Sample-Based Robust Data-Enabled Predictive Control for Safe Motion Planning of Unknown Systems

In this article, we consider the safe motion planning problem of controlling a constrained dynamical system subject to disturbances from some initial point to a target set in an environment with multiple polytopic obstacles. The mathematical model of the dynamical system is unknown, restricting us to utilizing only input-output-disturbance data. To address this, we introduce a novel sample-based robust data-enabled predictive control approach that divides the motion planning task into offline and online phases. In the offline phase, the system states are categorized as nominal and perturbed, and we develop an effective algorithm to create two series of convex safe sets from the starting point to the target set. This is achieved by integrating the sample-based motion planning algorithm (e.g., the (Formula presented.) algorithm) with the concept of constraint tightening for nominal and perturbed states, generating sequences of tightened safe sets and robust safe set sequences. The distance between the tightened safe set and any obstacle consistently exceeds the required safe distance, even in the presence of unknown system parameters and disturbances. Using historical disturbance data, the proposed algorithm evaluates the worst impact of disturbance on system control performance, adjusts the safe distance accordingly, and establishes nonempty intersections between adjacent tightened safe sets. During the online phase, system dynamics is described in a data-driven manner using behavioral systems theory. Subsequently, an efficient robust data-enabled predictive tracking control algorithm is introduced to sequentially track the robust safe set sequence. The proposed algorithm transforms the non-convex obstacle avoidance control problem into a convex optimization problem, which can be solved efficiently. Theoretical analysis, including recursive feasibility and closed-loop stability, is provided. We finally examine our results through numerical simulations.