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本文给出一种在时间域里实现带稳定性约束的线性定常系统的优化方法,它不同于最优控制理论所采用的解析方法,而是建立在用计算机解非线性规划问题的基础上的。优化的目标函数采用二次型积分泛函,利用模态矩阵导出了它的一个规范化的算法,然后用增广的拉格朗日乘子法来求解。这一方法适合于那些不能满足最优控制论要求的许多实际系统。对于可稳定的系统,无论原始设计参数是否满足稳定性条件,经优化后总能获得稳定的最优解。
In this paper, we present an optimization method to achieve a linear stationary system with stability constraints in the time domain, which is different from the analytical method used in the optimal control theory. Instead, it is based on solving the nonlinear programming problem by computer . The objective function of optimization uses quadratic integral functional, derives a normalized algorithm from the modal matrix, and then uses augmented Lagrange multiplier method to solve it. This method is suitable for many practical systems that do not satisfy the requirements of optimal cybernetics. For a stable system, no matter whether the original design parameters satisfy the stability conditions, the optimal optimal solution can always be obtained after optimization.