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Start Over Topic chance constraints Topic constraint satisfaction Topic model predictive control
2 results

1. Stochastic output feedback MPC with intermittent observations.

Author

Yan, Shuhao, Cannon, Mark, and Goulart, Paul J.

Subjects
*CONSTRAINT satisfaction, *STOCHASTIC systems, *LINEAR systems, *COMPUTER simulation, *PREDICTION models, *OPTIMAL control theory, *PSYCHOLOGICAL feedback
Abstract

This paper designs a model predictive control (MPC) law for constrained linear systems with stochastic additive disturbances and noisy measurements, minimising a discounted cost subject to a discounted expectation constraint. It is assumed that sensor data is lost with a known probability. Taking into account the data losses modelled by a Bernoulli process, we parameterise the predicted control policy as an affine function of future observations and obtain a convex linear-quadratic optimal control problem. Constraint satisfaction and a discounted cost bound are ensured without imposing bounds on the distributions of the disturbance and noise inputs. In addition, the average long-run undiscounted closed loop cost is shown to be finite if the discount factor takes appropriate values. We analyse robustness of the proposed control law with respect to possible uncertainties in the arrival probability of sensor data and we bound the impact of these uncertainties on constraint satisfaction and the discounted cost. Numerical simulations are provided to illustrate these results. [ABSTRACT FROM AUTHOR]

Published
2022
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2. The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations

Author

Lorenzo Fagiano, Christoph Frei, Georg Schildbach, and Manfred Morari

Subjects
Mathematical optimization, Computational complexity theory, 7. Clean energy, Control theory, FOS: Mathematics, Chance constraints, MPC, Scenario optimization, Scenario-Based, Soft constraints, Stochastic, Stochastic systems, Control and Systems Engineering, Electrical and Electronic Engineering, Mathematics - Optimization and Control, Mathematics, Linear system, Probabilistic logic, Constraint satisfaction, 16. Peace & justice, Optimal control, Constraint (information theory), Model predictive control, Optimization and Control (math.OC)
Abstract

Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control applications it suffices to keep the state constraints at least for a prescribed share of the time, as e.g. in building climate control or load mitigation for wind turbines. For such systems, a new control method of Scenario-Based Model Predictive Control (SCMPC) is presented in this paper. It optimizes the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. While previous approaches have shown to be conservative (i.e. to stay far below the specified rate of constraint violations), the new method is the first to account for the special structure of the MPC problem in order to significantly reduce the number of scenarios. In combination with a new framework for interpreting the probabilistic constraints as average-in-time, rather than pointwise-in-time, the conservatism is eliminated. The presented method retains the essential advantages of SCMPC, namely the reduced computational complexity and the handling of arbitrary probability distributions. It also allows for adopting sample-and-remove strategies, in order to trade performance against computational complexity., Pre-print submitted to Automatica

Published
2013