Optimal Stabilization using Lyapunov Measures

Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this paper. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional Lyapunov function-based stabilization methods, is used for optimal stabilization. The linear Perron-Frobenius transfer operator is used to pose the optimal stabilization problem as an infinite dimensional linear program. Set-oriented numerical methods are used to obtain the finite dimensional approximation of the linear program. We provide conditions for the existence of stabilizing feedback controls and show the optimal stabilizing feedback control can be obtained as a solution of a finite dimensional linear program. The approach is demonstrated on stabilization of period two orbit in a controlled standard map

On the effect of quantization on performance at high rates

We study the effect of quantization on the performance of a scalar dynamical system in the high rate regime. We evaluate the LQ cost for two commonly used quantizers: uniform and logarithmic and provide a lower bound on performance of any centroid-based quantizer based on entropy arguments. We also consider the case when the channel drops data packets stochastically

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Estimation and control with limited information and unreliable feedback

Advancement in sensing technology is introducing new sensors that can provide information that was not available before. This creates many opportunities for the development of new control systems. However, the measurements provided by these sensors may not follow the classical assumptions from the control literature. As a result, standard control tools fail to maximize the performance in control systems utilizing these new sensors. In this work we formulate new assumptions on the measurements applicable to new sensing capabilities, and develop and analyze control tools that perform better than the standard tools under these assumptions. Specifically, we make the assumption that the measurements are quantized. This assumption is applicable, for example, to low resolution sensors, remote sensing using limited bandwidth communication links, and vision-based control. We also make the assumption that some of the measurements may be faulty. This assumption is applicable to advanced sensors such as GPS and video surveillance, as well as to remote sensing using unreliable communication links. The first tool that we develop is a dynamic quantization scheme that makes a control system stable to any bounded disturbance using the minimum number of quantization regions. Both full state feedback and output feedback are considered, as well as nonlinear systems. We further show that our approach remains stable under modeling errors and delays. The main analysis tool we use for proving these results is the nonlinear input-to-state stability property. The second tool that we analyze is the Minimum Sum of Distances estimator that is robust to faulty measurements. We prove that this robustness is maintained when the measurements are also corrupted by noise, and that the estimate is stable with respect to such noise. We also develop an algorithm to compute the maximum number of faulty measurements that this estimator is robust to. The last tool we consider is motivated by vision-based control systems. We use a nonlinear optimization that is taking place over both the model parameters and the state of the plant in order to estimate these quantities. Using the example of an automatic landing controller, we demonstrate the improvement in performance attainable with such a tool