Algorithm 1 RCA neural networks based on the IrQL method with event triggering.

Set initial value:

1: Set initial values for ${\omega }_{r2i}\left(0\right),{\omega }_{a2i}\left(0\right),{\omega }_{c2i}\left(0\right)$ between $(0,1)$;

2: Set a low level of degree of precision for the calculation $\mathcal{E}$.

3: Initialize the score of $x_i\left(0\right),x_0\left(0\right)$ within $(0,1)$

The iterative process: Make $kisequalto0$. Error calculation at the localized level $e_i\left(k\right)$;

4: Keep on;

5: Based on actor NN, estimate ${\widehat{u}}_i\left(k\right)$ by $\left(37\right)$

6: Update the reinforce NN;

7: Via the inputting $[e_i\left(k\right),u_i\left(k\right),u_{-i}\left(k\right)]$ into the reinforce NN, and we can obtain the

estimated the function of IRR $R_i\left(Z_{ri}\left(k\right)\right)$ via $\left(27\right)$

8: Obtain $e_{ri}\left(k\right)$ by $\left(28\right)$;

9: Renew the matrices ${\omega }_{r2i}\left(k\right)$ by $\left(31\right)$;

10: Renew the critic NN:

11: Via the inputting $[{\widehat{R}}_i\left(Z_{ri}\left(k\right)\right),e_i\left(k\right),u_i\left(k\right),and{u}_{-i}\left(k\right)]$ into critic NN,

and we can obtain its estimated Q-function via $\left(32\right)$;

12: Obtain $e_{ci}\left(k\right)$ by $\left(33\right)$;

13: Renew the matrices ${\omega }_{c2i}\left(k\right)$ by $\left(36\right)$;

14: Renew the actor NN:

15: Input $\left[e_i\left(k\right)\right]$ to the actor NN, and we can obtain the estimated Q-function

${\widehat{u}}_i\left(k\right)$ via $\left(37\right)$

16: Calculation $e_{ai}\left(k\right)$ via $\left(38\right)$

17: In the event that the triggering conditions are met, renew the matrices

${\omega }_{a2i}\left(k\right)$ of the actor NN using $\left(41\right)$

18: Otherwise, do not update the weight matrices ${\omega }_{a2i}\left(k\right)$

19: Until $∥{\omega }_{c2i}(k+1)-{\omega }_{c2i}\left(k\right)∥\le \mathcal{E}$; otherwise, set $k=k+1$, then go to

procedure $\left(5\right)$

20: Keep on ${\omega }_{r2i}\left(k\right),{\omega }_{c2i}\left(k\right),{\omega }_{a2i}\left(k\right)$ as the optimal weights.