Direct and indirect methods for trajectory optimization

Stryk, Oskar von; Bulirsch, Roland

doi:10.1007/bf02071065

Cited by 591 publications

(300 citation statements)

References 14 publications

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“…This leads in general to a system of coupled differential equations, which sometimes, for simple problems, can be solved explicitly [22]. However, because the constraints in the present problem are highly non-linear and the number of variables is quite high, the above primal-dual approach is difficult to solve analytically [28]. Instead, one could attempt to solve the resulting multipoint boundary-value problem numerically, for example via indirect methods such as multiple shooting [10,28].…”

Section: Epidemic Optimal Control Formulationmentioning

confidence: 99%

Controlling the number of HIV infectives in a mobile population

Sani

Kroese

2008

Mathematical Biosciences

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Abstract. The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. We formulate various mathematical control problems for HIV spread in mobile heterosexual populations, and show how optimal regional control strategies can be obtained that minimize the national spread of HIV. We apply the cross-entropy method to solve these highly multi-modal and non-linear optimization problems. We demonstrate the effectiveness of the method via a range of experiments and illustrate how the form of the optimal control function depends on the mathematical model used for the HIV spread.

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Section: Epidemic Optimal Control Formulationmentioning

confidence: 99%

Controlling the number of HIV infectives in a mobile population

Sani

Kroese

2008

Mathematical Biosciences

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“…This above discretisation approach has been implemented in the DIRCOL [22,23] package which employed the sequential quadratic programming method SNOPT by Gill et al [24].…”

Section: Methodsmentioning

confidence: 99%

Trajectory Shaping of Surface-to-Surface Missile With Terminal Impact Angle Constraint

Subchan¹

2010

MST

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This paper presents trajectory shaping of a surface-to-surface missile attacking a fixed with terminal impact angle constraint. The missile must hit the target from above, subject to the missile dynamics and path constraints. The problem is reinterpreted using optimal control theory resulting in the formulation of minimum integrated altitude. The formulation entails nonlinear, two-dimensional missile flight dynamics, boundary conditions and path constraints. The generic shape of optimal trajectory is: level flight, climbing, diving; this combination of the three flight phases is called the bunt manoeuvre. The numerical solution of optimal control problem is solved by a direct collocation method. The computational results is used to reveal the structure of optimal solution which is composed of several arcs, each of which can be identified by the corresponding manoeuvre executed and constraints active.

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“…Most early investigators adopt the latter [3] . It is necessary for the indirect methods to derive the optimality condition called Hamiltonian boundary value.…”

Section: Introductionmentioning

confidence: 99%

Reentry trajectory optimization for hypersonic vehicles using fuzzy satisfactory goal programming method

Yue

2014

Int. J. Autom. Comput.

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Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.

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Direct and indirect methods for trajectory optimization

Cited by 591 publications

References 14 publications

Controlling the number of HIV infectives in a mobile population

Controlling the number of HIV infectives in a mobile population

Trajectory Shaping of Surface-to-Surface Missile With Terminal Impact Angle Constraint

Reentry trajectory optimization for hypersonic vehicles using fuzzy satisfactory goal programming method

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