Three-Dimensional Trajectory Optimization in Constrained Airspace

Dai, Ran; Cochran, John E.

doi:10.2514/1.39327

Cited by 28 publications

(13 citation statements)

References 20 publications

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“…The reference interception trajectory vector x m can be obtained via the following reference model

({, \begin{matrix} falsenonefalsearray \\ arrayaxis ẋ_{m} = A x_{m} + B a_{m}, \\ arrayaxis y_{m} = x_{m}, \end{matrix})

where a m is designed by some optimal control techniques and such that

(∥∥, a_{m}) \leq a_{n normalmax} MathClass-rel< a_{normalmax} MathClass-punc.

…”

Section: Application To Space Interceptionmentioning

confidence: 99%

“…By taking into consideration the terminal velocity and the time and fuel consumption, the optimal guidance law a m can be designed for the nominal system of such that the cost function

J_{r} MathClass-rel= MathClass-bin- ρ_{1} ((), ẋ {(t_{f})}^{2} MathClass-bin+ ẏ {(t_{f})}^{2} MathClass-bin+ ż {(t_{f})}^{2}) MathClass-bin+ {MathClass-op\int}_{0}^{t_{f}} ((), ρ_{2} MathClass-bin+ ρ_{3} a^{2}) normald t MathClass-punc,

subject to constraints

x (t_{f}) MathClass-rel= 0 MathClass-punc, y (t_{f}) MathClass-rel= 0 MathClass-punc, z (t_{f}) MathClass-rel= 0 MathClass-punc, 0 ≤ a ≤ a_{n normalmax} MathClass-punc,

is minimized, where ρ i , i = 1,2,3, are the weighting parameters to be designed. Because of the high accuracy of solutions and fast computations, the Gauss Pseudospectral Method is utilized here to tackle this optimal control problem. Here, we choose ρ 1 = ρ 3 = 1, ρ 2 = 0.01, and a n max = 4.5 m ∕ s 2 .…”

Section: Application To Space Interceptionmentioning

confidence: 99%

“…where a m is designed by some optimal control techniques [40][41][42][43] and such that ka m k 6 a n max < a max .…”

Section: Modeling and Problem Formulationmentioning

confidence: 99%

“…is minimized, where i , i D 1, 2, 3, are the weighting parameters to be designed. Because of the high accuracy of solutions and fast computations, the Gauss Pseudospectral Method [40][41][42][43] is utilized here to tackle this optimal control problem. Here, we choose 1 D 3 D 1, 2 D 0.01, and a n max D 4.5 m=s 2 .…”

Section: Numerical Simulationmentioning

confidence: 99%

See 3 more Smart Citations

Robust adaptive control for a class of cascaded nonlinear systems with applications to space interception

Zhang

Duan

Zhou

2013

Intl J Robust & Nonlinear

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SUMMARYThis paper proposes a robust H ∞ ‐based adaptive backstepping control scheme for the output stabilization of a special class of cascaded nonlinear systems. This kind of systems possess the feature that the first sub‐equation is a linear perturbed system, whereas the rest ones perform a general semi‐strict feedback form. Different from the conventional backstepping design approach, the special cascaded structure ensures to introduce the H ∞ technique to the backstepping procedure such that both the robust performance and the robust stability can be simultaneously guaranteed. Within the Lyapunov framework, the proposed control scheme is proved to guarantee (i) the uniformly ultimate boundedness of the system signals with a bound that can be made arbitrarily small by suitably choosing control parameters; (ii) asymptotic output stabilization as long as the uncertain nonlinearities and external disturbances vanish; and (iii) scriptL2‐performance of the closed‐loop system. A space interception scenario is utilized to demonstrate the effectiveness of the proposed control scheme. Copyright © 2013 John Wiley & Sons, Ltd.

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“…The reference interception trajectory vector x m can be obtained via the following reference model

({, \begin{matrix} falsenonefalsearray \\ arrayaxis ẋ_{m} = A x_{m} + B a_{m}, \\ arrayaxis y_{m} = x_{m}, \end{matrix})

where a m is designed by some optimal control techniques and such that

(∥∥, a_{m}) \leq a_{n normalmax} MathClass-rel< a_{normalmax} MathClass-punc.

…”

Section: Application To Space Interceptionmentioning

confidence: 99%

“…By taking into consideration the terminal velocity and the time and fuel consumption, the optimal guidance law a m can be designed for the nominal system of such that the cost function

J_{r} MathClass-rel= MathClass-bin- ρ_{1} ((), ẋ {(t_{f})}^{2} MathClass-bin+ ẏ {(t_{f})}^{2} MathClass-bin+ ż {(t_{f})}^{2}) MathClass-bin+ {MathClass-op\int}_{0}^{t_{f}} ((), ρ_{2} MathClass-bin+ ρ_{3} a^{2}) normald t MathClass-punc,

subject to constraints

x (t_{f}) MathClass-rel= 0 MathClass-punc, y (t_{f}) MathClass-rel= 0 MathClass-punc, z (t_{f}) MathClass-rel= 0 MathClass-punc, 0 ≤ a ≤ a_{n normalmax} MathClass-punc,

Section: Application To Space Interceptionmentioning

confidence: 99%

“…where a m is designed by some optimal control techniques [40][41][42][43] and such that ka m k 6 a n max < a max .…”

Section: Modeling and Problem Formulationmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

See 2 more Smart Citations

Robust adaptive control for a class of cascaded nonlinear systems with applications to space interception

Zhang

Duan

Zhou

2013

Intl J Robust & Nonlinear

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show abstract

“…It has been studied extensively throughout the recent years, and our knowledge has been extended through many important works. In some of them Dai and Cochran demonstrated a trajectory optimization problem in three dimensional space and in constrained airspace [1] , Bicchi and Pallottino studied optimal cooperative conflict resolution for Air traffic management systems as a trajectory optimization problem [2], in Discrete Vehicle routing problem any useful trajectory optimization problems have been explored [3]. Tan, Lee, Zhu and Ou investigated heuristic methods for vehicle routing problem with time windows [4], Hargraves and Paris, in their infamous article, discussed the first known application of collocation method using nonlinear programming [5], which will be the essence of this study as well, with a slightly different implementation on trajectory optimization.…”

mentioning

confidence: 99%

Short-term turning in presence of wind as a trajectory optimization problem

Turkoglu

2014

2014 IEEE Aerospace Conference

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In this paper, we concentrate on formulating a short-term-turn of an aircraft as an optimal control problem.Our main aim will be to analyze the problem by investigating the optimal turn at minimum time in existence of given path constraints. In this problem formulation, heading angle becomes a state variable and therefore cannot be used as a control action. On the other hand, with the assumption that 'bank angle changes could occur instantaneously', it is possible to convert bank angle into a control variable, together with thrust. Thus, in our problem formulation, optimal control problem becomes a 'minimum time' problem.Correspondingly, solution strategies are provided in the paper.for this purpose method of collocation will be used to analyze the problem numerically. Solution strategies are limited to 2Dproblems in x-y axis. Moreover, a 2D-wind model has been defined to demonstrate the effects of the wind in (constrained) trajectory optimization. Obtained results show that better minimum time solution(s) in existence of wind conditions could be obtained and solution(s) could provide unique insights into the trajectory optimization problem in existence of wind.

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