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• W4205652914 abstract "In this paper, we present a Model-Free Stochastic Inverse Optimal Control (IOC) algorithm for the discrete-time infinite-horizon stochastic linear quadratic regulator (LQR). Our proposed algorithm exploits the richness of the available system trajectories to recover the control gain <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$K$ </tex-math></inline-formula> and cost function parameters <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$(Q,R)$ </tex-math></inline-formula> in a low (space, sample, and computational) complexity manner. By leveraging insights on the stochastic LQR, we guarantee well-posedness of the Model-Free Stochastic IOC LQR via satisfaction of the <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Certainty Equivalence</i> optimality conditions. The exact solution of the control gain <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$K$ </tex-math></inline-formula> is recovered via a deterministic, low complexity Least Squares approach. Using <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$K$ </tex-math></inline-formula> , we solve a completely model-free non-iterative SemiDefinite Programming (SDP) problem to obtain a unique (up to a scalar ambiguity) <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$(Q,R)$ </tex-math></inline-formula> , in which optimality and feasibility are jointly ensured. Via derivation of the sample complexity bounds, we show that the non-asymptotic performance of the Model-Free Stochastic IOC LQR can be characterized by the signal-to-noise (SNR) ratio of the finite set of system state and input signals. We present a model-based version of the algorithm for the special case where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$(A,B)$ </tex-math></inline-formula> is available, and we, further, provide the extension to the Stochastic Model-Free IOC linear quadratic tracking (LQT) case." @default.
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• W4205652914 date "2022-01-01" @default.
• W4205652914 modified "2023-09-26" @default.
• W4205652914 title "A Low Complexity Approach to Model-Free Stochastic Inverse Linear Quadratic Control" @default.
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• W4205652914 doi "https://doi.org/10.1109/access.2022.3144933" @default.
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