Penalty boundary sequential convex programming algorithm for non-convex optimal control problems

2018 ◽  
Vol 72 ◽  
pp. 229-244
Author(s):  
Zhe Zhang ◽  
Gumin Jin ◽  
Jianxun Li
Keyword(s):  
Optimal Control ◽  
Convex Programming ◽  
Optimal Control Problems ◽  
Programming Algorithm ◽  
Control Problems ◽  
Sequential Convex Programming

A Constraining Hyperplane Technique for State Variable Constrained Optimal Control Problems

1973 ◽  
Vol 95 (4) ◽  
pp. 380-389 ◽  
Author(s):  
K. Martensson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Control Problems ◽  
State Control ◽  
Constrained Optimal Control ◽  
State Variable

A new approach to the numerical solution of optimal control problems with state-variable inequality constraints is presented. It is shown that the concept of constraining hyperplanes may be used to approximate the original problem with a problem where the constraints are of a mixed state-control variable type. The efficiency and the accuracy of the combination of constraining hyperplanes and a second-order differential dynamic programming algorithm are investigated on problems of different complexity, and comparisons are made with the slack-variable and the penalty-function techniques.

Rapid ascent trajectory optimization for guided rockets via sequential convex programming

2019 ◽  
Vol 233 (13) ◽  
pp. 4800-4809 ◽  
Author(s):  
Kai Zhang ◽  
Shuxing Yang ◽  
Fenfen Xiong
Keyword(s):  
Optimal Control ◽  
Convex Programming ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Aerodynamic Drag ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Dynamical Equations ◽  
Control Variables ◽  
Sequential Convex Programming

A sequential convex programming algorithm is proposed to solve the complex ascent trajectory optimization problems for guided rockets in this paper. Due to the nonlinear dynamics and constraints, especially, the nonlinear thrust terms and aerodynamic drag, ascent trajectory optimization problems for guided rockets are always difficult to be solved rapidly. In this paper, first, the complex thrust terms in the dynamic equation are approximately transformed into linear (convex) functions of the angle of attack. Secondly, the nonlinear drag coefficient is transformed into a linear (convex) function of design variables by introducing two new control variables. The relaxation technique is used to relax the constraints between the control variables to avoid non- convexity, and the accuracy of the relaxation is proved using the optimal control theory. Then, nonconvex objective functions and dynamical equations are convexified by first-order Taylor expansions. At last, a sequential convex programming iterative algorithm is proposed to solve the ascent trajectory planning problem accurately and rapidly. The ascent trajectory optimization problem for the terminal velocity maximum is simulated comparing with the general pseudospectral optimal control software method, which demonstrates the effectiveness and rapidity of the proposed method.

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