Trajectory Planning under Current-State Opacity Constraints

Abstract

Privacy and security guarantee against curious observers or malicious actors has recently emerged as a critical aspect for maintaining, protecting, and securing complex automated systems that are implemented over shared (thus, non-secure) cyber-infrastructures, such as the Internet. In this paper, we discuss how current-state opacity formulations can be used to capture privacy properties of interest in automated systems that are modeled as controlled finite automata that need to be steered from one state (initial location) to another state (target location), while maintaining certain privacy guarantees. More specifically, given a deterministic finite automaton that is externally observed via some output mapping, along with a subset of states S that are considered critical/secret, we aim to drive it from a given initial state (starting location) to a given target state (final location) while ensuring that, in the process, the state (location) of the finite automaton at any given time is not exposed (i.e., the external observer cannot be certain that the state of the system belongs to the set of critical/secret states S). We develop two algorithms that can be used to solve this constrained trajectory planning problem and obtain an appropriate sequence of inputs (if one exists) or conclude that no such sequence exists (otherwise). The first algorithm has complexity O(N2N) and the second algorithm has complexity O(NK+2), where N (K) is the number of states (secret states).