A novel optimal control method based on sparsity

What is it about?

Maximum hands-off control is a control that maximises the time duration on which the control is 0. Maximum hands-off control is a kind of green control, since the control can maximally stop actuators, such as a gasoline engine, so that CO2 emission, vibration, and noise can be reduced. The optimal control is described as an L0 optimal control, which is non-convex and discontinuous, and it is shown to be equivalent to convex and continuous L1 optimal control under a simple assumption, called normality. We also extend the finite-horizon maximum hands-off control to model predictive control (MPC) and provide stability conditions.

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Photo by Phillip Glickman on Unsplash

Photo by Phillip Glickman on Unsplash

Why is it important?

In view of application, maximum hands-off control has great potential to revolutionise the industry for its green characteristic; saving energy, reducing CO2, and eliminating vibration/noise, as mentioned above. On the other hand, in view of control theory, the paper gives a new theorem of the equivalence of L0 optimality and L1 optimality, which has been recently investigated in wide area of research such as signal processing, machine learning, statistics, etc.

Perspectives