Probabilistic Safety Analysis for Model Predictive Control with a Case Study on Aircraft Upset Recovery
摘要
NonlinearNonlinear Model Predictive Control (MPC)Model Predictive Control (MPC) is a powerful control method for systems with highly nonlinear dynamics amid critical state and inputFlight constraints. This makes MPC well suited to recover an aircraftAircraft in case of an upset flightFlight condition, a major threat in civil aviation and a challenging flightFlight controlSpace problem. Despite an extensive literature on stabilityStability and robustness of nonlinearNonlinear MPC, analyzing the domain of safeSafe operation requires a careful investigation of both the system and the proposed control scheme. In this chapter, we make use of the equivalency of stable closed-loop operation of MPC with terminalTerminal constraints, feasibility of the underlyingOptimal control optimalOptimal control problemOptimal Control Problem (OCP), and open-loop reachability of the terminalTerminal setSet subject to state constraints. To that extent, we propose a novel approach for probabilisticProbabilistic estimation of the reach-avoid setSet based on scenario optimizationOptimization and the viscosity solutionSolution of the Hamilton–Jacobi–Bellman PDE for reachability. We illustrate our method on an eight state nonlinearNonlinear prediction model for aircraftAircraft upset recovery and obtain probabilityProbability bounds on falsely predicting safeSafe recovery through MPC.