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Optimal Covariance Steering for Discrete-Time Linear Stochastic Systems
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Optimal Covariance Steering for Discrete-Time Linear Stochastic Systems
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In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a quadratic cost function. Then, we show the separation of the optimal mean and the covariance steering problems. We also develop efficient computational methods to solve for the optimal control law, which is identified as the solution to a semi-definite program. The effectiveness of the proposed approach is demonstrated through numerical examples. In the process, we also obtain some novel theoretical results for a matrix Riccati difference equation, which may be of independent interest.
Forward citations
Cited by 1 Pith paper
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CS-P2L couples covariance steering with Pick-to-Learn to synthesize and certify controllers against high-fidelity simulators, certifying a 4.9% violation bound on a spacecraft powered-descent problem.
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