A Method for Estimating the Peak Upper Limit of the Impulse Response of a Nonlinear System

Abstract

The invention discloses a method for estimating the upper limit of the peak value of the impulse response of a nonlinear system, comprising: establishing a Lyapunov polynomial level set describing the system state trajectory; Search and convex optimization method obtain effective estimated value; Adopt balance point transfer method to be applied to the situation when nonlinear system equilibrium state value is non-zero, the present invention assumes that the estimated value of the peak upper limit of nonlinear system impulse response is c∈(0, ∞), establish the condition that the constant c is the upper limit of the peak value of the impulse response of the nonlinear system, and finally implement the condition as a convex optimization problem of several linear matrix inequalities obtained by linearly transforming the system Lyapunov polynomials, and the system impulse The degree of conservatism in the estimate of the upper bound of the peak response can be reduced by increasing the degree of the system Lyapunov polynomial.

Description

technical field [0001] The invention belongs to the field of process control system and computational control theory, in particular to a method for estimating the upper limit of peak value of nonlinear system impulse response. Background technique [0002] The input-output relationship of the system can be characterized by various metrics, especially the H-∞ norm (for example, the maximum value of the amplitude gain of the system's frequency response) and the H-2 norm (for example, the square root of the sum of the impulse response energies) . These indicators play a vital role in system analysis and synthesis, so for a long time researchers have proposed a large number of methods to calculate and control the values ​​of these indicators. [0003] The impulse response of the system reflects some inherent characteristics of the system itself; while the peak value of the impulse response of the system, as an important indicator, there are relatively few research literatures o...

AI Technical Summary

Problems solved by technology

Some classic index estimation methods, such as the set invariance method based on the quadratic Lyapunov function function, are used to determine the maximum value of the amplitude gain of the system frequency response and the square root value of the sum of the impulse response energy. The results are conservative However, the estimation results obtained by determining the peak value of the impulse response are usually relatively conservative, which is in sharp contrast to the non-conservative estimation results applied to the H-∞ norm and H-2 norm

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