Remote control over communication networks with bandwidth-constrained channels has attracted considerable recent attention because it holds the promise of enabling a large number of real-time applications, such as autonomous driving, smart grids, and the industrial internet of things (IIoT). However, due to the limited bandwidth, the sub-packets or even bits have to be transmitted successively, thereby experiencing non-negligible latency and inducing serious performance loss in remote control. To overcome this, we introduce an incremental coding method, in which the actuator acts in real time based on a partially received packet instead of waiting until the entire packet is decoded. On this basis, we applied incremental coding to a linear control system to obtain a remote-control scheme. Both its stability conditions and average linear-quadratic-Gaussian-(LQG) cost are presented. Then, we further investigated a multi-user remote-control method, with a particular focus on its applications in the demand response of smart grids over bandwidth-constrained communication networks. The utility loss due to the bandwidth constraint and communication latency are minimized by jointly optimizing the source coding and real-time demand response. The numerical results show that the incremental-coding-aided remote control performed well in both single-user and multi-user scenarios and outperformed the conventional zero-hold control scheme significantly under the LQG metric.