如何去除“无限"while 循环来改进 MATLAB 代码?

问题描述

我正在实现一个对数量化器，我想做的是尽可能地优化代码.我想进行更改的确切点是最后一个 else 语句，其中要实现的等式是:

I am implementing a logarithmic quantizer and what I would like to do is to optimize the code as much as possible. The precise point where I would like to make a change is the last else statement where the equation to be implemented is:

q(u) = u_i 如果 u_i/(1+step) u_i = p^(1-i)u_o for i=1,2,...

参数p, step, u_o是一些需要选择的常量.

The parameters p, step, u_o are some constants to be chosen.

关于量化器的更多信息可以在这篇论文中找到:具有输入的不确定非线性系统的自适应反步控制量化.

More information regarding the quantizer can be found at this paper: Adaptive Backstepping Control of Uncertain Nonlinear Systems with Input Quantization.

为了在 MATLAB 中编写一个函数来实现它，我编写了以下代码:

In order to code a function to implement it in MATLAB, I wrote the following piece of code:

function q_u = logarithmic_hysteretic_quantizer(u,step,u_min)

    u_o = u_min*(1+step);
    p = (1-step)/(1+step);

    if u < 0
        q_u = -logarithmic_hysteretic_quantizer(-u,step,u_min);
    elseif ( (u >= 0) && (u <= u_o/(1+step)) )
        q_u = 0;
    else
        i = 1;
        while (1)
            u_i = p^(1-i) * u_o;
            if ( (u > u_i/(1+step)) && (u <= u_i/(1-step)) )
                q_u = u_i;
                break;
            end
            i = i + 1;
        end
    end
end

现在，我的问题是尽可能地改进代码.例如，对不同量化级别进行编码的 while(1) 循环可能会消失并被替换.任何想法将不胜感激.

Now, my issue is to improve the code as much as I can. For example, the while(1) loop, which codes the different quantization levels, is something that could probably go away and be replaced. Any thoughts would be really appreciated.

推荐答案

假设 u_min>0 和 0，你可以简化 (u> u_i/(1+step)) &&(u 到:

Assuming u_min>0 and 0<p<1, you can simplify (u > u_i/(1+step)) && (u <= u_i/(1-step)) to:

u/u_min > p^(1-i) && p^-i >= u/u_min

由于 log 是单调的，所以简化为

Which since log is monotonic, simplifies to

-log(u/u_min)/log(p) > i-1 && i >= -log(u/u_min)/log(p)

这使得while循环等价于简单

Which makes the while loop equivalent to simply

i = floor(-log(u/u_min)/log(p));
q_u = p^(1-i) * u_o;

此外，elseif 分支中的 (u >= 0) 总是为真，你可能可以去掉 u 测试，通过在正确的位置将 u 替换为 abs(u).

Furthermore, (u >= 0) in the elseif branch is always true, and you probably can get rid of the u<0 test, by replacing u by abs(u) at the right places.

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