Near-Optimal Guidance with Impact Angle and Velocity Constraints Using Sequential Convex Programming

This paper proposes a near-optimal air-to-ground missile guidance law with impact angle and impact velocity constraints based on sequential convex programming. A realistic aerodynamic model is introduced into the problem formulation, such that traditional optimization theory cannot obtain an analytical solution to the optimization problem under state constraints. The original problem is considered as an optimization problem, and the angle of attack is replaced with the angle of attack rate as a new control variable to reconstruct the problem and simplify the solving process. Next, the independent variable is changed in the differential equations to linearize and discretize the problem such that the reconstructed problem can be solved using sequential convex programming. The results obtained by numerical simulations confirmed that the proposed algorithm is valid and faster than the general-purpose nonlinear optimal control problem solver. Finally, it was verified that different impact angles and impact velocities were achieved.

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A New Optimal Guidance Law with Impact Time and Angle Constraints Based on Sequential Convex Programming

Mathematical Problems in Engineering ◽

10.1155/2021/6618351 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Pei Pei ◽

Jiang Wang

Keyword(s):

Convex Programming ◽

Optimization Problem ◽

Impact Angle ◽

Lateral Acceleration ◽

Optimal Time ◽

Proportional Navigation ◽

Impact Time ◽

Guidance Law ◽

Sequential Convex Programming ◽

Optimal Guidance

This paper proposed an optimal time-varying proportional navigation guidance law based on sequential convex programming. The guidance law can achieve the desired impact angle and impact time with look angle and lateral acceleration constraints. By treating the multiconstraints’ guidance problem as an optimization problem and changing the independent variable to linearize the problem and constraints, the original nonlinear and nonconvex problem is transformed into a series of convex optimization problem so that it can be quickly solved by sequential convex programming. Numerical simulations compared to nonlinear programming and traditional analytical guidance law demonstrate the effectiveness and efficiency of the proposed algorithm. Finally, the proposed guidance law is verified to satisfy different impact time periods and impact angle constraints.

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Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion

Mathematical Problems in Engineering ◽

10.1155/2016/9461021 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13 ◽

Cited By ~ 7

Author(s):

Ye Wang ◽

Yanju Chen ◽

YanKui Liu

Keyword(s):

Convex Programming ◽

Portfolio Selection ◽

Optimization Problem ◽

Fuzzy Variable ◽

Optimization Method ◽

General Purpose ◽

Convex Programming Problem ◽

Fuzzy Variables ◽

Return Rates ◽

Fuzzy Expected Value

This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.

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Multiple Simultaneous Receive Beam Synthesis of Overlapped Subarray Structure via Alternative Sequential Convex Programming

IEEE Antennas and Wireless Propagation Letters ◽

10.1109/lawp.2021.3075058 ◽

2021 ◽

pp. 1-1

Author(s):

Hui Zeng ◽

Zhen-Hai Xu ◽

Gongqing Yang ◽

Shun-Ping Xiao

Keyword(s):

Convex Programming ◽

Sequential Convex Programming

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Real-Time Sequential Convex Programming for Optimal Control Applications

Modeling, Simulation and Optimization of Complex Processes ◽

10.1007/978-3-642-25707-0_8 ◽

2012 ◽

pp. 91-102 ◽

Cited By ~ 5

Author(s):

Tran Dinh Quoc ◽

Carlo Savorgnan ◽

Moritz Diehl

Keyword(s):

Optimal Control ◽

Real Time ◽

Convex Programming ◽

Control Applications ◽

Sequential Convex Programming

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Disease control as an optimization problem

PLoS ONE ◽

10.1371/journal.pone.0257958 ◽

2021 ◽

Vol 16 (9) ◽

pp. e0257958

Author(s):

Miguel Navascués ◽

Costantino Budroni ◽

Yelena Guryanova

Keyword(s):

Disease Control ◽

Stochastic Models ◽

Optimization Problem ◽

Initial Conditions ◽

Optimization Theory ◽

Model Parameters ◽

Grid Search ◽

Brute Force ◽

Time Required ◽

Policy Optimization

In the context of epidemiology, policies for disease control are often devised through a mixture of intuition and brute-force, whereby the set of logically conceivable policies is narrowed down to a small family described by a few parameters, following which linearization or grid search is used to identify the optimal policy within the set. This scheme runs the risk of leaving out more complex (and perhaps counter-intuitive) policies for disease control that could tackle the disease more efficiently. In this article, we use techniques from convex optimization theory and machine learning to conduct optimizations over disease policies described by hundreds of parameters. In contrast to past approaches for policy optimization based on control theory, our framework can deal with arbitrary uncertainties on the initial conditions and model parameters controlling the spread of the disease, and stochastic models. In addition, our methods allow for optimization over policies which remain constant over weekly periods, specified by either continuous or discrete (e.g.: lockdown on/off) government measures. We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler et al. (March, 2020).

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