Modified quasilinearization algorithm for optimal control problems with nondifferential constraints

Miele, A.; Mangiavacchi, A.; Aggarwal, A. K.

doi:10.1007/bf00932847

Cited by 31 publications

(6 citation statements)

References 6 publications

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“…The problem is reduced to a two-point boundary-value problem (TPBVP). The authors have developed some efficient solvers for this type of problem by employing fine algorithms such as the steepest ascent method [24], the sequential conjugate gradient-restoration algorithm SCGRA [25,26], and the modified quasi-linearization algorithm MQA [27]. In this paper, the problem is solved by the STP-CODE.…”

Section: Derivation Of An Aircraft Vs Two-missiles Problemmentioning

confidence: 99%

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Imado

Kuroda

2011

Journal of Guidance, Control, and Dynamics

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The engagement tactics for two missiles to attack an aircraft are studied. A tail chase scenario between two aircraft is assumed where the attacker tries to kill the evader with two missiles, while the evader employs optimal maneuvers for avoiding two missiles. The algorithm to solve this optimal control problem is first developed. For the aircraft, in order to simultaneously maximize the miss distances against two missiles, a special type of performance index is introduced and the problems are solved by the solver based on the steepest ascent method. The result shows that the aircraft optimal maneuvers are divided into three patterns. Next, the optimal timing for the attacker to launch the two missiles, in order to minimize both miss distances against the aircraft is studied. The effect of their taking trajectory shaping is also studied. Nomenclature= missile navigation gain n = power of penalty function p = penalty function for the first missile r = slant range between missile and aircraft r 12 = initial distance between two missiles r 1a = reference value of the slant range between the first missile and aircraft r 1f , r 2f = closest ranges (miss distances) between the aircraft and the first and second missiles, respectively r m = the mean miss distance between two missiles, r 1f :r 2f 1 2 S = reference area T = thrust t = time t e = sustainer burning time t f = interception time t w1 , t w2 = start time and end time of window function u = control vector v = velocity v c = closing velocity w = window function x, y = longitudinal and lateral coordinates x = state vector , 0 = angle-of-attack and zero-lift angle, respectively = adjoint vector = air density , = line-of-sight and azimuth angles, respectively = missile time constant = performance index for minimizing both miss distances = stopping condition = terminal constraints = time derivative Subscripts a = aircraft c = command signal i = ith missile m = missile max, min = maximum and minimum values, respectively

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Section: Derivation Of An Aircraft Vs Two-missiles Problemmentioning

confidence: 99%

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Imado

Kuroda

2011

Journal of Guidance, Control, and Dynamics

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“…On the other hand, for constrained NLP problems the performance index is defined as R = P + Q, which comprises both the feasibility index P = h T h, and optimality index Q = F T x F x , with F = f +λ T h, where f is the objective function, h is the constraint function, and λ is the vector of Lagrange multipliers associate to the constraint function. Convergence to the desired solution is achieved when the performance index Q ≤ ε 1 or R ≤ ε 2 , with ε 1 and ε 2 small preselected positive constants, for the unconstrained and constrained case respectively (Miele and Iyer 1971;Miele, Mangiavacchi, and Aggarwal 1974). Unlike SQA, characterized by a unitary step size, MQA reduces progressively the step size 0 < α < 1 to enforce an improvement in optimality.…”

Section: Mqamentioning

confidence: 99%

Nonlinear Programming Solvers for Unconstrained and Constrained Optimization Problems: a Benchmark Analysis

Lavezzi¹,

Guye²,

Ciarcià³

2022

Preprint

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In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained and constrained nonlinear programming problems. The comparison involves accuracy, convergence rate, and convergence speed. Because of its popularity among research teams in academia and industry, MATLAB is used as common implementation platform for the solvers. Our study includes solvers which are either freely available, or require a license, or are fully described in literature. In addition, we differentiate solvers if they allow the selection of different optimal search methods. As result, we examine the performances of 23 algorithms to solve 60 benchmark problems. To enrich our analysis, we will describe how, and to what extent, convergence speed and accuracy can be improved by changing the inner settings of each solver.

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“…The modified quasilinearization algorithm 20 (QUASIM) is a modification of a similar method due to Miele et al 9 (MQA). It is an iterative technique for improving estimates of the state x(.t), the parameters vector /?, and the Lagrange multiplier \(t) so as to satisfy, simultaneously, the feasibility conditions, Eqs.…”

Section: B a Modified Quasilinearization Algorithmmentioning

confidence: 99%

Efficient combinations of numerical techniques applied to aircraft turning performance optimization

Blank

Shinar

1982

Journal of Guidance, Control, and Dynamics

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This paper presents efficient combinations of numerical optimization techniques summarizing their relative merits. Four basic methods handling contraints without penalty functions, are considered: 1) sequential gradient-restoration, 2) quasilinearization, 3) neighboring extremals, and 4) direct shooting. The first two are modifications of algorithms introduced by Miele, avoiding numerical differentiation and eliminating the anchoring effect of the original formulation. The third one is a generalization of an algorithm due to Bryson and Ho. The individual and combined methods are tested by solving the optimization of vertical and threedimensional turning maneuvers as examples. Results show that an appropriate combination of algorithms reduces the computational effort by more than 50%.

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Modified quasilinearization algorithm for optimal control problems with nondifferential constraints

Cited by 31 publications

References 6 publications

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Nonlinear Programming Solvers for Unconstrained and Constrained Optimization Problems: a Benchmark Analysis

Efficient combinations of numerical techniques applied to aircraft turning performance optimization

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