Sufficient Optimality Conditions for Hybrid Systems of Variable Dimension

Bortakovskii, A. S.

doi:10.1134/s0081543820010071

Cited by 5 publications

(9 citation statements)

References 8 publications

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“…The proved necessary conditions for optimality of the HSVD and the previously obtained sufficient conditions [14] can be used for a wide range of control problems with switching: continuous-discrete [15], logical-dynamic, composite [1,2], step systems [5], and systems with intermediate conditions [2,8,9,16], with a variable or branched structure [3,4,17,18]. The application of the necessary conditions for the optimality of the HSVD is demonstrated by an academic example.…”

Section: Optimal Controlmentioning

confidence: 66%

The Necessary Conditions for Optimal Hybrid Systems of Variable Dimensions

Bortakovsky

2021

J. Comput. Syst. Sci. Int.

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The problem of the optimal control of a hybrid system (HS), the continuous motion of which alternates with discrete changes (switchings) in which the state space changes, is considered. The change in the dimension of the state space occurs, for example, when the number of controlled objects changes, which is typical, in particular, for the problems of controlling groups of moving objects of variable compositions. The switching times are not predefined. They are determined as a result of minimizing the functional, while processes with instantaneous multiple switchings are not excluded. The necessary conditions for the optimality of the control of such systems are proved. Due to the presence of instantaneous multiple switchings, these conditions differ from traditional ones, in particular, by the equations for auxiliary variables. The application of optimality conditions is demonstrated by an academic example.

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Section: Optimal Controlmentioning

confidence: 66%

The Necessary Conditions for Optimal Hybrid Systems of Variable Dimensions

Bortakovsky

2021

J. Comput. Syst. Sci. Int.

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“…We assume that Equation (2.3) contains no the so-called dummy switchings at which the state of the system is preserved, i.e., x i (t i ) = x i−1 (t i ) and there is no actual switching. If the successive times in (2.1) are equal, then this means that the system has multiple instantaneous switchings [11,12].…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…For hybrid systems with intermediate conditions necessary conditions generalizing the maximum principle [10] were obtained in [8,9], where the number of switchings was given, whereas the switchings themselves were uncontrolled. For hybrid systems of variable dimension with unknown time and number of switchings, but controlled switchings of states were considered in [11], where sufficient conditions were obtained, in particular, in the case of processes with multiple instantaneous switchings [12].…”

Section: Introductionmentioning

confidence: 99%

“…In this problem, the number of switchings is determined by the number of purposes, switching times are not given, and switchings themselves are controlled. Processes with multiple instantaneous switchings [12,11] are not excluded from the consideration.…”

Section: Introductionmentioning

confidence: 99%

“…To synthesize an optimal hybrid system of variable dimension, not the value function itself is used, but the so-called generating (conditional) value functions [14,15]. Differential and recurrence equations for the generators are obtained by using the sufficient optimality conditions for hybrid systems of variable dimension [11]. Application of these equations is demonstrated by academic examples of multipurpose time-optimal operation.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis of Optimal Hybrid Systems for Multipurpose Time-Optimal Operation

Bortakovskii

Evdokimova

2021

J Math Sci

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We consider a time-optimal control problem for a hybrid system of variable dimension. Continuous motion of the system alternates with discrete variations (switchings) at which the dimension of the state space changes. The change of the space of states of the system can occur if the number of control objects changes, which is typical, for example, for the control problems for groups of a variable number of aircrafts. We obtain sufficient conditions for the time-optimal achievement of all purposes by a group of control objects. The application of optimality conditions is demonstrated by academic examples. Bibliography: 18 titles. Illustrations: 3 figures.

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Necessary Optimality Conditions for Hybrid System of Variable Dimension with Intermediate Constraints

Bortakovskii

2023

J Math Sci

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We consider an optimal control problem for a hybrid system. The continuous motion of the system alternates with discrete variations (switchings) at which the dimension of the state space changes. The switching times are found by minimizing a functional taking into account the cost of switchings. We obtain necessary optimality conditions for such systems under additional constraints at the switching times. The application of optimality conditions is illustrated by an academic example. Bibliography: 22 titles.

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Sufficient Optimality Conditions for Hybrid Systems of Variable Dimension

Cited by 5 publications

References 8 publications

The Necessary Conditions for Optimal Hybrid Systems of Variable Dimensions

The Necessary Conditions for Optimal Hybrid Systems of Variable Dimensions

Synthesis of Optimal Hybrid Systems for Multipurpose Time-Optimal Operation

Necessary Optimality Conditions for Hybrid System of Variable Dimension with Intermediate Constraints

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