Numerical Computation of Optimal Atmospheric Trajectories

Hargraves, C. R.; Johnson, F. T.; Paris, Stephen; Retties, Ian

doi:10.2514/3.56093

Cited by 37 publications

(6 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hargraves et al (1981) present the state trajectories with high-order patched polynomials, whose coefficients are the decision variables. Betts and Huffman (1993) discuss trapetzoidal, HermiteSimpson and Runge-Kutta discretization.…”

Section: Introductionmentioning

confidence: 99%

Aircraft trajectory optimization using nonlinear programming

Raivio¹,

Ehtamo²,

Hämäläinen³

1996

System Modelling and Optimization

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Aircraft trajectory optimization using nonlinear programming

Raivio¹,

Ehtamo²,

Hämäläinen³

1996

System Modelling and Optimization

View full text Add to dashboard Cite

show abstract

“…In order to convert the trajectory optimization problem into a mathematical programming problem, the control variables and possibly the state variables need to be parameterized over time. Several schemes have been reported for this purpose: polynomials, 15 cubic splines, 7 " 9 and Chebychev polynomials, 6 Rayleigh-Ritz type parameterizations 11 being typical. If the control variables alone are parameterized, one requires a numerical simulation of the missile system to generate state variable histories, constraint violations, and performance index.…”

Section: Trajectory and Propulsion System Optimizationmentioning

confidence: 99%

High-performance missile synthesis with trajectory and propulsion system optimization

Menon

Cheng

Lin

et al. 1987

Journal of Spacecraft and Rockets

View full text Add to dashboard Cite

Synthesis of a high-performance two-pulse-motor-propelled missile by simultaneous optimization of trajectory and propulsion systems in two operational scenarios is described. This work employed a quasiNewton parameter optimization scheme with penalty functions to meet terminal and path constraints. The trajectory control variables were parameterized using piecewise linear open-loop commands and piecewise constant linear feedback gains. The pulse motor parameters optimized were pulse split, average thrust levels, neutrality factors, pulse burn times, and the interpiilse delay. Optimization of the rocket motor thrust time curve in addition to the trajectory increased the range by up to 11% when compared with the trajectories optimized with originally specified rocket motor propulsion data.

show abstract

“…The three degree of freedom formulation of the minimum time to climb problem [11], [21] illustrates a number of features of the new technique. Table 7 presents a summary of the mesh refinement iterations for this problem.…”

Section: Minimum Time T O Climbmentioning

confidence: 99%

“…NLQR Guidance Problem [9] (a) Minimum Deviation-simple aerodynamics, straight line path (b) Minimum Deviation-complex aerodynamics, atmosphere, and path 6. Minimum Time to Climb [11], [21] (a) Three degree of freedom formulation…”

Section: Trajectory Test Setmentioning

confidence: 99%

Path constrained trajectory optimization using sparse sequential quadratic programming

Betts

Huffman

1991

Navigation and Control Conference

View full text Add to dashboard Cite

One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with a discretization of the trajectory dynamics. The resulting mathematical programming problem is characterized by matrices which are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied by the nonlinear program. This paper describes a nonlinear programming algorithm which exploits the matrix sparsity produced by the transcription formulation. Numerical experience is reported for trajectories with both state and control variable equality and inequality path constraints. nt roduct ion nary differential equations -the first set defined by the vehicle dynamics and the second set (of adjoint differential equations) defined by the optimality conditions. Boundary conditionz are imposed from the problem requirements as well as the optimality criteria. By discretizing the dynamic variables, this boundary value problem can be reduced to the solution of a set of nonlinear algebraic equations. This approach has been successfully utilized (cf. [I], [SI, [12], [13]: [24],) for applications without path constraints. Since the approach requires the adjoint equations it is subject to a number of difficulties. First, the adjoint equations are often very nonlinear and cumbersome to obtain for complex vehicle dynamics, especially when thrust and aerodynamic forces are given by tabular data. Second, the iterative procedure requires an initial guess for the adjoint variables, and this can be quite difficult because they lack a physical interpretation. Third, convergence of the iterations is often quite sensitive t o the accuracy of the adIt is well known that the solution of an op-joint guess. Finally, the adjoint variables may timal control or trajectory optimization probl em can be posed as ,.he solution of a two-be discontinuous when the solution enters or lem requires solving a set of nonlinear ordiDifficulties associated with adjoint equapoint boundary value problem. This p r o b leaves an inequality Path constraint*

show abstract

Numerical Computation of Optimal Atmospheric Trajectories

Cited by 37 publications

References 11 publications

Aircraft trajectory optimization using nonlinear programming

Aircraft trajectory optimization using nonlinear programming

High-performance missile synthesis with trajectory and propulsion system optimization

Path constrained trajectory optimization using sparse sequential quadratic programming

Contact Info

Product

Resources

About