On Data-driven Attack-resilient Gaussian Process Regression for Dynamic Systems

This paper studies attack-resilient Gaussian process regression of partially unknown nonlinear dynamic systems subject to sensor attacks and actuator attacks. The problem is formulated as the joint estimation of states, attack vectors, and system functions of partially unknown systems. We propose a new learning algorithm by incorporating our recently developed unknown input and state estimation technique into the Gaussian process regression algorithm. Stability of the proposed algorithm is formally studied. We also show that average case learning errors of system function approximation are diminishing if the number of state estimates whose estimation errors are non-zero is bounded by a constant. We demonstrate the performance of the proposed algorithm by numerical simulations on the IEEE 68-bus test system.