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Linear identification of nonlinear systems: A lifting technique based on the Koopman operator Mauroy, Alexandre ; Goncalves, Jorge in Proceedings of the 55th IEEE Conference on Decision and Control (2016, December) We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state ... [more ▼] We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to a component of the Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is “projected back” to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics. [less ▲] Detailed reference viewed: 164 (8 UL)Optimising time-series experimental design for modelling of circadian rhythms: the value of transient data Mombaerts, Laurent ; Mauroy, Alexandre ; Goncalves, Jorge in IFAC-PapersOnLine (2016, October) Circadian clocks consist of complex networks that coordinate the daily cycle of most organisms. In light/dark cycles, the clock is synchronized (or entrained) by the environment, which corresponds to a ... [more ▼] Circadian clocks consist of complex networks that coordinate the daily cycle of most organisms. In light/dark cycles, the clock is synchronized (or entrained) by the environment, which corresponds to a constant rephasing of the oscillations and leads to a steady state regime. Some circadian clocks are endogenous oscillators with rhythms of about 24-hours that persist in constant light or constant darkness. This operating mechanism with and without entrainment provides flexibility and robustness to the clock against perturbations. Most of the clock-oriented experiments are performed under constant photoperiodic regime, overlooking the transitory regime that takes place between light/dark cycles and constant light or darkness. This paper provides a comparative analysis of the informative potential of the transient time-series data with the other regimes for clock modelling. Realistic data were simulated from 2 experimentally validated plant circadian clock models and sliced into several time windows. These windows represent the different regimes that take place before, meanwhile and after the switch to constant light. Then, a network inference tool was used over each window and its capability of retrieving the ground-truth of the network was compared for each window. The results suggest that including the transient data to the network inference technique significally improves its performance. [less ▲] Detailed reference viewed: 198 (21 UL)Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator ; Mauroy, Alexandre ; Goncalves, Jorge in 10th IFAC Symposium on Nonlinear Control Systems (2016, August) In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and ... [more ▼] In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g. synthetic biology), where it is generally di cult to build feedback control systems due to technical limitations in sensing and actuation. The original framework was derived for monotone systems and all the extensions relied on monotone systems theory. In contrast, we introduce the concept of switching function which is related to eigenfunctions of the so-called Koopman operator subject to a xed control pulse. Using the level sets of the switching function we can (i) compute the set of all pulses that drive the system toward the steady state in a synchronous way and (ii) estimate the time needed by the ow to reach an epsilon neighborhood of the target steady state. Additionally, we show that for monotone systems the switching function is also monotone in some sense, a property that can yield e cient algorithms to compute it. This observation recovers and further extends the results of the original framework, which we illustrate on numerical examples inspired by biological applications. [less ▲] Detailed reference viewed: 123 (1 UL) |
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