Suboptimal solution solving method based on optimal control problem pseudo-spectral method solving framework

Abstract

The present invention provides a suboptimal solution rapid solving method based on an optimal control problem pseudo-spectral method solving framework. The method is based on the pseudo-spectral method solving framework of an optimal control problem, combined with the technology of dynamic inverse optimization method of a parameterized state variable and a strategy of broadening an NLP problem solution, the rapid solution of constrained control problem suboptimal feasible solution is realized. The method comprises the following steps of: firstly selecting a basic state variable, utilizing a state equation and equality constraint to backstep other state variables and control variables to obtain a solution satisfying the state equation and the equality constraint; secondly complementing the constraint to realize the satisfaction of a backstepping state variable terminal condition and inequality path constraint; thirdly no longer clinging to the optimality of the solution for the NLP solution, not requiring the success of the NLP problem solution, broadening an NLP calculation end criterion as satisfaction of all constraint; fourthly carrying out inspection of the feasibility of the solution, if the feasibility is satisfied, ending the solution, if the feasibility is not satisfied, adopting recalculation of measures of strengthening the inequality path constrain or encoding pseudo-spectral method collocation.

Description

technical field [0001] The invention relates to a suboptimal feasible solution solving method of a constraint control problem in the engineering field, in particular to a path planning method in a guidance problem. The method can be applied to the problem of spacecraft attitude maneuver path planning or the problem of aircraft flight trajectory planning and other problems to which the present invention is applicable. Background technique [0002] Various constrained control problems are often encountered in the engineering field. This control problem contains various constraints. For a constrained control problem, there may be many feasible solutions. A feasible solution is a solution that satisfies various constraints and can achieve the control goal. , the optimal (suboptimal) solution is the optimal (suboptimal) feasible solution corresponding to a specific index. For constrained control problems, the commonly used solution strategy is the optimization solution method....

AI Technical Summary

Problems solved by technology

However, the solution obtained by using the pseudospectral method generally only approximately satisfies the constraints of the state equation. Strictly speaking, it is not a feasible solution. The fewer nodes, the worse the approximation

For more complex optimal control problems, more nodes are needed to obtain the optimal solution with satisfactory accuracy. Due to the large number of nodes, the solution will be time-consuming or even impossible.

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