Stochastic MPC Approach to Drift Counteraction

摘要

The contribution of this paper is a novel tree-based stochastic model predictive control (SMPC) approach to solve the optimal exit-time control problem for stochastic systems, that is to maximize the expected value of the first time instant at which prescribed constraints are violated. A scenario tree with a specified number of tree nodes is used to encode the most likely system behavior, where each path on the tree corresponds to a distinct disturbance scenario. For linear discrete-time systems with an additive random disturbance, a mixed-integer linear program (MILP) obtains solutions arbitrarily close to the optimal solution for a sufficient number of tree nodes. In order to compensate for an incomplete scenario tree and/or unmodeled effects, feedback is provided by recomputing the MILP solution over a receding time horizon based on the current state and disturbance / scenario tree. Two numerical case studies, including an adaptive cruise control problem, demonstrate the effectiveness of the proposed SMPC scheme compared to dynamic programming solutions.