Optimal Near-Minimum-Time Control Design for Flexible Structures

Albassam, Bassam A.

doi:10.2514/2.4945

Cited by 25 publications

(22 citation statements)

References 17 publications

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“…This contradicts (51); therefore, (x ∞ (t), u ∞ (t)) must be a solution of the differential equation (1). The path constraint can be proved by the same contradiction argument.…”

Section: B Z (Q T))mentioning

confidence: 87%

“…Step 1 To prove that (x ∞ (t), u ∞ (t)) is a feasible solution to Problem B, we first need to show that (x ∞ (t), u ∞ (t)) satisfies the state equation (1). By the contradiction argument, suppose (x ∞ (t), u ∞ (t)) is not a solution of the differential equation (1).…”

Section: B Z (Q T))mentioning

confidence: 99%

“…By the contradiction argument, suppose (x ∞ (t), u ∞ (t)) is not a solution of the differential equation (1). Then there is a time t ∈ [−1, 1] so thaṫ…”

Section: B Z (Q T))mentioning

confidence: 99%

“…Historically, many early numerical methods [6,35] were indirect methods; that is, methods based on finding solutions that satisfy a set of necessary optimality conditions resulting from Pontryagin's Minimum Principle. Implementations of indirect methods have been successfully applied to many real-world problems that include control of flexible structures, launch vehicle trajectory design and low-thrust orbit transfer [1,3,5,6]. Nonetheless, indirect methods suffer from many drawbacks [3,6].…”

Section: Introductionmentioning

confidence: 99%

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Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control

et al. 2007

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In recent years, many practical nonlinear optimal control problems have been solved by pseudospectral (PS) methods. In particular, the Legendre PS method offers a Covector Mapping Theorem that blurs the distinction between traditional direct and indirect methods for optimal control. In an effort to better understand the PS approach for solving control problems, we present consistency results for nonlinear optimal control problems with mixed state and control constraints. A set of sufficient conditions is proved under which a solution of the discretized optimal control problem converges to the continuous solution. Convergence of the primal variables does not necessarily imply the convergence of the duals. This leads to a clarification of the Covector Mapping Theorem in its relationship to the convergence properties of PS methods and its connections to constraint qualifications. Conditions for the convergence of the duals are described and illustrated. An application of the ideas to the The research was supported in part by NPS, the Secretary of the Air Force, and AFOSR under grant number, F1ATA0-60-6-2G002. optimal attitude control of NPSAT1, a highly nonlinear spacecraft, shows that the method performs well for real-world problems.

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“…This contradicts (51); therefore, (x ∞ (t), u ∞ (t)) must be a solution of the differential equation (1). The path constraint can be proved by the same contradiction argument.…”

Section: B Z (Q T))mentioning

confidence: 87%

Section: B Z (Q T))mentioning

confidence: 99%

“…By the contradiction argument, suppose (x ∞ (t), u ∞ (t)) is not a solution of the differential equation (1). Then there is a time t ∈ [−1, 1] so thaṫ…”

Section: B Z (Q T))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control

et al. 2007

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“…Time optimal rest-to-rest maneuver of flexible structures, as linear systems, has been investigated by several authors [7]- [10]. The time optimal control of robots is investigated in many researches [11]- [14].…”

Section: Introductionmentioning

confidence: 99%

An iterative method for time optimal control of dynamic systems

Kashiri¹,

Ghasemi²,

Dardel³

2011

Archives of Control Sciences

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An iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.

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Closed-Form Solutions for Single-Axis Slew Maneuvers Under a Fixed Final Time Constraint

Lee,

Song

2023

Int. J. Aeronaut. Space Sci.

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Optimal Near-Minimum-Time Control Design for Flexible Structures

Cited by 25 publications

References 17 publications

Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control

Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control

An iterative method for time optimal control of dynamic systems

Closed-Form Solutions for Single-Axis Slew Maneuvers Under a Fixed Final Time Constraint

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