Information-Based Optimization Approaches to Dynamical System Safety Verification

Given a heuristic estimate of the relative safety of a hybrid dynamical system trajectory, we transform the initial safety problem for dynamical systems into a global optimization problem. We introduce MLLO-IQ and MLLO-RIQ, two new information-based optimization algorithms. After demonstrating their strengths and weaknesses, we describe the class of problems for which diierent optimization methods are best-suited. The transformation of an initial safety problem for dynamical systems into a global optimization problem is accomplished through construction of a heuristic function which simulates a system trajectory and returns a heuristic evaluation of the relative safety of that trajectory. Since each heuristic function evaluation may be computationally expensive, it becomes desirable to invest more computational eeort in intelligent use of function evaluation information to reduce the average number of evaluations needed. To this end, we've developed MLLO-IQ and MLLO-RIQ, information-based methods which approximate optimal optimization decision procedures.