A Survey of the Maximum Principles for Optimal Control Problems with State Constraints

Hartl, Richard F.; Sethi, Suresh P.; Vickson, Raymond G.

doi:10.1137/1037043

Cited by 800 publications

(546 citation statements)

References 93 publications

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“…The next proposition is due to Jacobson et al [20]. Its proof was later clarified in Maurer [28], see also the survey by Hartl et al [16].…”

Section: Junction Condition Analysismentioning

confidence: 84%

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No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

Bonnans

Hermant

2007

Math. Program.

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“…The next proposition is due to Jacobson et al [20]. Its proof was later clarified in Maurer [28], see also the survey by Hartl et al [16].…”

Section: Junction Condition Analysismentioning

confidence: 84%

“…Thus we may extend continuously DJ(u) and DG(u) over L 2 (0, T ) (we keep the same notations for the extensions). Since DG(u) : L 2 (0, T ) → C[0, T ], it makes sense to extend the critical cone C(u) defined in (16) to critical directions in L 2 , as follows:…”

Section: Extended Second-order Necessary Conditionsmentioning

confidence: 99%

No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

Bonnans

Hermant

2007

Math. Program.

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“…As in [12], the optimality conditions derived here are based on the so-called direct approach (see [9]). However, the necessary conditions in [12] contain the conditions (20) but not the condition (19).…”

Section: Discussion Of the New Necessary Optimality Conditionsmentioning

confidence: 99%

“…The optimality conditions in [2,16] are formulated based on an so-called indirect approach (see [9]), which a priori leads to weaker results compared with the direct approach.…”

Section: Discussion Of the New Necessary Optimality Conditionsmentioning

confidence: 99%

New Necessary Conditions for Optimal Control Problems in Discontinuous Dynamic Systems

Kostina

Kostyukova

Schmidt

2013

IFIP Advances in Information and Communication Technology

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Part 2: Control of Distributed Parameter SystemsInternational audienceIn the paper we derive new necessary optimality conditions for optimal control of differential equations systems with discontinuous right hand side. The main attention is paid to a situation when an optimal trajectory slides on the discontinuity surface. The new conditions, derived in the paper, are essential and do not follow from any known necessary conditions for such systems

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“…is the augmented objective obtained through the direct adjoining method [11], and * x and * u denote the optimal solutions corresponding to a specified parameter a. Note that the sensitivity given by Rehbock et al [9] is a special case of (17).…”

Section: Sensitivity Analysismentioning

confidence: 99%

Multi-objective Optimization of Zero Propellant Spacecraft Attitude Maneuvers

Zhang

Tang

Friswell

et al. 2014

J Optim Theory Appl

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The zero propellant maneuver is an advanced space station, large angle attitude maneuver technique, using only control momentum gyroscopes. Path planning is the key to success and this paper studies the associated multi-objective optimization problem. Three types of maneuver optimal control problem are formulated: (i) momentum-optimal, (ii) time-optimal and, (iii) energy-optimal. A sensitivity analysis approach is used to study the Pareto optimal front and allows the tradeoffs between the performance indices to be investigated. For example, it is proved that the minimum peak momentum decreases as the maneuver time increases, and the minimum maneuver energy decreases if a larger momentum is available from the control momentum gyroscopes. The analysis is verified and complemented by the numerical computations. Among the three types of zero propellant maneuver paths, the momentum-optimal solution and the time-optimal solution generally possess the same structure, and they are singular. The energy-optimal solution saves significant energy, while generally maintaining a smooth control profile.

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A Survey of the Maximum Principles for Optimal Control Problems with State Constraints

Cited by 800 publications

References 93 publications

No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

New Necessary Conditions for Optimal Control Problems in Discontinuous Dynamic Systems

Multi-objective Optimization of Zero Propellant Spacecraft Attitude Maneuvers

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