Chance-Constraint-Based Design of Open-Loop Controllers for Linear Uncertain Systems

This paper considers the problem of state-to-state transition with state and control constraints, for a linear system with time-invariant model parameter uncertainties. Polynomial chaos is used to transform the stochastic model to a deterministic surrogate model. This surrogate model is used to pose a chance-constrained optimal control problem where the state constraints and the residual energy cost are represented in terms of the mean and variance of the stochastic states. The resulting convex optimization problem is numerically illustrated on the problem of rest-to-rest maneuver of the benchmark floating oscillator and on an experimental two-tank setup.