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非线性系统即使在最简单的情况下也会对某些参数τ∈T(一般的参数集)有很大的依存性,当τ超过临界点τ_0时,系统将产生突变,原平衡态失去稳定性,即产生分歧。当出现分歧时,系统的状态常会产生突变跳跃。这种突变对实际系统的运行常常是有害的,常需防止这类现象产生。在系统优化过程中,由于控制 u 的作用,对某些系统也会产生类似现象。对于梯度系统=f(W)+Cu W(0)=W_0其中,W∈R~n,u∈R~,f 是 C~K(k≥z)的,f(0)=0,u(t)关于[0,∞)分段连续。怎样做到既保证系统无分歧又使系统优化?本文将从结构稳定性观点出发,应用中心流形定理和突变理论推导出一类非线性梯度系统无分歧优化的较实用的做法和算式。
The nonlinear system has a great dependency on some parameters τ∈T (general parameter set) even in the simplest case. When τ exceeds the critical point τ_0, the system will make a mutation and the original equilibrium state loses its stability Sexuality is disagreement. When disagreements arise, the state of the system often produces sudden jumps. Such abrupt changes are often detrimental to the operation of real systems and often require the prevention of such phenomena. In the system optimization process, due to the control of the role of u, some systems will have a similar phenomenon. For gradient system = f (W) + Cu W (0) = W_0 where W∈R ~ n, u∈R ~, f is C ~ K (k≥z), f t) About [0, ∞) Segment continuous. How to do it not only to ensure that the system is disagreeable but also to optimize the system? In this paper, from the structural stability point of view, we apply the central manifold theory and catastrophe theory to derive a more practical approach and formula for a class of nonlinear gradient system without disagreement optimization.