Second-Order Conditions for Fuel-Optimal Control Problems with Variable Endpoints

Chen, Zheng

doi:10.2514/1.g005865

Cited by 4 publications

(5 citation statements)

References 29 publications

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“…In [11], second-order optimality conditions are studied for optimal fuel control problems with both ends on manifolds. Each locally optimal candidate extremal from Pontryagin's maximum principle is embedded in a parametrized family of extremals with classical second-order conditions for the absence of conjugate points or focal points.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The boundary value problem ( 9)- (11) with fixed values will be called the direct problem. To calculate the first variation of functional (9), we compose the Lagrange function of problem ( 5)-( 9):…”

Section: Application Of the Myatiev-girinsky Scheme Describing The Un...mentioning

confidence: 99%

“…Here H=ψ(0, t)Q (t) is the Hamilton function for the problem ( 9)- (12). Expressions ( 13)-( 15) define the adjoint boundary value problem for the direct problem ( 9)- (11).…”

Section: T L P X T P X P X T X T P P P X T a P P X T T Xmentioning

confidence: 99%

“…For the numerical solution of the problem by the gradient projection method based on the calculation of the gradient of the functional (12), as a rule, at each step of the iterative process, it is necessary to solve two boundary problemsproblem ( 9)- (11) and problem ( 16)-( 18), and then use the formula to calculate the gradient.…”

Section: Finding a Formula For The Gradient Of The Functional Charact...mentioning

confidence: 99%

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Numerical solution of the control problem on the depletion of gas reservoirs with weakly permeable top

Mamtiyev

Rzayeva

Abdulova

2023

EEJET

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The current stage in the development of mathematical and software support for the processes of designing the development of hydrocarbon fields is characterized not only by the improvement of the means of geological and hydrodynamic modeling of reservoir fluid filtration but also by the use of algorithms for optimizing the development of gas deposits. The paper considers the problem of optimal control of the depletion of a gas reservoir with a low-permeability top. Using the so-called Myatiev-Girinsky hydraulic scheme, a two-dimensional equation describing the unsteady gas flow in a reservoir with a jumper is averaged over the capacity of the productive reservoir. This comes down to a one-dimensional equation with an additional term, taking into account gas-dynamic relationships between the reservoir and the jumper. For the numerical solution of process control problems, a formula for the gradient of the functional characterizing the reservoir depletion is found, and the method of successive approximations based on Pontryagin’s maximum principle is applied. In this case, the direct and conjugate boundary value problems are solved by the method of straight lines, and the required flow rate, without taking it beyond the maximum and minimum possible, is found by the gradient projection method with a special choice of step. A brief block diagram of the algorithm for solving the problem is shown; on its basis, a computer program was compiled. The results of calculations are presented to identify the influence of the values of the complex communication parameter not only on the state of the object but also on the operating mode of the well. The expediency of using the presented optimization tool is dictated by an increase in the share of deposits

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Application Of the Myatiev-girinsky Scheme Describing The Un...mentioning

confidence: 99%

“…Here H=ψ(0, t)Q (t) is the Hamilton function for the problem ( 9)- (12). Expressions ( 13)-( 15) define the adjoint boundary value problem for the direct problem ( 9)- (11).…”

Section: T L P X T P X P X T X T P P P X T a P P X T T Xmentioning

confidence: 99%

Section: Finding a Formula For The Gradient Of The Functional Charact...mentioning

confidence: 99%

See 2 more Smart Citations

Numerical solution of the control problem on the depletion of gas reservoirs with weakly permeable top

Mamtiyev

Rzayeva

Abdulova

2023

EEJET

View full text Add to dashboard Cite

show abstract

“…In practice, TPBVPs are solved through a variety of numerical methods. For nonlinear OCPs, all known methods must come to terms, in a given application, with the issue of whether a particular extremal satisfying the local necessary conditions is, in fact, the global extremal [10], [11]. Another major difficulty frequently encountered during the solution procedure is associated with the structure of the extremal controls that introduces non-smoothness into the underlying dynamics.…”

Section: Introductionmentioning

confidence: 99%

L2 Norm-Based Control Regularization for Solving Optimal Control Problems

Taheri,

2023

IEEE Access

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Solutions to practical optimal control problems (OCPs) may consist of control profiles that switch between control limits or assume values interior to its admissible set, either due to activation of inequality state path constraints or existence of singular control arcs. Moreover, abrupt switches in the control (i.e., bang-bang control) jeopardizes the numerical solution of OCPs unless care is taken to isolate precise time transition points where sharp switches occur (excluding the chattering phenomenon). We propose a novel control regularization method, called Bang-Bang Singular Regularization (BBSR), based on L2 norm-based regularization. We present an analysis on the L2 norm-based regularization at two levels: 1) its connection to trigonometric regularization and 2) its ability to approximate regular and singular control arcs. The utility of the method is demonstrated in solving three classes of trajectory optimization problems: 1) space low-thrust minimum-fuel maneuvers, 2) Goddard rocket problem with its known "bang-singularbang" control structure, and 3) minimum-time spacecraft reorientation. The results demonstrate the utility of the BBSR regularization method in approximating extremal control profiles that may consist of pure regular and/or mixed regular and singular arcs.

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Nonlinear Optimal Guidance for Intercepting Stationary Targets with Impact-Time Constraints

Wang

Chen

Wang

et al. 2022

Journal of Guidance, Control, and Dynamics

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Second-Order Conditions for Fuel-Optimal Control Problems with Variable Endpoints

Cited by 4 publications

References 29 publications

Numerical solution of the control problem on the depletion of gas reservoirs with weakly permeable top

Numerical solution of the control problem on the depletion of gas reservoirs with weakly permeable top

L2 Norm-Based Control Regularization for Solving Optimal Control Problems

Nonlinear Optimal Guidance for Intercepting Stationary Targets with Impact-Time Constraints

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