**Appendix A**

Table A1 shows the searching area of parameters, they are established through trial and error. The target values of characteristics of AUV motion control system, which are defined in Equation (12), are depicted in Table A2. The MATLAB function code for particle distance is given as follows:

> function DM = Distance\_Matrix (X,xmin,xmax) n = size (X,1); DM = zeros (n,n); Normal = xmax-xmin; for t = 1:n Dif = (X (t,:)-X)./Normal; Dis = sum (Dif.ˆ2,2); DM (t,:) = Dis; end

where X represents the parameters of particle swarm, xmin and xmax denote the searching bound of parameters. DM is a square matrix and DM (i,j) is the distance between the i-th particle and j-th particle. By the way, if the distance is less than 1, we consider them as local particles.

**Table A1.** Searching range of parameters for three control systems.


**Table A2.** Target performance of control system.

