Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version

Abstract

We present a stochastic model predictive control (SMPC) framework for linear systems subject to possibly unbounded disturbances. State of the art SMPC approaches with closed-loop chance constraint satisfaction recursively initialize the nominal state based on the previously predicted nominal state or possibly the measured state under some case distinction. We improve these initialization strategies by allowing for a continuous optimization over the nominal initial state in an interpolation of these two extremes. The resulting SMPC scheme can be implemented as one standard quadratic program and is more flexible compared to state-of-the-art initialization strategies. As the main technical contribution, we show that the proposed SMPC framework also ensures closed-loop satisfaction of chance constraints and suitable performance bounds.

arXiv commentExtended version of accepted paper in IEEE Control Systems Letters, 2022. Contains additional details regarding the proof and an additional example

References in corpus (10)

• The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations
• Receding-horizon Stochastic Model Predictive Control with Hard Input Constraints and Joint State Chance Constraints
• Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets
• Comments on Truncation Errors for Polynomial Chaos Expansions
• Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version
• Minimization of Constraint Violation Probability in Model Predictive Control
• Data-driven Distributionally Robust MPC: An indirect feedback approach
• A stochastic output-feedback MPC scheme for distributed systems
• Stochastic Model Predictive Control using Initial State Optimization
• Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints

Cited by in corpus (4)

• Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version
• Recursively feasible Data-driven Distributionally Robust Model Predictive Control with additive disturbances
• Predictive control for nonlinear stochastic systems: Closed-loop guarantees with unbounded noise
• LQG for Constrained Linear Systems: Indirect Feedback Stochastic MPC with Kalman Filtering