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This paper studies the problem of steering the distribution of a linear time-invariant system from an initial normal distribution to a terminal normal distribution under no knowledge of the system dynamics. This data-driven control framework uses data collected from the input and the state and utilizes the seminal work by Willems et al. to construct a databased parametrization of the mean and the covariance control problems. These problems are then solved to optimality as convex programs using standard techniques from the covariance control literature. We also discuss the equivalence of indirect and direct data-driven covariance steering designs, as well as a regularized version of the problem that provides a balance between the two. We illustrate the proposed framework through a set of randomized trials on a double integrator system and show that the results match up almost exactly with the corresponding model-based method in the noiseless case. We then analyze the robustness properties of the data-free and data-driven covariance steering methods and demonstrate the trade-offs between performance and optimality among these methods in the presence of data corrupted with exogenous noise.

This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control problem as a semi-definite program (SDP), which can be solved efficiently using standard SDP solvers. We adopt the Iterative Risk Allocation (IRA) formalism from [1], which uses a twostage approach to solve the optimal risk allocation problem for covariance steering. The upper-stage of IRA optimizes the risk, which is proved to be a convex problem, while the lowerstage optimizes the controller with the new constraints. This is done iteratively so as to find the optimal risk allocation that achieves the lowest total cost. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies. We also introduce two novel convex relaxation methods to approximate quadratic chance constraints as second-order cone constraints. We finally demonstrate the approach to a spacecraft rendezvous problem and compare the results.

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