    \begin{equation} \label{eqn:opt-x-pwc}
        x_t =  \left\{ x_{\frac{kT}{n}} + \left( R^{(k)} - x_{\frac{kT}{n}} \right) \cdot {\rm TC}_{t-\frac{(k-1)T}{n}} + \left( x_{\frac{(k-1)T}{n}}-R^{(k)}\right) \cdot {\rm IS}_{t-\frac{(k-1)T}{n}}\right\} \mathbb{1}_{\left\{\frac{(k-1)T}{n} \le t < \frac{kT}{n} \right\}},
    \end{equation}
