Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

A time-varying matrix solution to the Brockett decentralized stabilization problem

This paper proposes a time-varying matrix solution to the Brockett stabilization problem. The key matrix condition shows that if the system matrix product $CB$ is a Hurwitz H-matrix, then there exists a time-varying diagonal gain matrix $K(t)$ such that the closed-loop minimum-phase linear system with decentralized output feedback is exponentially convergent. The proposed solution involves several analysis tools such as diagonal stabilization properties of special matrices, stability conditions of diagonal-dominant linear systems, and solution bounds of linear time-varying integro-differential systems. A review of other solutions to the general Brockett stabilization problem (for a general unstructured time-varying gain matrix $K(t)$) and a comparison study are also provided

Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds

We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot’s local obstacle-free convex neighborhood, affording a reactive (online-computed) piecewise smooth and continuous closed-loop vector field whose smooth flow brings almost all configurations in the robot’s free space to a designated goal location, with the guarantee of no collisions along the way. We further extend these provable properties to practically motivated limited range sensing models

Formation Control for a Fleet of Autonomous Ground Vehicles: A Survey

Autonomous/unmanned driving is the major state-of-the-art step that has a potential to fundamentally transform the mobility of individuals and goods. At present, most of the developments target standalone autonomous vehicles, which can sense the surroundings and control the vehicle based on this perception, with limited or no driver intervention. This paper focuses on the next step in autonomous vehicle research, which is the collaboration between autonomous vehicles, mainly vehicle formation control or vehicle platooning. To gain a deeper understanding in this area, a large number of the existing published papers have been reviewed systemically. In other words, many distributed and decentralized approaches of vehicle formation control are studied and their implementations are discussed. Finally, both technical and implementation challenges for formation control are summarized

Adaptive and learning-based formation control of swarm robots

Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation

Output Consensus Control for Heterogeneous Multi-Agent Systems

We study distributed output feedback control of a heterogeneous multi-agent system (MAS), consisting of N different continuous-time linear dynamical systems. For achieving output consensus, a virtual reference model is assumed to generate the desired trajectory for which the MAS is required to track and synchronize. A full information (FI) protocol is assumed for consensus control. This protocol includes information exchange with the feed-forward signals. In this dissertation we study two different kinds of consensus problems. First, we study the consensus control over the topology involving time delays and prove that consensus is independent of delay lengths. Second, we study the consensus under communication constraints. In contrast to the existing work, the reference trajectory is transmitted to only one or a few agents and no local reference models are employed in the feedback controllers thereby eliminating synchronization of the local reference models. Both significantly lower the communication overhead. In addition, our study is focused on the case when the available output measurements contain only relative information from the neighboring agents and reference signal. Conditions are derived for the existence of distributed output feedback control protocols, and solutions are proposed to synthesize the stabilizing and consensus control protocol over a given connected digraph. It is shown that the H-inf loop shaping and LQG/LTR techniques from robust control can be directly applied to design the consensus output feedback control protocol. The results in this dissertation complement the existing ones, and are illustrated by a numerical example. The MAS approach developed in this dissertation is then applied to the development of autonomous aircraft traffic control system. The development of such systems have already started to replace the current clearance-based operations to trajectory based operations. Such systems will help to reduce human errors, increase efficiency, provide safe flight path, and improve the performance of the future flight

A Decoupling Principle for Simultaneous Localization and Planning Under Uncertainty in Multi-Agent Dynamic Environments

