Algorithm 1 Variational Autoencoder-based Controller Synthesis under STL Constraints

1:$\Phi ,D^j\leftarrow$ Initialize($\Xi$)   2:${\xi }_{cur}\leftarrow {\xi }_{init},{\xi }_{past}\leftarrow \varnothing$   3:for $t=t_0:dt:t_1$ do   4:     $f_{lin}\leftarrow$ Linearize($f,{\xi }_{cur}$)   5:     for $j=1:1:N$ do   6:          $r_j\leftarrow$ CVAE($\varphi \left({\xi }_{cur}\right)$)   7:          $C_{{\phi }_j,r_j}\leftarrow$ EncodeSTLConstraints(${\phi }_j,r_j$)   8:     end for   9:     $C_{STL}\leftarrow C_{{\phi }_1,r_1}\wedge \dots \wedge C_{{\phi }_N,r_N}$ 10:     $C\leftarrow C_{STL}\wedge f_{lin}\wedge [\xi (t_0,\cdots ,t-dt)={\xi }_{past}]$ 11:     ${\mathbf{u}}^{H,t}\leftarrow$ Optimize($J\left({\xi }^H\right),C$) 12:     ${\mathrm{x}}_{next}=f({\mathrm{x}}_{cur},{\mathbf{u}}^{H,t}\left(t\right))$ 13:     ${\xi }_{past}\leftarrow \left[{\xi }_{past}{\xi }_{cur}\right]$ 14:     ${\xi }_{cur}\leftarrow ({\mathrm{x}}_{next},{\mathbf{u}}^{H,t}\left(t\right))$ 15:end for