A unified framework for the numerical solution of optimal control problems using pseudospectral methods

Garg, Divya; Patterson, Michael; Hager, William W.; Rao, Anil V.; Benson, David A.; Huntington, Geoffrey T.

doi:10.1016/j.automatica.2010.06.048

Cited by 613 publications

(468 citation statements)

References 14 publications

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“…It is one of the shooting methods of indirect method which transforms the problem from the original optimal control problem to finding initial values of costates. By using this method to a simple missile model, solutions obtained by applying pseudospectral method [6] can be verified. Also numerical optimization is conducted on missile model with aerodynamic forces and thrust.…”

Section: Introductionmentioning

confidence: 99%

Terminal Velocity Maximization of Air-to-Air Missiles in Agile Turn Phase

Tahk

Park³

et al. 2016

MATEC Web Conf.

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Abstract.Terminal velocity maximization of air-to-air agile missiles during agile turn phase is studied. It is important to make sure that agile missiles have enough velocity after agile turn stage in order to impact the target. The agile turn is operated during the boost phase. Thus, the agile turn problem is formulated as terminal velocity maximization with given final time. Optimal solutions are obtained by two different methods, pseudospectral method and parameterized costate optimization method. The parameterized costate optimization method is a part of shooting method of indirect method which is proposed to verify the solutions obtained by pseudospectral method. At first, the basic missile model with constant axial acceleration is treated in the two dimensional yaw plane. After looking into the basic missile model, missile model with aerodynamic forces and thrust is analyzed.

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Section: Introductionmentioning

confidence: 99%

Terminal Velocity Maximization of Air-to-Air Missiles in Agile Turn Phase

Tahk

Park³

et al. 2016

MATEC Web Conf.

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“…It is well-known that pseudospectral methods, especially LR pseudospectral method, provide accurate approximations that converge exponentially when the solution of the problem is smooth (Elnagar et al, 1995;Garg et al, 2010). However, SOCPs are known to have nonsmooth solutions and so the application of the pseudospectral methods can be problematic and high-order accuracy of the method may be deteriorated.…”

Section: Introductionmentioning

confidence: 99%

“…Then, by collocating the state equations and path constraints and using the differentiation matrix, the problem is transcribed to a non-linear programming problem(NLP), which can be solved by the well-developed parameter optimization algorithms. The three most common types of the pseudospectral method are LGL pseudospectral (Elnagar, Kazemi, & Razzaghi, 1995;Fahroo & Ross, 2001), LG pseudospectral (Benson, Huntington, Thorvaldsen, & Rao, 2006) and LR pseudospectral (Garg, 2011;Garg et al, 2010) methods.…”

Section: Introductionmentioning

confidence: 99%

“…For recent advances in the pseudospectral methods, see, for example, Gong, Ross, and Fahroo (2016) ;Tang, Liu, and Hu (2016). Pseudospectral methods approximate the state and control variables using interpolating polynomials with specific collocation points such as Legendre-Gauss-Lobatto(LGL), Legendre-Gauss(LG) (Mehrpouya, Shamsi, & Azhmyakov, 2014) and Legendre-Radau(LR) points (Garg et al, 2010). Then, by collocating the state equations and path constraints and using the differentiation matrix, the problem is transcribed to a non-linear programming problem(NLP), which can be solved by the well-developed parameter optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

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A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

Foroozandeh

Shamsi

Pinho

2017

International Journal of Control

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This paper presents a new approach for the efficient and accurate solution of Singular Optimal Control Problems (SOCP). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of the solution. As the first step of this method, the SOCP is converted into a binary optimal control problem. Then, by utilizing the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the original optimal control and to compute the approximating solution of it (getting both the optimal state and control). The main advantages of the present method are that: (i) without a priori information, the structure of optimal control is detected; (ii) it produces good results even using a small number of collocation points; and (iii) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples.

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“…Thus the sensitivity analysis may be used to gain insight into the Pareto optimal front. To verify and complement the resulting conclusions, numerical computations are also performed using GPOPS (version 5.2) [6], which employs the Radau Pseudo Spectral (PS) method [7].…”

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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 unified framework for the numerical solution of optimal control problems using pseudospectral methods

Cited by 613 publications

References 14 publications

Terminal Velocity Maximization of Air-to-Air Missiles in Agile Turn Phase

Terminal Velocity Maximization of Air-to-Air Missiles in Agile Turn Phase

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

Multi-objective Optimization of Zero Propellant Spacecraft Attitude Maneuvers

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