Optimal sampled-data control, and generalizations on time scales

In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for which the state variable evolves on a given time scale (arbitrary non-empty closed subset of R), and the control variable evolves on a smaller time scale. Sampled-data systems are then a particular case. Our proof is based on the construction of appropriate needle-like variations and on the Ekeland variational principle.Comment: arXiv admin note: text overlap with arXiv:1302.351

Sampled-data and discrete-time H2 optimal control

This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This discrete-time H2 problem is always singular. Motivated by this, in this paper we give a treatment of the discrete-time H2 optimal control problem in its full generality. The results we obtain are then applied to the singular discrete-time H2 problem arising from the sampled-data H2 problem. In particular, we give conditions for the existence of optimal sampled data controllers. We also show that the H2 performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, we show that the optimal sampled-data H2 performance converges to the continuous-time optimal H2 performance as the sampling period converges to zero.

Sampled-data and discrete-time H2H_2 optimal control

This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This discrete-time H2 problem is always singular. Motivated by this, in this paper we give a treatment of the discrete-time H2 optimal control problem in its full generality. The results we obtain are then applied to the singular discrete-time H2 problem arising from the sampled-data H2 problem. In particular, we give conditions for the existence of optimal sampled data controllers. We also show that the H2 performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, we show that the optimal sampled-data H2 performance converges to the continuous-time optimal H2 performance as the sampling period converges to zero