Observability-Based Approach to Design, Analysis and Optimization of Dynamical Systems
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The present dissertation aims to use the coupling between actuation and sensing in nonlinear systems to alternatively design a set of feasible control policies, to find the minimum number of sensors, or to find an optimal sensors configuration. Feasibility, here, means a combination of sen- sory system and control policy which guarantees observability. In some cases the optimality of the obtained solution is also considered. In some nonlinear systems, full observability requires active sensing, and will be shown how control policies that guarantee observability can be obtained by con- sidering the geometry of the system dynamics. The observability matrix is used to test observability, whereas for the optimization problem observability Gramian matrix is used. This dissertation also considers the stability in designing controllers. The problem of designing a stabilizing control pol- icy for a control-affine nonlinear system is addressed. The effect of time-varying control on the observability is investigated and shown to potentially improve the system observability. A particular application of the techniques considered here is the problem of designing network sensing and topology based on the observability criteria. The goal is to develop a protocol for the network which guarantees privacy. Furthermore, given a network of connected agents, we would like to determine which nodes should be observed to maximize information about the entire network. This dissertation begins with theoretical basis then moves towards applications of the theory. The first application is navigation of an autonomous ground robot with limited inertial sensing, motivated by the visuomotor system of insects. The second application is the problem of detecting an epidemic disease, which demonstrates design of an observability-based optimal network.