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Chance Constrained Model Predictive Control

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost function subject to probabilistic constraints, over a finite horizon. The control laws provided have a predefined (low) risk of not reaching the desired target set. Building on the theory of measures and moments, a sequence of finite semidefinite programmings are provided, whose solution is shown to converge to the optimal solution of the original problem. Numerical examples are presented to illustrate the computational performance of the proposed approach.

Problem Formulation

Equivalent Convex Problem on Measures
Semidefinite Programming Relaxations on Moments
Numerical Results