A Low Complexity Approach to Model-Free Stochastic Inverse Linear Quadratic Control

A Low Complexity Approach to Model-Free Stochastic Inverse Linear Quadratic Control
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DOI：
10.1109/access.2022.3144933
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发表时间：
2022
期刊：
IEEE Access
影响因子：
3.9
通讯作者：
Shanelle G. Clarke;Sooyung Byeon;Inseok Hwang
Shanelle G. Clarke;Sooyung Byeon;Inseok Hwang
中科院分区：
计算机科学3区
文献类型：
--
作者：
Shanelle G. Clarke;Sooyung Byeon;Inseok Hwang

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针对离散时间无限时域随机线性二次型调节器（LQR），提出了一种无模型随机逆最优控制（IOC）算法。我们提出的算法利用丰富的可用系统轨迹，以低（空间，样本和计算）复杂度的方式恢复控制增益K和成本函数参数（Q，R）。通过利用对随机LQR的见解，我们通过满足等价最优性条件来保证无模型随机IOC LQR的适定性。控制增益K的精确解通过确定性的、低复杂度的最小二乘法来恢复。使用K，我们解决了一个完全无模型的非迭代半定规划（SDP）问题，以获得一个唯一的（标量模糊度）（Q，R），其中最优性和可行性是共同确保的。通过推导样本复杂度的界，我们表明，非渐近性能的无模型随机IOC LQR的信号噪声比（SNR）的系统状态和输入信号的有限集的特点。我们提出了一个基于模型的版本的算法的特殊情况下，（A，B）是可用的，我们，进一步，提供扩展的随机无模型IOC线性二次跟踪（LQT）的情况下。
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 K and cost function parameters (Q,R) 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 Certainty Equivalence optimality conditions. The exact solution of the control gain K is recovered via a deterministic, low complexity Least Squares approach. Using K, we solve a completely model-free non-iterative SemiDefinite Programming (SDP) problem to obtain a unique (up to a scalar ambiguity) (Q,R), 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 (A,B) is available, and we, further, provide the extension to the Stochastic Model-Free IOC linear quadratic tracking (LQT) case.