The stabilizing composite control in a weakly nonlinear singularly perturbed control system

Dmitriev, Mikhail; Макаров, Д. А.

doi:10.1109/icstcc.2017.8107099

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…In doing so, we propose an efficient algorithm in terms of the computation volume of the Riccati equation ( 15) that does not require multiple integration of matrix differential equations with state-dependent coefficients. The state of the system y(t) satisfies differential equation (21), and the synthesizing control u(y,t) is defined by formula (22).…”

Section: Discussionmentioning

confidence: 99%

“…Fig. 1, 2 show trajectories at y(t 0 )-y s = =(-200, -100, -100)*, where control is performed by formula (22). The balance relations (3)-( 5) are satisfied.…”

Section: Algorithm For Solving the Optimal Control Problem And Constr...mentioning

confidence: 99%

“…where Q and R are positive semidefinite and positive definite (3×3) matrices, respectively. Studies of the stability of nonlinear systems in the form (7) were carried out by [21,22] describing optimal stabilization of these systems over an infinite time interval.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…1. Graphs for optimum trajectories and optimum controls: a -Graphs of the optimal trajectories (capacity to labor ratio) for the system (7) with the initial condition (43) under the control (22); b -Graphs of the optimal controls for the system (7) with the initial condition (43) a b Fig. 2.…”

Section: Algorithm For Solving the Optimal Control Problem And Constr...mentioning

confidence: 99%

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Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster

Murzabekov

Miłosz

Tussupova

et al. 2022

EEJET

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The problem of optimal control over a finite time interval for a mathematical model of a three-sector economic cluster is posed. The economic system is reduced by means of transformations to the optimal control problem for one class of nonlinear systems with coefficients depending on the state of the control object. Two optimal control problems for one class of nonlinear systems with and without control constraints are considered. The nonlinear objective functional in these problems depends on the control and state of the object. Then, using the results of solving optimal control problems on a finite interval, an algorithm for solving the problem for a nonlinear system of a three-sector economic cluster is developed. A nonlinear control based on the feedback principle using Lagrange multipliers of a special kind is found. The results obtained for nonlinear systems are used to construct the control parameters of a mathematical model of a three-sector economic cluster at a finite time interval with a given functional and various initial conditions. The results of the system state calculation are shown in the figures, the optimal controls satisfy the given constraints. The optimal distribution of labor and investment resources for a three-sector economic cluster is determined. They ensure that the system is brought into an equilibrium state and satisfy balance ratios. These results are useful for practice and are important because there are a number of optimal control problems when it is necessary to transfer a system from an initial state to a desired final state for a given time interval. Such problems often arise for an economic system when a certain level of development is required.

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Section: Discussionmentioning

confidence: 99%

“…Fig. 1, 2 show trajectories at y(t 0 )-y s = =(-200, -100, -100)*, where control is performed by formula (22). The balance relations (3)-( 5) are satisfied.…”

Section: Algorithm For Solving the Optimal Control Problem And Constr...mentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Algorithm For Solving the Optimal Control Problem And Constr...mentioning

confidence: 99%

See 2 more Smart Citations

Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster

Murzabekov

Miłosz

Tussupova

et al. 2022

EEJET

View full text Add to dashboard Cite

show abstract

“…The ambiguity of the representation of a nonlinear system in the form of a system of linear structure and the absence of su±ciently universal algorithms for solving the Riccati equation whose parameters also depend on the state give rise to many possible suboptimal solutions. Due to the fact that there are many di®erent types of nonlinearities in technical and economic systems, di®erent approaches to constructing feedback control laws that are rational with respect to a given quality criterion arise (Afanas'ev 15 and Dmitriev 16 ).…”

Section: Introductionmentioning

confidence: 99%

Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster

Murzabekov

Miłosz

Tussupova

et al. 2020

Vietnam J. Comp. Sci.

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For the mathematical model of a three-sector economic cluster, the problem of optimal control with fixed ends of trajectories is considered. An algorithm for solving the optimal control problem for a system with a quadratic functional is proposed. Control is defined on the basis of the principle of feedback. The problem is solved using the Lagrange multipliers of a special form, which makes it possible to find a synthesizing control. The problem of optimal stabilization for a class of nonlinear systems with coefficients that depend on the state of the control object is considered. The results obtained for nonlinear systems are used in the construction of control parameters for a three-sector economic cluster on an infinite time interval.

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SDRE based stabilization of the affine control system with the stationary linear part

Dmitriev

Murzabekov

Макаров

et al. 2019

2019 23rd International Conference on System Theory, Control and Computing (ICSTCC)

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The stabilizing composite control in a weakly nonlinear singularly perturbed control system

Cited by 9 publications

References 19 publications

Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster

Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster

Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster

SDRE based stabilization of the affine control system with the stationary linear part

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