  Search for the optimizer in computationally demanding model predictive
control (MPC) setups can be facilitated by Cloud as a service provider in
cyber-physical systems. This advantage introduces the risk that Cloud can
obtain unauthorized access to the privacy-sensitive parameters of the system
and cost function. To solve this issue, i.e., preventing Cloud from accessing
the parameters while benefiting from Cloud computation, random affine
transformations provide an exact yet light weight in computation solution. This
research deals with analyzing privacy preserving properties of these
transformations when they are adopted for MPC problems. We consider two common
strategies for outsourcing the optimization required in MPC problems, namely
separate and dense forms, and establish that random affine transformations
utilized in these forms are vulnerable to side-knowledge from Cloud.
Specifically, we prove that the privacy guarantees of these methods and their
extensions for separate form are undermined when a mild side-knowledge about
the problem in terms of structure of MPC cost function is available. In
addition, while we prove that outsourcing the MPC problem in the dense form
inherently leads to some degree of privacy for the system and cost function
parameters, we also establish that affine transformations applied to this form
are nevertheless prone to be undermined by a Cloud with mild side-knowledge.
Numerical simulations confirm our results.
