Robust Optimization of Fixed Points of Nonlinear Discrete Time Systems with Uncertain Parameters
Robust Optimization of Fixed Points of Nonlinear Discrete Time Systems with Uncertain Parameters
复制标题
参数不确定的非线性离散时间系统不动点的鲁棒优化
DOI：
10.1137/09075696x
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Mönnigmann
中科院分区：
文献类型：
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作者：
Darya Kastsian;M. Mönnigmann
这一贡献将参数不确定动力系统优化的法向量方法推广到一般的非线性离散系统。在离散时间动力系统的优化中，法向量本质上是用来对不动点的动力学性质进行状态约束的。在该方法的典型应用中，技术动态系统相对于经济利润函数进行优化，而法向量约束用于保证最优不动点的稳定性。我们推导出翻转、折叠和Neimark-Sacker分叉点的法向量系统，因为这些分叉点构成了一大类离散时间系统的稳定边界。此外，我们推导出正常的向量系统的相关类型的临界点，可用于确保用户指定的干扰抑制率参数不确定系统的优化。我们通过将其应用于优化来说明该方法。
This contribution extends the normal vector method for the optimization of parametrically uncertain dynamical systems to a general class of nonlinear discrete time systems. Essentially, normal vectors are used to state constraints on dynamical properties of fixed points in the optimization of discrete time dynamical systems. In a typical application of the method, a technical dynamical system is optimized with respect to an economic profit function, while the normal vector constraints are used to guarantee the stability of the optimal fixed point. We derive normal vector systems for flip, fold, and Neimark–Sacker bifurcation points, because these bifurcation points constitute the stability boundary of a large class of discrete time systems. In addition, we derive normal vector systems for a related type of critical point that can be used to ensure a user-specified disturbance rejection rate in the optimization of parametrically uncertain systems. We illustrate the method by applying it to the optimization...