Abstract

We consider multicriteria minimax optimization problems with criteria in the form of the maxima of functionals given by the induced norms of linear operators taking the system inputs and/or initial state to the outputs. It is shown that replacing the difficult minimization of the linear convolution of such criteria by the minimization of the maximum of the linear convolution of the corresponding functionals leads to suboptimal solutions with an estimate of the degree of suboptimality with respect to Pareto optimal solutions. This approach is applied to Pareto suboptimal control design for linear finite-horizon time-varying and infinite-horizon time-invariant continuous- and discrete-time systems with uncertain initial states and/or disturbances. Numerical simulation results are presented.

中文翻译：

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多准则极小极大问题：帕累托集的定位和次优控制设计

摘要

我们考虑多准则极小极大优化问题，其准则为函数极大值形式，由线性算子的诱导范数给出，将系统输入和/或初始状态带到输出。结果表明，通过最小化相应函数的线性卷积的最大值来代替此类标准的线性卷积的困难最小化会导致次优解，并估计相对于帕累托最优解的次优程度。该方法应用于具有不确定初始状态和/或扰动的线性有限范围时变和无限范围时不变连续和离散时间系统的帕累托次优控制设计。给出了数值模拟结果。