Approximating Reachable Sets for Neural Network based Models in Real-Time via Optimal Control

In this paper, we present a data-driven framework for real-time estimation of reachable sets for control systems where the plant is modeled using neural networks (NNs). We utilize a running example of a quadrotor model that is learned using trajectory data via NNs. The NN learned offline, can be excited online to obtain linear approximations for reachability analysis. We use a dynamic mode decomposition based approach to obtain linear liftings of the NN model. The linear models thus obtained can utilize optimal control theory to obtain polytopic approximations to the reachable sets in real-time. The polytopic approximations can be tuned to arbitrary degrees of accuracy. The proposed framework can be extended to other nonlinear models that utilize NNs to estimate plant dynamics. We demonstrate the effectiveness of the proposed framework using an illustrative simulation of quadrotor dynamics.Comment: 14 pages, 11 figures, journal paper that has been conditionally accepte

Data-Driven Safety & Security of Cyberphysical Systems

Cyberphysical systems (CPSs) are expected to operate in safety-critical scenarios, and are increasingly getting distributed and physically separated. CPSs are characterized by complex dynamical behavior arising from emergent inter-agent interactions, having discrete logic-based programs, data-driven methods employed in-the-loop, or by simply having highly nonlinear dynamics. Despite this, safety and security properties for CPSs need to be computed, often in real-time over analytically accurate solutions of the associated high dimensional partial differential equations (PDEs). In this dissertation, we investigate numerical approximation schemes to compute safety properties (or reachable sets) for CPSs with differing natures of complexities, without solving the associated PDEs. We solve for reachable sets for unknown dynamical systems with polynomial approximations. Similar approximation schemes can be extended to multi-agent systems and dynamical systems with neural-networks-in-the-loop. Such systems are increasingly applicable in real life instances, such as internet of things, urban air mobility, and data-driven controllers in-the-loop. We utilize the system\u27s trajectory data to compute equivalent system models, and utilize the data-driven models to find approximate reachable sets using polytopic or interval approximations, thereby side stepping PDE solutions. We also investigate cyberphysical vulnerabilities in CPSs from emergent multi-agent behavior, and single agent interacting with multiple controllers via supervisory cyber layers. Each problem is accompanied with associated illustrative examples and numerical simulations. Finally, we present an extensive discussion of possible directions for future work, both, that result directly from the works presented in this dissertation, and those that stem from the assumptions that can be handled immediately

Kalman Filtering for LTI Systems with State Dependent Packet Losses

Due to recent advances in networked control systems and wireless networked control systems, most systems of interest operate in environments susceptible to sensor malfunctions. The increased dependency on communication channels to transfer measurement data due to the geographical separation of sensors from actuators and plants further contributes to the issue. Most existing methods that deal with the problem of estimation under packet losses assume the packet arrival process to have stationary statistics. In this work we relax this assumption and address the problem of state estimation under state dependent packet losses. This problem presents inherent modeling of practical applications of systems operating in hostile environments, sensor denied environments, or the presence of sensor disruptors/jammers. This estimation problem is formulated as a linear system which a state dependent hybrid measurement model. An optimal estimation algorithm is proposed using a Projection based approach. A special case of this estimation problem is also presented, in the form of a measurement model with Markovian sensor malfunctions (packet losses—full and partial, and multiplicative sensor degradations), which is modeled as a Markov jump linear system. Stability results for the Markovian problem are presented in the form of bounds on the error covariance. Finally, the two estimators demonstrated using illustrative and practical instances and compared against existing estimation algorithms