An Efficient Method to Estimate the Suboptimality of Affine Controllers
An Efficient Method to Estimate the Suboptimality of Affine Controllers
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DOI：
10.1109/tac.2011.2139390
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发表时间：
2011-04
影响因子：
6.8
通讯作者：
Michael J. Hadjiyiannis;P. Goulart;D. Kuhn
中科院分区：
文献类型：
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作者：
Michael J. Hadjiyiannis;P. Goulart;D. Kuhn
我们考虑对随时间变化的线性离散时间系统在有限的地平线上运行的强大反馈控制。对于此类系统，我们考虑设计可靠的因果控制器的问题，该问题可最大程度地减少凸二次成本函数的期望值，但要遵守混合线性状态和输入约束。对于此类问题的最佳控制策略的确定通常在计算上是棘手的，但是可以通过限制可接受的策略的类别来计算次优政策，以使观察结果成为现实。通过使用合适的重新参数化和可靠的优化技术，可以将这些近似值作为凸优化问题有效求解。我们研究了由于使用此类仿射政策而导致的最优损失。使用二元参数并通过对双重变量施加仿射结构，我们提供了一种有效的方法来估算任何因果策略的最佳成本函数值的下限，通过求解锥度程序，该程序的大小是大小的多项式功能问题数据。然后可以使用该下限来量化仿射政策产生的最优性损失。
We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally intractable, but suboptimal policies can be computed by restricting the class of admissible policies to be affine on the observation. By using a suitable re-parameterization and robust optimization techniques, these approximations can be solved efficiently as convex optimization problems. We investigate the loss of optimality due to the use of such affine policies. Using duality arguments and by imposing an affine structure on the dual variables, we provide an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data. This lower bound can then be used to quantify the loss of optimality incurred by the affine policy.