Biblio

Information communicated within cyber-physical systems (CPSs) is often used in determining the physical states of such systems, and malicious adversaries may intercept these communications in order to infer future states of a CPS or its components. Accordingly, there arises a need to protect the state values of a system. Recently, the notion of differential privacy has been used to protect state trajectories in dynamical systems, and it is this notion of privacy that we use here to protect the state trajectories of CPSs. We incorporate a cloud computer to coordinate the agents comprising the CPSs of interest, and the cloud offers the ability to remotely coordinate many agents, rapidly perform computations, and broadcast the results, making it a natural fit for systems with many interacting agents or components. Striving for broad applicability, we solve infinite-horizon linear-quadratic-regulator (LQR) problems, and each agent protects its own state trajectory by adding noise to its states before they are sent to the cloud. The cloud then uses these state values to generate optimal inputs for the agents. As a result, private data are fed into feedback loops at each iteration, and each noisy term affects every future state of every agent. In this paper, we show that the differentially private LQR problem can be related to the well-studied linear-quadratic-Gaussian (LQG) problem, and we provide bounds on how agents' privacy requirements affect the cloud's ability to generate optimal feedback control values for the agents. These results are illustrated in numerical simulations.

In this paper we consider connected and autonomous vehicles (CAV) in a traffic network as moving waves defined by their frequency and phase. This outlook allows us to develop a multi-layer decentralized control strategy that achieves the following desirable behaviors: (1) safe spacing between vehicles traveling down the same road, (2) coordinated safe crossing at intersections of conflicting flows, (3) smooth velocity profiles when traversing adjacent intersections. The approach consist of using the Kuramoto equation to synchronize the phase and frequency of agents in the network. The output of this layer serves as the reference trajectory for a back-stepping controller that interfaces the first-order dynamics of the phase-domain layer and the second order dynamics of the vehicle. We show the performance of the strategy for a single intersection and a small urban grid network. The literature has focused on solving the intersection coordination problem in both a centralized and decentralized manner. Some authors have even used the Kuramoto equation to achieve synchronization of traffic lights. Our proposed strategy falls in the rubric of a decentralized approach, but unlike previous work, it defines the vehicles as the oscillating agents, and leverages their inter-connectivity to achieve network-wide synchronization. In this way, it combines the benefits of coordinating the crossing of vehicles at individual intersections and synchronizing flow from adjacent junctions.

Autonomous active exploration requires search algorithms that can effectively balance the need for workspace coverage with energetic costs. We present a strategy for planning optimal search trajectories with respect to the distribution of expected information over a workspace. We formulate an iterative optimal control algorithm for general nonlinear dynamics, where the metric for information gain is the difference between the spatial distribution and the statistical representation of the time-averaged trajectory, i.e. ergodicity. Previous work has designed a continuous-time trajectory optimization algorithm. In this paper, we derive two discrete-time iterative trajectory optimization approaches, one based on standard first-order discretization and the other using symplectic integration. The discrete-time methods based on first-order discretization techniques are both faster than the continuous-time method in the studied examples. Moreover, we show that even for a simple system, the choice of discretization has a dramatic impact on the resulting control and state trajectories. While the standard discretization method turns unstable, the symplectic method, which is structure-preserving, achieves lower values for the objective.