Robust dynamic programming for min-max model predictive control of constrained uncertain systems

Diehl M.; Bjornberg J.

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Robust dynamic programming for min-max model predictive control of constrained uncertain systems

机译：约束不确定系统的最小-最大模型预测控制的鲁棒动态规划

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We address min-max model predictive control (MPC) for uncertain discrete-time systems by a robust dynamic programming approach, and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The method uses polyhedral representations of the cost-to-go functions and feasible sets, and performs multiparametric programming by a duality based approach in each recursion step. We show how to apply the method to robust MPC, and give conditions guaranteeing closed loop stability. Finally, we apply the method to a tutorial example, a parking car with uncertain mass.

机译：我们通过鲁棒的动态规划方法解决了不确定离散时间系统的最小-最大模型预测控制（MPC），并开发了适用于具有分段仿射成本函数的线性约束多主题系统的算法。该方法使用成本函数和可行集的多面体表示，并在每个递归步骤中通过基于对偶的方法执行多参数编程。我们展示了如何将该方法应用于鲁棒的MPC，并给出了保证闭环稳定性的条件。最后，我们将该方法应用于一个教学示例，即质量不确定的停车场。

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《IEEE Transactions on Automatic Control》 |2004年第12期|p.2253-2257|共5页
作者
Diehl M.; Bjornberg J.;
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正文语种 eng
中图分类自动化系统;
关键词
closed loop systems; discrete time systems; dynamic programming; minimax techniques; predictive control; stability; uncertain systems; closed loop stability; constrained uncertain discrete-time systems; linearly constrained polytopic systems; min-max model predict;

机译：闭环系统;离散时间系统;动态编程;最小极大值技术;预测控制;稳定性;不确定性系统;闭环稳定性;约束的不确定离散时间系统;线性约束的多变量系统;最小-最大模型预测;

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2. The Explicit Constrained Min-Max Model Predictive Control of a Discrete-Time Linear System With Uncertain Disturbances [J] . Gao Y., Chong K. T. Automatic Control, IEEE Transactions on . 2012,第9期

机译：具有不确定扰动的离散线性系统的显式约束最小-最大模型预测控制
3. Robust stabilization of uncertain time-varying discrete systems and comments on "an improved approach for constrained robust model predictive control" [J] . Mao WH. Automatica . 2003,第6期

机译：不确定时变离散系统的鲁棒镇定，并评论“一种改进的约束鲁棒模型预测控制方法”
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5. Analytical modeling, analysis and robust control of uncertain nonlinear dynamical systems by using sliding mode control (SMC) and quantitative feedback theory (QFT). [D] . Rajapakse, Nuraj I. 2006

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6. Robust Time-Delay Feedback Control of Vehicular CACC Systems with Uncertain Dynamics [O] . Xiulan Song, Li Chen, Ke Wang, 2020

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7. Robust Dynamic Programming for Min-Max Model Predictive Control of Constrained Uncertain Systems [O] . Moritz Diehl, Jakob Björnberg 2011

机译：受限不确定系统最小-最大模型预测控制的鲁棒动态规划
8. Robust Control Design for Uncertain Dynamic Systems Using Approximate Models. Part 2: The Multivariable Case [R] . Owens, D. H., Chotai, A. 1982

机译：基于近似模型的不确定动态系统鲁棒控制设计。第2部分：多变量案例

Robust dynamic programming for min-max model predictive control of constrained uncertain systems

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