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Suboptimal receding horizon control for continuous-time systems

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3 Author(s)
Blanchini, F. ; Univ. of Udine, Italy ; Miani, S. ; Pellegrino, F.A.

Solving a continuous-time optimal control problem under state and control constraints is known to be a very hard task. In this note, we propose a suboptimal solution based on the Euler auxiliary system (EAS). We show that we can determine a continuous-time stabilizing control whose cost not only converges to the optimal as the EAS time parameter vanishes, but it is also upper bounded by the discrete-time cost, no matter how such a parameter is chosen. In particular, continuous-time linear problems with convex cost can be solved by considering a fictitious receding-horizon scheme. Both stability and constraints satisfaction are guaranteed for the continuous-time system. This scheme turns out to be very useful when, due to unstable or poorly damped dynamics, the digital implementation of the control requires a very small (virtually zero) sampling time, since the "time parameter" of the EAS can be much greater than the sampling time, without compromising stability, with a strongly reduced computational burden.

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Automatic Control, IEEE Transactions on  (Volume:48 ,  Issue: 6 )