Optimal sensor placement is an important yet unsolved problem in control theory. In this paper, we make use of the Koopman observability gramian to develop an algorithm for optimal sensor placement of discrete time autonomous nonlinear dynamical systems. The Koopman operator lifts nonlinear dynamics to a higher dimensional space where the dynamics evolve approximately linearly in time. Data in biology are often sampled sparsely in time, therefore a method is developed to compute a temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator. In the case of noisy data, a closed form expression for the error in the coarse-grained Koopman operator is derived. A novel algorithm for optimal sensor placement is developed for the case of a fixed initial condition. The method is finally demonstrated on a simulation example.

No abstract

No abstract

No abstract

No abstract