Many complex systems are still optimized by linear models rather than deep neural networks (DNNs) due to DNNs are typically nonlinear and non-convex. Input convex neural networks (ICNNs) have proven to successfully achieve the globally optimal solution via maintaining convexity within optimization problem and solving it by convex optimization algorithms. This paper leverages ICNNs principle to introduce a novel ICNN combining with Transformer for optimal control problem, and its specific objective is to mitigate the gradient explosion and gradient vanishing problems in current ICNNs and improving its ability for complex tasks. In addition, a Lyapunov-based constraint is incorporated into optimization problem to address the theoretical closed-loop stability, which has been usually ignored by existing research. We implement both image de-noising experiment and building energy optimization experiment to indicate that our proposed approach has powerful modeling and control capabilities. Compared with the state-of-the-art (SOTA) methods, our proposed approach can averagely attain 1.73db improvements of peak signal-to-noise ratio (PSNR) in image de-noising experiment and 20.38% energy consumption saving in building energy optimization experiment.