Abstract
Maximum hands-off control is a control mechanism that maximizes the length of the time duration on which the control is exactly zero. Such a control is important for energy-aware control applications, since it can stop actuators for a long duration and hence the control system needs much less fuel or electric power. In this article, we formulate the maximum hands-off control for linear discrete-time plants by sparse optimization based on the l 1 norm. For this optimization problem, we derive an efficient algorithm based on the alternating direction method of multipliers (ADMM). We also give a model predictive control formulation, which leads to a robust control system based on a state feedback mechanism. Simulation results are included to illustrate the effectiveness of the proposed control method.
Highlights
Sparsity is one of the most important notions in recent signal/image processing [1], machine learning [2], communications engineering [3], and high-dimensional statistics [4]
1.1 Contributions In this paper, we first analyze discrete-time finite-horizon hands-off control, where we give a feasibility condition based on the system controllability, and develop an equivalence theorem between 0- and 1-optimal controls based on the idea of restricted isometry property (RIP)
To calculate discrete-time hands-off control, we propose to use alternating direction method of multipliers (ADMM), which is widely applied to signal/image processing [21], and we prove by simulation that ADMM is very effective in feedback control since it requires very few iterations
Summary
Sparsity is one of the most important notions in recent signal/image processing [1], machine learning [2], communications engineering [3], and high-dimensional statistics [4]. 1.1 Contributions In this paper, we first analyze discrete-time finite-horizon hands-off control, where we give a feasibility condition based on the system controllability, and develop an equivalence theorem between 0- and 1-optimal controls based on the idea of RIP These are different from the case of continuous-time hands-off control in [16], where the concept of normality for an optimal control problem was adopted. To calculate discrete-time hands-off control, we propose to use ADMM, which is widely applied to signal/image processing [21], and we prove by simulation that ADMM is very effective in feedback control since it requires very few iterations. 1.2 Outline The paper is organized as follows: in Section 2, we formulate the discrete-time maximum hands-off control, and prove the feasibility property and the 0- 1 equivalence based on the RIP.
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