Electrical Engineering And Systems Science

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating sets of given complexity. A probabilistic scaling procedure then allows to rescale these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problem in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems.

The problem of optimizing affine feedback laws that explicitly steer the mean and covariance of an uncertain system state in the presence of a Gaussian random field is considered. Spatially-dependent disturbances are successively approximated with respect to a nominal trajectory by a sequence of jointly Gaussian random vectors. Sequential updates to the nominal control inputs are computed via convex optimization that includes the effect of affine state feedback, the perturbing effects of spatial disturbances, and chance constraints on the closed-loop state and control. The developed method is applied to solve for an affine feedback law to minimize the 99th percentile of ?v required to complete an aerocapture mission around a planet with a randomly disturbed atmosphere.

This paper formulates a chance-constrained optimal distribution network partitioning (ODNP) problem addressing uncertainties in load and renewable energy generation; and presents a solution methodology using sample average approximation (SAA). The objective is to identify potential sub-networks in the existing distribution grid; that are likely to survive as self-adequate islands if supply from the main grid is lost. {This constitutes a planning problem.} Practical constraints like ensuring network radiality and availability of grid-forming generators are considered. Quality of the obtained solution is evaluated by comparison with: a) an upper bound on the probability that the identified islands are supply-deficient, and b) a lower bound on the optimal value of the true problem. Performance of the ODNP formulation is illustrated on a modified IEEE 37-bus feeder. It is shown that the network flexibility is well utilized; the partitioning changes with risk budget; and that the SAA method is able to yield good quality solutions with modest computation cost.

Urban Air Mobility (UAM), or the scenario where multiple manned and Unmanned Aerial Vehicles (UAVs) carry out various tasks over urban airspaces, is a transportation concept of the future that is gaining prominence. UAM missions with complex spatial, temporal and reactive requirements can be succinctly represented using Signal Temporal Logic (STL), a behavioral specification language. However, planning and control of systems with STL specifications is computationally intensive, usually resulting in planning approaches that do not guarantee dynamical feasibility, or control approaches that cannot handle complex STL specifications. Here, we present an approach to co-design the planner and control such that a given STL specification (possibly over multiple UAVs) is satisfied with trajectories that are dynamically feasible and our controller can track them with a bounded tracking-error that the planner accounts for. The tracking controller is formulated for the non-linear dynamics of the individual UAVs, and the tracking error bound is computed for this controller when the trajectories satisfy some kinematic constraints. We also augment an existing multi-UAV STL-based trajectory generator in order to generate trajectories that satisfy such constraints. We show that this co-design allows for trajectories that satisfy a given STL specification, and are also dynamically feasible in the sense that they can be tracked with bounded error. The applicability of this approach is demonstrated through simulations of multi-UAV missions.

The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of the conditions under which agents within a network can reach an agreement (consensus) or develop coordinated behavior, such as synchronization. However, much less understood is the phenomenon of network coherence. Network coherence generally refers to nodes' ability in a network to have a similar dynamic response despite heterogeneity in their individual behavior. In this paper, we develop a general framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property of the system. More precisely, for a networked system with linear dynamics and coupling, we show that, as the network connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior. Interestingly, the non-zero eigenvalue of such a rank-one matrix is given by the harmonic mean of individual nodal dynamics, and we refer to it as the coherent dynamics. Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology. We further show that many networked systems can exhibit similar coherent behavior by establishing a concentration result in a setting with randomly chosen individual nodal dynamics.

This paper concentrates on the collaborative target tracking control of a pair of tracking vehicles with formation constraints. The proposed controller requires only distance measurements between tracking vehicles and the target. Its novelty lies in two aspects: 1) the elliptic coordinates are used to represent an arbitrary tracking formation without singularity, which can be deduced from inter-agent distances, and 2) the regulation of the tracking vehicle system obeys a binocular coordination principle, which simplifies the design of the control law by leveraging rich physical meanings of elliptic coordinates. The tracking system with the proposed controller is proven to be exponentially convergent when the target is stationary. When the target drifts with a small velocity, the desired tracking formation is achieved within a small margin proportional to the magnitude of the target's drift velocity. Simulation examples are provided to demonstrate the tracking performance of the proposed controller.

American football is a leading sport for contact-related injuries such as cervical spine injuries, some of which result from an unforeseen hit. The use of a feedback mechanism to alert an athlete of a potential hit may mitigate the risk for sport-related concussion and catastrophic injury by allowing athletes to effectively brace for an otherwise unforeseen impact. In this project, we created a proximity sensor system using radio frequency identification (RFID) technology to send haptic feedback to the wearer before a potential impact. Our pilot test consisted of three participants who wore our novel sensor system, who ran simulated routes to represent player-to-player contact. Additionally, we used simulated data from a Network Live Football (NFL) league game to further validate our contact prediction algorithm. Results show that our method can predict players' collisions with less than 14% false-alarms.

Developing the collision-free flocking behavior for a dynamic squad of fixed-wing UAVs is still a challenge due to kinematic complexity and environmental uncertainty. In this paper, we deal with the decentralized leader-follower flocking control problem through deep reinforcement learning (DRL). Specifically, we formulate a decentralized DRL-based decision making framework from the perspective of every follower, where a collision avoidance mechanism is integrated into the flocking controller. Then, we propose a novel reinforcement learning algorithm CACER-II for training a shared control policy for all the followers. Besides, we design a plug-n-play embedding module based on convolutional neural networks and the attention mechanism. As a result, the variable-length system state can be encoded into a fixed-length embedding vector, which makes the learned DRL policies independent with the number or the order of followers. Finally, numerical simulation results demonstrate the effectiveness of the proposed method, and the learned policies can be directly transferred to semiphysical simulation without any parameter finetuning.

We consider decentralized optimization over time-varying directed networks. Network nodes can access only their local objectives, and aim to collaboratively minimize a global function by exchanging messages with their neighbors. Leveraging sparsification, gradient tracking and variance-reduction, we propose a novel communication-efficient decentralized optimization scheme that is suitable for resource-constrained time-varying directed networks. We prove that in the case of smooth and strongly-convex objective functions, the proposed scheme achieves an accelerated linear convergence rate. To our knowledge, this is the first decentralized optimization framework that achieves such a convergence rate and applies to settings requiring sparsified communication. Experimental results on both synthetic and real datasets verify the theoretical results and demonstrate efficacy of the proposed scheme.

Opacity is an information flow property characterizing whether a system reveals its secret to a passive observer. Several notions of opacity have been introduced in the literature. We study the notions of language-based opacity, current-state opacity, initial-state opacity, initial-and-final-state opacity, K-step opacity, and infinite-step opacity. Comparing the notions is a natural question that has been investigated and summarized by Wu and Lafortune, who provided transformations among current-state opacity, initial-and-final-state opacity, and language-based opacity, and, for prefix-closed languages, also between language-based opacity and initial-state opacity. We extend these results by showing that all the discussed notions of opacity are transformable to each other. Besides a deeper insight into the differences among the notions, the transformations have applications in complexity results. In particular, the transformations are computable in polynomial time and preserve the number of observable events and determinism, and hence the computational complexities of the verification of the notions coincide. We provide a complete and improved complexity picture of the verification of the discussed notions of opacity, and improve the algorithmic complexity of deciding language-based opacity, infinite-step opacity, and K-step opacity.