Fast Reachable Set Approximations via State Decoupling Disturbances

With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis of safety-critical systems. In particular, the Hamilton-Jacobi (HJ) formulation of differential games provides a flexible way to compute the reachable set, which can characterize the set of states which lead to either desirable or undesirable configurations, depending on the application. While HJ reachability is applicable to many small practical systems, the curse of dimensionality prevents the direct application of HJ reachability to many larger systems. To address computation complexity issues, various efficient computation methods in the literature have been developed for approximating or exactly computing the solution to HJ partial differential equations, but only when the system dynamics are of specific forms. In this paper, we propose a flexible method to trade off optimality with computation complexity in HJ reachability analysis. To achieve this, we propose to simplify system dynamics by treating state variables as disturbances. We prove that the resulting approximation is conservative in the desired direction, and demonstrate our method using a four-dimensional plane model.Comment: in Proceedings of the IEE Conference on Decision and Control, 201

Safe Sequential Path Planning Under Disturbances and Imperfect Information

Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited to small-scale systems of no more than two vehicles due to an exponentially-scaling computational complexity. Previously, the sequential path planning (SPP) method, which assigns strict priorities to vehicles, was proposed; SPP allows multi-vehicle path planning to be done with a linearly-scaling computational complexity. However, the previous formulation assumed that there are no disturbances, and that every vehicle has perfect knowledge of higher-priority vehicles' positions. In this paper, we make SPP more practical by providing three different methods to account for disturbances in dynamics and imperfect knowledge of higher-priority vehicles' states. Each method has different assumptions about information sharing. We demonstrate our proposed methods in simulations.Comment: American Control Conference, 201

Safe Sequential Path Planning of Multi-Vehicle Systems via Double-Obstacle Hamilton-Jacobi-Isaacs Variational Inequality

We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically, especially given the growing interest in utilizing unmanned aircraft systems for civil purposes. The direct solution of this problem by solving a single-obstacle Hamilton-Jacobi-Isaacs (HJI) variational inequality (VI) is numerically intractable due to the exponential scaling of computation complexity with problem dimensionality. Furthermore, the single-obstacle HJI VI cannot directly handle situations in which vehicles do not have a common scheduled arrival time. Instead, we perform sequential path planning by considering vehicles in order of priority, modeling higher-priority vehicles as time-varying obstacles for lower-priority vehicles. To do this, we solve a double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined as the set of states from which a vehicle can reach its target while staying within a time-varying state constraint set. From the solution of the double-obstacle HJI VI, we can also extract the latest start time and the optimal control for each vehicle. This is a first application of the double-obstacle HJI VI which can handle systems with time-varying dynamics, target sets, and state constraint sets, and results in computation complexity that scales linearly, as opposed to exponentially, with the number of vehicles in consideration.Comment: European Control Conference 201

A Classification-based Approach for Approximate Reachability

Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very generally, computational complexity can be a serious impediment for many systems of practical interest. Much prior work has been devoted to computing approximate solutions to large reachability problems, yet many of these methods may only apply to very restrictive problem classes, do not generate controllers, and/or can be extremely conservative. In this paper, we present a new method for approximating the optimal controller of the HJ reachability problem for control-affine systems. While also a specific problem class, many dynamical systems of interest are, or can be well approximated, by control-affine models. We explicitly avoid storing a representation of the reachability value function, and instead learn a controller as a sequence of simple binary classifiers. We compare our approach to existing grid-based methodologies in HJ reachability and demonstrate its utility on several examples, including a physical quadrotor navigation task

A Study of Potential Security and Safety Vulnerabilities in Cyber-Physical Systems

The work in this dissertation focuses on two examples of Cyber-Physical Systems (CPS), integrations of communication and monitoring capabilities to control a physical system, that operate in adversarial environments. That is to say, it is possible for individuals with malicious intent to gain access to various components of the CPS, disrupt normal operation, and induce harmful impacts. Such a deliberate action will be referred to as an attack. Therefore, some possible attacks against two CPSs will be studied in this dissertation and, when possible, solutions to handle such attacks will also be suggested. The first CPS of interest is vehicular platoons wherein it is possible for a number of partially-automated vehicles to drive autonomously towards a certain destination with as little human driver involvement as possible. Such technology will ultimately allow passengers to focus on other tasks, such as reading or watching a movie, rather than on driving. In this dissertation three possible attacks against such platoons are studied. The first is called ”the disbanding attack” wherein the attacker is capable of disrupting one platoon and also inducing collisions in another intact (non-attacked) platoon vehicles. To handle such an attack, two solutions are suggested: The first solution is formulated using Model Predictive Control (MPC) optimal technique, while the other uses a heuristic approach. The second attack is False-Data Injection (FDI) against the platooning vehicular sensors is analyzed using the reachability analysis. This analysis allows us to validate whether or not it is possible for FDI attacks to drive a platoon towards accidents. Finally, mitigation strategies are suggested to prevent an attacker-controlled vehicle, one which operates inside a platoon and drives unpredictably, from causing collisions. These strategies are based on sliding mode control technique and once engaged in the intact vehicles, collisions are reduced and eventual control of those vehicles will be switched from auto to human to further reduce the impacts of the attacker-controlled vehicle. The second CPS of interest in this dissertation is Heating, Ventilating, and Air Conditioning (HVAC) systems used in smart automated buildings to provide an acceptable indoor environment in terms of thermal comfort and air quality for the occupants For these systems, an MPC technique based controller is formulated in order to track a desired temperature in each zone of the building. Some previous studies indicate the possibility of an attacker to manipulate the measurements of temperature sensors, which are installed at different sections of the building, and thereby cause them to read below or above the real measured temperature. Given enough time, an attacker could monitor the system, understand how it works, and decide which sensor(s) to target. Eventually, the attacker may be able to deceive the controller, which uses the targeted sensor(s) readings and raises the temperature of one or multiple zones to undesirable levels, thereby causing discomfort for occupants in the building. In order to counter such attacks, Moving Target Defense (MTD) technique is utilized in order to constantly change the sensors sets used by the MPC controllers and, as a consequence, reduce the impacts of sensor attacks

Safe Spacecraft Rendezvous and Proximity Operations via Reachability Analysis

The rapid expansion of the utilization of space by nations and industry has presented new challenges and opportunities to operate efficiently and responsibly. Reachability analysis is the process of computing the set of states that can be reached given all admissible controls and can be a valuable component in an autonomous mission planning system if conducted efficiently. In the current research, reachability analysis is used with several relative motion models to show that all ranges of orbits can be computed in milliseconds, and that it is a feasible approach for on-board autonomous mission planning. Reachability analysis is then combined with an Artificial Potential Function (APF) derived guidance control law to conduct safe spacecraft rendezvous between a deputy in a Natural Motion Circumnavigation (NMC) relative orbit around a chief while avoiding obstacles. While the APF employed in this research requires improvements for trajectory computation, this research demonstrates the feasibility of combining reachability analysis with an APF for safe, on-board, autonomous mission planning