously, intelligent transportation control systems have been widely used to improve traffic safety on roadways. Among them, dynamic speed control is a novel technique that has been increasingly used for reducing collision risks. However, previous studies did not consider using any heuristic searching algorithm to obtain the optimal solution to improve traffic safety. The objective of this study is to evaluate the application of using heuristic searching algorithm to optimize the safety effects of dynamic speed control system. The results showed that the evolution process in the heuristic searching algorithm can promote the strategy towards better solutions for the optimization of the safety effects of dynamic speed control. The optimal control reduces collision risks by 12.7% and increased travel time only by 1.4%.


1993 ◽  
Vol 115 (2B) ◽  
pp. 392-401 ◽  
Author(s):  
Rahmat Shoureshi

The fundamental concept of feedback to control dynamic systems has played a major role in many areas of engineering. Increases in complexity and more stringent requirements have introduced new challenges for control systems. This paper presents an introduction to and appreciation for intelligent control systems, their application areas, and justifies their need. Specific problem related to automated human comfort control is discussed. Some analytical derivations related to neural networks and fuzzy optimal control as elements of proposed intelligent control systems, along with experimental results, are presented. A brief glossary of common terminology used in this area is included.


2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Svitlana V. Antonyuk ◽  
Marian F. Byrka ◽  
Mykola Y. Gorbatenko ◽  
Taras O. Lukashiv ◽  
Igor V. Malyk

The problem of synthesis of the optimal control for a stochastic dynamic system of a random structure with Poisson perturbations and Markov switching is solved. To determine the corresponding functions for Bellman functional and optimal control the system of ordinary differential equation is investigated.


2018 ◽  
Vol 10 (1) ◽  
pp. 115
Author(s):  
Gladys Denisse Salgado Suárez ◽  
Hugo Cruz-Suárez ◽  
José Dionicio Zacar´ias Flores

This paper provides necessary conditions in order to guarantee the existence of an unique equilibrium point in a deterministic control system. Furthermore, under additional conditions, it is proved the convergence of the optimal control sequence to this equilibrium point. The methodology to obtain these statements is based on the Euler's equation approach. A consumption-investment problem is presented with the objective to illustrate the results exposed.


1993 ◽  
Vol 6 (2) ◽  
pp. 181-185
Author(s):  
Farzana A. McRae

The problem of optimal controllability of a nonlinear impulsive control system is studied using the method of vector Lyapunov functions and the generalized comparison principle.


Author(s):  
Z. H. Liu ◽  
S. Migórski

We deal with the optimal control of systems driven by differential inclusions with anti-periodic conditions in Banach spaces. The operators in the differential inclusions, describing the control system, all depend on control variables. By a solution of the control system we mean a ‘trajectory-control’ pair. We first prove that, for fixed control variables, the set of solutions is non-empty for the corresponding differential inclusion with anti-periodic conditions. We then show the functional-topological properties of the set of solutions. Finally, we investigate the existence of solutions to the optimal control problem. These abstract results can be used to study optimal control systems of evolutionary hemi-variational inequalities.


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