A stochastic output-feedback MPC scheme for distributed systems

In this paper, we present a novel stochastic output-feedback MPC scheme for distributed systems with additive process and measurement noise. The chance constraints are treated with the concept of probabilistic reachable sets, which, under an unimodality assumption on the disturbance distributions are guaranteed to be satisfied in closed-loop. By conditioning the initial state of the optimization problem on feasibility, the fundamental property of recursive feasibility is ensured. Closed-loop chance constraint satisfaction, recursive feasibility and convergence to an asymptotic average cost bound are proven. The paper closes with a numerical example of three interconnected subsystems, highlighting the chance constraint satisfaction and average cost compared to a centralized setting.Comment: 2020 American Control Conferenc

Stochastic MPC with Distributionally Robust Chance Constraints

In this paper we discuss distributional robustness in the context of stochastic model predictive control (SMPC) for linear time-invariant systems. We derive a simple approximation of the MPC problem under an additive zero-mean i.i.d. noise with quadratic cost. Due to the lack of distributional information, chance constraints are enforced as distributionally robust (DR) chance constraints, which we opt to unify with the concept of probabilistic reachable sets (PRS). For Wasserstein ambiguity sets, we propose a simple convex optimization problem to compute the DR-PRS based on finitely many disturbance samples. The paper closes with a numerical example of a double integrator system, highlighting the reliability of the DR-PRS w.r.t. the Wasserstein set and performance of the resulting SMPC.Comment: Extended version with proofs; accepted for presentation at the 21st IFAC World Congress 202

Stochastic Model Predictive Control with Dynamic Chance Constraints

In this work, we introduce a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance and subject to chance constraints that are defined by time-varying probabilities with a common, fixed lower bound. By utilizing probabilistic reachable tubes with dynamic cross-sections, we are reformulating the stochastic optimization problem into a deterministic tube-based MPC problem with time-varying tightened constraints. We show that the resulting deterministic MPC formulation with dynamic tightened constraints is recursively feasible and that the closed-loop stochastic system will satisfy the corresponding dynamic chance constraints. In addition, we will also introduce a novel implementation using zonotopes to describe the tightening analytically. Finally, we will end with an example to illustrate the benefits of the developed approach to stochastic MPC with dynamic chance constraints.Comment: 8 pages, 3 figure

Robust data-based predictive control of systems with parametric uncertainties: Paving the way for cooperative learning

This article combines data and tube-based predictive control to deal with systems with bounded parametric uncertainty. This integration generates robustly feasible control sequences that can also be exploited in cooperative scenarios where controllers learn from each other’s data. In particular, the approach is based on a database that contains information from previous executions of the same and other controllers handling similar systems. By the combination of feasible histories plus an auxiliary control law that deals with bounded uncertainties, which only needs to be stabilizing for at least one of the system realizations within the uncertainty set, this scheme provides a finite-horizon predictive controller that guarantees exponential stability and robust constraint satisfaction. The validity and benefits of the proposed scheme are shown in case studies with linear and non-linear dynamics.Unión Europea : OCONTSOLAR (ref. 789051)Ministerio de Ciencia e Innovación PID2020-119476RB-I00Ministerio de Ciencia e Innovación PID2022- 141159OB-I0

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