Yes, the sparsity-promoting priors can be generalized to capture structured sparsity patterns in the control inputs by employing group sparsity or block sparsity models. These models allow for the incorporation of prior knowledge about the relationships between different input components, enabling the algorithms to exploit the inherent structure in the data.
For instance, one could use a group ℓ1 norm, which encourages sparsity at the group level rather than individual components. This approach is particularly useful in scenarios where certain groups of inputs are expected to be active together, such as in networked control systems where inputs may correspond to specific nodes or agents.
Incorporating structured sparsity into the estimation framework can significantly enhance estimation performance by improving recovery accuracy and reducing the number of required measurements. The algorithms would be better equipped to distinguish between active and inactive groups of inputs, leading to more robust estimates of the states and inputs. Furthermore, structured sparsity can also lead to improved computational efficiency, as the algorithms can focus on estimating only the relevant groups rather than all individual components, thus reducing the dimensionality of the optimization problem.