Iterative encoder-controller design based on approximate dynamic programming

In this paper, we study the iterative optimization of the encoder-controller pair for closed-loop control of a multi-dimensional plant over a noisy discrete memoryless channel. With the objective to minimize the expected linear quadratic cost over a finite horizon, we propose a joint design of the sensor measurement quantization, channel error protection, and optimal controller actuation. It was shown in our previous work that despite this optimization problem is known to be hard in general, an iterative design procedure can be derived to obtain a local optimal solution. However, in the vector case, optimizing the encoder for a fixed controller is in general not practically feasible due to the curse of dimensionality. In this paper, we propose a novel approach that uses the approximate dynamic programming (ADP) to implement a computationally feasible encoder updating policy with promising performance. Especially, we introduce encoder updating rules adopting the rollout approach. Numerical experiments are carried out to demonstrate the performance obtained by employing the proposed iterative design procedure and to compare it with other relevant schemes.