Simultaneous localization and planning for nonlinear stochastic systems under process and measurement uncertainties is a challenging problem. In its most general form, it is formulated as a stochastic optimal control problem in the space of feedback policies. The Hamilton-Jacobi-Bellman equation provides the theoretical solution of the optimal problem; but, as is typical of almost all nonlinear stochastic systems, optimally solving the problem is intractable. Moreover, even if an optimal solution was obtained, it would require centralized control, while multi-agent mobile robotic systems under dynamic environments require decentralized solutions. In this study, we aim for a theoretically sound solution for various modes of this problem, including the single-agent and multi-agent variations with perfect and imperfect state information, where the underlying state, control and observation spaces are continuous with discrete-time models. We introduce a decoupling principle for planning and control of multi-agent nonlinear stochastic systems based on a small noise asymptotics. Through this decoupling principle, under small noise, the design of the real-time feedback law can be decoupled from the off-line design of the nominal trajectory of the system. Further, for a multi-agent problem, the design of the feedback laws for different agents can be decoupled from each other, reducing the centralized problem to a decentralized problem requiring no communication during execution. The resulting solution is quantifiably near-optimal. We establish this result for all the above-mentioned variations, which results in the following variants: Trajectory-optimized Linear Quadratic Regulator (T-LQR), Multi-agent T-LQR (MT-LQR), Trajectory-optimized Linear Quadratic Gaussian (T-LQG), and Multi-agent T-LQG (MT-LQG). The decoupling principle provides the conditions under which a decentralized linear Gaussian system with a quadratic approximation of the cost, obtained by linearization around an optimally designed nominal trajectory can be utilized to control the nonlinear system. The resulting decentralized feedback solution at runtime, being decoupled with respect to the mobile agents, requires no communication between the agents during the execution phase. Moreover, the complexity of the solution vis-a-vis the computation of the nominal trajectory as well as the closed-loop gains is tractable with low polynomial orders of computation. Experimental implementation of the solution shows that the results hold for moderate levels of noise with high probability. Further optimizing the performance of this approach we show how to design a special cost function for the problem with imperfect state measurement that takes advantage of the fact that the estimation covariance of a linear Gaussian system is deterministic and not dependent on the observations. This design, which corresponds in our overall design to “belief space planning”, incorporates the consequently deterministic cost of the stochastic feedback system into the deterministic design of the nominal trajectory to obtain an optimal nominal trajectory with the best estimation performance. Then, it utilizes the T-LQG approach to design an optimal feedback law to track the designed nominal trajectory. This iterative approach can be used to further tune both the open loop as well as the decentralized feedback gain portions of the overall design. We also provide the multi-agent variant of this approach based on the MT-LQG method. Based on the near-optimality guarantees of the decoupling principle and the TLQG approach, we analyze the performance and correctness of a well-known heuristic in robotic path planning. We show that optimizing measures of the observability Gramian as a surrogate for estimation performance may provide irrelevant or misleading trajectories for planning under observation uncertainty. We then consider systems with non-Gaussian perturbations. An alternative heuristic method is proposed that aims for fast planning in belief space under non- Gaussian uncertainty. We provide a special design approach based on particle filters that results in a convex planning problem implemented via a model predictive control strategy in convex environments, and a locally convex problem in non-convex environments. The environment here refers to the complement of the region in Euclidean space that contains the obstacles or “no fly zones”. For non-convex dynamic environments, where the no-go regions change dynamically with time, we design a special form of an obstacle penalty function that incorporates non-convex time-varying constraints into the cost function, so that the decoupling principle still applies to these problems. However, similar to any constrained problem, the quality of the optimal nominal trajectory is dependent on the quality of the solution obtainable for the nonlinear optimization problem. We simulate our algorithms for each of the problems on various challenging situations, including for several nonlinear robotic models and common measurement models. In particular, we consider 2D and 3D dynamic environments for heterogeneous holonomic and non-holonomic robots, and range and bearing sensing models. Future research can potentially extend the results to more general situations including continuous-time models

A Decoupling Principle for Simultaneous Localization and Planning Under Uncertainty in Multi-Agent Dynamic Environments

