COMPUTATION OF AVOIDANCE REGIONS FOR DRIVER ASSISTANCE SYSTEMS BY USING A HAMILTON-JACOBI APPROACH

International audienceWe consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation of level set functions for obstacle avoidance is given and sufficient conditions for granting the obstacle avoidance on the whole time interval are obtained, even though the conditions are checked only at discrete times. Different scenarios including various road configurations, different geometry of vehicle and obstacles, as well as fixed or moving obstacles, are then studied and computed. Computations involve solving nonlinear partial differential equations of up to five space dimensions plus time with nonsmooth obstacle representations, and an efficient solver is used to this end. A comparison with a direct optimal control approach is also done for one of the examples

Correct-By-Construction Control Synthesis for Systems with Disturbance and Uncertainty

This dissertation focuses on correct-by-construction control synthesis for Cyber-Physical Systems (CPS) under model uncertainty and disturbance. CPSs are systems that interact with the physical world and perform complicated dynamic tasks where safety is often the overriding factor. Correct-by-construction control synthesis is a concept that provides formal performance guarantees to closed-loop systems by rigorous mathematic reasoning. Since CPSs interact with the environment, disturbance and modeling uncertainty are critical to the success of the control synthesis. Disturbance and uncertainty may come from a variety of sources, such as exogenous disturbance, the disturbance caused by co-existing controllers and modeling uncertainty. To better accommodate the different types of disturbance and uncertainty, the verification and control synthesis methods must be chosen accordingly. Four approaches are included in this dissertation. First, to deal with exogenous disturbance, a polar algorithm is developed to compute an avoidable set for obstacle avoidance. Second, a supervised learning based method is proposed to design a good student controller that has safety built-in and rarely triggers the intervention of the supervisory controller, thus targeting the design of the student controller. Third, to deal with the disturbance caused by co-existing controllers, a Lyapunov verification method is proposed to formally verify the safety of coexisting controllers while respecting the confidentiality requirement. Finally, a data-driven approach is proposed to deal with model uncertainty. A minimal robust control invariant set is computed for an uncertain dynamic system without a given model by first identifying the set of admissible models and then simultaneously computing the invariant set while selecting the optimal model. The proposed methods are applicable to many real-world applications and reflect the notion of using the structure of the system to achieve performance guarantees without being overly conservative.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145933/1/chenyx_1.pd

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability approaches for safety certification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While backward reachability strategies have been developed for systems without NN components, the nonlinearities in NN activation functions and general noninvertibility of NN weight matrices make backward reachability for NFLs a challenging problem. To avoid the difficulties associated with propagating sets backward through NNs, we introduce a framework that leverages standard forward NN analysis tools to efficiently find over-approximations to backprojection (BP) sets, i.e., sets of states for which an NN policy will lead a system to a given target set. We present frameworks for calculating BP over approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.Comment: 17 pages, 15 figures. Journal extension of arXiv:2204.0831

Optimal control for safety-critical systems

Enforcing safety plays a crucial role within the optimisation and control literature. Despite notable advances in recent years, optimal control for safety-critical and high-dimensional systems remains a challenging problem. Developing a general theoretical framework for integrating safety within optimal control is not tractable as the numerical inaccuracy and computational cost often grow exponentially with the number of states. Furthermore, different notions of safety require different methodologies and present unique theoretical and computational challenges. This thesis focuses on the challenges that arise when addressing scalability and safety considerations simultaneously. Safety is a multi-facet problem that involves hard constraint satisfaction, avoiding sharing information considered as private, as well as robustifying towards uncertainty that could otherwise compromise safety. The initial chapters of the thesis focus on Hamilton-Jacobi reachability, which has become a well-established method of computing reachable sets for complex nonlinear systems. In addition to enforcing that the system remains within a safe part of the state-space, we consider application-specific abstractions to deal with scalability, the interplay between competing performance objectives and safety objectives, and the challenges arising from multi-objective optimal control problems. We then investigate safety considerations due to the amount of information that needs to be shared between agents in a multi-agent networked control setting. Extending classical state-aggregation in approximate dynamic programming, we introduce a method of solving a large-scale Markov Decision Process in a fully distributed manner. The final chapter considers stochastic safety constraints under a statistical learning theoretic lens. Utilising randomised algorithms, we establish probably approximately correct (PAC) bounds on predicting a future label in a binary classification problem whereby the classifier changes in an unknown structured manner