Locally Optimal Reach Set Over-approximation for Nonlinear Systems

Safety verification of embedded systems modeled as hybrid systems can be scaled up by employing simulation-guided reach set over-approximation techniques. Existing methods are applicable only to restricted classes of systems, overly conservative, or computationally expensive. We present new techniques to compute a locally optimal bloating factor based on discrepancy functions, which allow construction of reach set over-approximations from simulation traces for general nonlinear systems. The discrepancy functions are critical for tools like C2E2 to verify bounded time safety properties for complex hybrid systems with nonlinear continuous dynamics. The new discrepancy function is computed using local bounds on a matrix measure under an optimal metric such that the exponential change rate of the discrepancy function is minimized. The new technique is less time consuming and less conservative than existing techniques and does not incur significant computational overhead. We demonstrate the effectiveness of our approach by comparing the performance of a prototype implementation with the state-of-the-art reachability analysis tool Flow*.National Science Foundation/CCF 1422798Ope

An hybrid system approach to nonlinear optimal control problems

We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton. Given a sequence of states, we introduce an hybrid approximation of the nonlinear controllable domain and propose a new algorithm computing a controllable, piecewise convex approximation. The same way the nonlinear optimal control problem is replaced by an hybrid piecewise affine one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce the global structure of the hybrid optimal control steering the system to the target

Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731