Simultaneous localization and planning for nonlinear stochastic systems under process and measurement uncertainties is a challenging problem. In its most general form, it is formulated as a stochastic optimal control problem in the space of feedback policies. The Hamilton-Jacobi-Bellman equation provides the theoretical solution of the optimal problem; but, as is typical of almost all nonlinear stochastic systems, optimally solving the problem is intractable. Moreover, even if an optimal solution was obtained, it would require centralized control, while multi-agent mobile robotic systems under dynamic environments require decentralized solutions. In this study, we aim for a theoretically sound solution for various modes of this problem, including the single-agent and multi-agent variations with perfect and imperfect state information, where the underlying state, control and observation spaces are continuous with discrete-time models. We introduce a decoupling principle for planning and control of multi-agent nonlinear stochastic systems based on a small noise asymptotics. Through this decoupling principle, under small noise, the design of the real-time feedback law can be decoupled from the off-line design of the nominal trajectory of the system. Further, for a multi-agent problem, the design of the feedback laws for different agents can be decoupled from each other, reducing the centralized problem to a decentralized problem requiring no communication during execution. The resulting solution is quantifiably near-optimal. We establish this result for all the above-mentioned variations, which results in the following variants: Trajectory-optimized Linear Quadratic Regulator (T-LQR), Multi-agent T-LQR (MT-LQR), Trajectory-optimized Linear Quadratic Gaussian (T-LQG), and Multi-agent T-LQG (MT-LQG). The decoupling principle provides the conditions under which a decentralized linear Gaussian system with a quadratic approximation of the cost, obtained by linearization around an optimally designed nominal trajectory can be utilized to control the nonlinear system. The resulting decentralized feedback solution at runtime, being decoupled with respect to the mobile agents, requires no communication between the agents during the execution phase. Moreover, the complexity of the solution vis-a-vis the computation of the nominal trajectory as well as the closed-loop gains is tractable with low polynomial orders of computation. Experimental implementation of the solution shows that the results hold for moderate levels of noise with high probability. Further optimizing the performance of this approach we show how to design a special cost function for the problem with imperfect state measurement that takes advantage of the fact that the estimation covariance of a linear Gaussian system is deterministic and not dependent on the observations. This design, which corresponds in our overall design to “belief space planning”, incorporates the consequently deterministic cost of the stochastic feedback system into the deterministic design of the nominal trajectory to obtain an optimal nominal trajectory with the best estimation performance. Then, it utilizes the T-LQG approach to design an optimal feedback law to track the designed nominal trajectory. This iterative approach can be used to further tune both the open loop as well as the decentralized feedback gain portions of the overall design. We also provide the multi-agent variant of this approach based on the MT-LQG method. Based on the near-optimality guarantees of the decoupling principle and the TLQG approach, we analyze the performance and correctness of a well-known heuristic in robotic path planning. We show that optimizing measures of the observability Gramian as a surrogate for estimation performance may provide irrelevant or misleading trajectories for planning under observation uncertainty. We then consider systems with non-Gaussian perturbations. An alternative heuristic method is proposed that aims for fast planning in belief space under non- Gaussian uncertainty. We provide a special design approach based on particle filters that results in a convex planning problem implemented via a model predictive control strategy in convex environments, and a locally convex problem in non-convex environments. The environment here refers to the complement of the region in Euclidean space that contains the obstacles or “no fly zones”. For non-convex dynamic environments, where the no-go regions change dynamically with time, we design a special form of an obstacle penalty function that incorporates non-convex time-varying constraints into the cost function, so that the decoupling principle still applies to these problems. However, similar to any constrained problem, the quality of the optimal nominal trajectory is dependent on the quality of the solution obtainable for the nonlinear optimization problem. We simulate our algorithms for each of the problems on various challenging situations, including for several nonlinear robotic models and common measurement models. In particular, we consider 2D and 3D dynamic environments for heterogeneous holonomic and non-holonomic robots, and range and bearing sensing models. Future research can potentially extend the results to more general situations including continuous-time models

Data Mining in Smart Grids

Effective smart grid operation requires rapid decisions in a data-rich, but information-limited, environment. In this context, grid sensor data-streaming cannot provide the system operators with the necessary information to act on in the time frames necessary to minimize the impact of the disturbances. Even if there are fast models that can convert the data into information, the smart grid operator must deal with the challenge of not having a full understanding of the context of the information, and, therefore, the information content cannot be used with any high degree of confidence. To address this issue, data mining has been recognized as the most promising enabling technology for improving decision-making processes, providing the right information at the right moment to the right decision-maker. This Special Issue is focused on emerging methodologies for data mining in smart grids. In this area, it addresses many relevant topics, ranging from methods for uncertainty management, to advanced dispatching. This Special Issue not only focuses on methodological breakthroughs and roadmaps in implementing the methodology, but also presents the much-needed sharing of the best practices. Topics include, but are not limited to, the following: Fuzziness in smart grids computing Emerging techniques for renewable energy forecasting Robust and proactive solution of optimal smart grids operation Fuzzy-based smart grids monitoring and control frameworks Granular computing for uncertainty management in smart grids Self-organizing and decentralized paradigms for information processin