Linear-Cubic Locally Optimal Control of Linear Systems and Its Application for Aircraft Guidance
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ROL SYSTEMS OF MOVING OBJECTS
Linear-Cubic Locally Optimal Control of Linear Systems and Its Application for Aircraft Guidance V. S. Verbaa,*, V. I. Merkulova, and E. A. Rudenkob,** a Vega
b Moscow
Radio Engineering Corporation, Moscow, 121170 Russia Aviation Institute (National Research University), Moscow, 125993 Russia *e-mail: [email protected] **e-mail: [email protected]
Received March 25, 2020; revised April 28, 2020; accepted May 25, 2020
Abstract—In the paper, the requirements for aircraft guidance methods are considered. It is noted that the existing methods of optimization of linear control systems based mainly on the minimization of quadratic functionals of quality do not allow providing the set of requirements for interception systems of aerial objects. It is proposed to use new local quadratic-biquadratic quality functionals, whose minimization makes it possible to obtain more general linear-cubic control laws that are adequate for modern requirements. The biquadratic terminal part of the functional contains fourth-degree summands. An example of the synthesis of a specific guidance method is considered and analyzed. DOI: 10.1134/S1064230720050123
INTRODUCTION The base of the perfection of any aviation interception system is the guidance method used in it, which provides building the required trajectory of the flight that allows hitting the target [1]. Nowadays, in order to synthesize guidance methods, the representation of processes and systems in a multidimensional space of states is applied. Within this representation, the Bellman dynamic programming and the Pontryagin maximum principle are the most widely used [2, 3]. These methods have a common disadvantage, namely, the highly complicated procedure of the control synthesis. Thus, the Bellman method, even in the simplest case of using linear state models and quadratic quality functionals is reduced to the solution in inverse time of the Riccati equation for calculation of the control error transfer ratios [2–4], including the more complex modern problems [5, 6]. Note that, handling the types of initial models and quality functionals in them, we can obtain a large set of particular control laws adapted for solving specific problems [7–9]. In the simplest case, by increasing the dimension of the initial models of the control object, we can obtain more complex control laws adapted for the interception of maneuverable targets. However, the changes that have taken place in recent decades in the military-technical confrontation [10, 11] impose stricter and often conflicting requirements on guidance methods, including the enhancement of functionalities when working with new promising types of targets [12–14]. Below we present a brief analysis of the requirements for the procedures of synthesis of guidance methods, propose a more universal way to optimize them based on minimizing more complex quadratic-biquadratic functionals, and consider an example of its use. 1. THE ANALYSIS OF REQUIREMENTS FOR ADVANCED GUIDANCE SYSTEMS AND METHODS OF THEIR SYNTHE
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