Learning Robustness with Bounded Failure: An Iterative MPC Approach

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain the true support of the disturbance distribution with a given probability. As more data is collected, the Confidence Supports converge to the true support of the disturbance. This enables design of an MPC controller that avoids conservative estimate of the disturbance support, while simultaneously bounding the probability of constraint violation. The efficacy of the proposed approach is then demonstrated with a detailed numerical example.Comment: Added GitHub link to all source code

Stochastic MPC with Realization-Adaptive Constraint Tightening

This paper presents a stochastic model predictive controller (SMPC) for linear time-invariant systems in the presence of additive disturbances. The distribution of the disturbance is unknown and is assumed to have a bounded support. A sample-based strategy is used to compute sets of disturbance sequences necessary for robustifying the state chance constraints. These sets are constructed offline using samples of the disturbance extracted from its support. For online MPC implementation, we propose a novel reformulation strategy of the chance constraints, where the constraint tightening is computed by adjusting the offline computed sets based on the previously realized disturbances along the trajectory. The proposed MPC is recursive feasible and can lower conservatism over existing SMPC approaches at the cost of higher offline computational time. Numerical simulations demonstrate the effectiveness of the proposed approach.Comment: Submitted to ACC 202

Learning to Satisfy Unknown Constraints in Iterative MPC

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a detailed numerical example.Comment: Long version of the final paper for IEEE-CDC 2020. First two authors contributed equall

Output Feedback Stochastic MPC with Hard Input Constraints

We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm.Comment: IEEE American Control Conference (ACC) 2023, May 31 - June 2, San Diego, CA, US