输入饱和时的间接自适应最优控制
Indirect Adaptive Optimal Control in the Presence of Input Saturation
摘要：
本文提出了一种结合幅值饱和自适应控制（MSAC）和模型预测控制（MPC）的方法来解决具有参数不确定性和输入饱和的线性二次型跟踪最优控制问题。所提出的MSAC-MPC方法首先关注于稳定解和参数估计，并且当参数学习完成时切换到MPC。我们表明，MSAC，高阶调谐器的基础上，导致参数收敛到真值，同时提供稳定性保证。我们还表明，切换到MPC后，最优性差距是明确的，并与参数估计误差成正比。我们证明了建议MSAC-MPC算法的有效性，通过一个数值例子的基础上的线性二阶，两个输入，不稳定系统。
英文摘要：
In this paper, we propose a combined Magnitude Saturated Adaptive Control (MSAC)-Model Predictive Control (MPC) approach to linear quadratic tracking optimal control problems with parametric uncertainties and input saturation. The proposed MSAC-MPC approach first focuses on a stable solution and parameter estimation, and switches to MPC when parameter learning is accomplished. We show that the MSAC, based on a high-order tuner, leads to parameter convergence to true values while providing stability guarantees. We also show that after switching to MPC, the optimality gap is well-defined and proportional to the parameter estimation error. We demonstrate the effectiveness of the proposed MSAC-MPC algorithm through a numerical example based on a linear second-order, two input, unstable system.
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