Value function in maximum hands-off control for linear systems
Value function in maximum hands-off control for linear systems
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DOI：
10.1016/j.automatica.2015.10.043
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
Takuya Ikeda;M. Nagahara
中科院分区：
文献类型：
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作者：
Takuya Ikeda;M. Nagahara
在本文中，我们研究了最大不干预控制的值函数。最大放手控制，又称稀疏控制，是可行控制中的L 0-最优控制。在受控对象模型的假设下，虽然L 0测度是不连续的、非凸的，但我们证明了在受控对象模型的假设下，值函数或控制的最小L 0范数是可达集中初始状态的连续严格凸函数。然后将有限域最大越界控制推广到模型预测控制(MPC)，并利用值函数的连续性和凸性证明了递推的可行性和稳定性。
In this brief paper, we study the value function in maximum hands-off control. Maximum hands-off control, also known as sparse control, is the L 0-optimal control among the feasible controls. Although the L 0 measure is discontinuous and non-convex, we prove that the value function, or the minimum L 0 norm of the control, is a continuous and strictly convex function of the initial state in the reachable set, under an assumption on the controlled plant model. We then extend the finite-horizon maximum hands-off control to model predictive control (MPC), and prove the recursive feasibility and the stability by using the continuity and convexity properties of the value function.