On stability and stabilization of periodic discrete-time systems with an application to satellite attitude control

An alternative stability analysis theorem for nonlinear periodic discrete-time systems is presented. The developed theorem offers a trade-off between conservatism and complexity of the corresponding stability test. In addition, it yields a tractable stabilizing controller synthesis method for linear periodic discrete-time systems subject to polytopic state and input constraints. It is proven that in this setting, the proposed synthesis method is strictly less conservative than available tractable synthesis methods. The application of the derived method to the satellite attitude control problem results in a large region of attraction

An Offline-Sampling SMPC Framework with Application to Automated Space Maneuvers

In this paper, a sampling-based Stochastic Model Predictive Control algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need of real-time implementability of guidance and control strategies for automated rendezvous and proximity operations between spacecraft. The paper presents considers the validation of the proposed control algorithm on an experimental testbed, showing how it may indeed be implemented in a realistic framework. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simultaneously considered. The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided, and under mild assumptions, asymptotic stability in probability of the origin can be established. The offline sampling approach in the control design phase is shown to reduce the computational cost, which usually constitutes the main limit for the adoption of Stochastic Model Predictive Control schemes, especially for low-cost on-board hardware. These characteristics are demonstrated both through simulations and by means of experimental results

Threshold-Free Population Analysis Identifies Larger DRG Neurons to Respond Stronger to NGF Stimulation

Sensory neurons in dorsal root ganglia (DRG) are highly heterogeneous in terms of cell size, protein expression, and signaling activity. To analyze their heterogeneity, threshold-based methods are commonly used, which often yield highly variable results due to the subjectivity of the individual investigator. In this work, we introduce a threshold-free analysis approach for sparse and highly heterogeneous datasets obtained from cultures of sensory neurons. This approach is based on population estimates and completely free of investigator-set parameters. With a quantitative automated microscope we measured the signaling state of single DRG neurons by immunofluorescently labeling phosphorylated, i.e., activated Erk1/2. The population density of sensory neurons with and without pain-sensitizing nerve growth factor (NGF) treatment was estimated using a kernel density estimator (KDE). By subtraction of both densities and integration of the positive part, a robust estimate for the size of the responsive subpopulations was obtained. To assure sufficiently large datasets, we determined the number of cells required for reliable estimates using a bootstrapping approach. The proposed methods were employed to analyze response kinetics and response amplitude of DRG neurons after NGF stimulation. We thereby determined the portion of NGF responsive cells on a true population basis. The analysis of the dose dependent NGF response unraveled a biphasic behavior, while the study of its time dependence showed a rapid response, which approached a steady state after less than five minutes. Analyzing two parameter correlations, we found that not only the number of responsive small-sized neurons exceeds the number of responsive large-sized neurons—which is commonly reported and could be explained by the excess of small-sized cells—but also the probability that small-sized cells respond to NGF is higher. In contrast, medium-sized and large-sized neurons showed a larger response amplitude in their mean Erk1/2 activity

Constrained stabilization of periodic discrete-time systems via periodic Lyapunov functions

This article considers the problem of constrained stabilization of periodically time-varying discrete-time systems, or shortly, periodic systems. A modification of a recent result on periodic Lyapunov functions, which are required to decrease at every period rather than at every time instant, is exploited to obtain a new stabilizing controller synthesis method for periodic systems. We demonstrate that for the relevant class of linear periodic systems subject to polytopic state and input constraints, the developed synthesis method is advantageous compared to the standard Lyapunov synthesis method. An illustrative example demonstrates the effectiveness of the proposed method