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DC Field | Value | Language |
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dc.contributor.advisor | Mhaskar, Prashant | - |
dc.contributor.author | Homer, Tyler | - |
dc.date.accessioned | 2019-02-20T16:50:41Z | - |
dc.date.available | 2019-02-20T16:50:41Z | - |
dc.date.issued | 2019 | - |
dc.identifier.uri | http://hdl.handle.net/11375/23925 | - |
dc.description.abstract | In this thesis, we report advances to the theory of stabilization of control systems. A first contribution of this thesis is to utilize the concept of stability regions to derive control laws to stabilize nonlinear systems with stochastic disturbances and subject to lack of availability of state measurements. In this direction, the probability of destabilizing behavior is approximated that incorporates the effect of the observation error. In a second contribution, we determine, for any given input-constrained nonlinear control system, the largest region from which stabilization can be achieved, termed the null controllable region (NCR). Indeed, a key result of this thesis is to propose a control law that induces stabilization from the entire NCR. In this direction, two methods to construct NCRs are proposed using completely different principles. In one major contribution, the NCR is given by special smooth optimal trajectories integrated in reverse-time using Pontryagin's Maximum Principle. In another major contribution, this same region is given by iteratively expanding an initial Lyapunov-based stability region by applying a reachability test to boundary cells. A further contribution of this thesis is to use the geometry of a collection of NCRs, corresponding to modulated input constraints, to construct a control law that guarantees the stabilization of the closed-loop system. In this direction, special modifications are introduced in order to apply this technique to a chemical reactor example. In a final contribution, knowledge of the NCR is used to enable the formulation of a simple finite difference scheme to solve otherwise intractable Hamilton-Jacobi-Bellman equations in order to generate Lyapunov functions with maximal regions of attraction. | en_US |
dc.language.iso | en | en_US |
dc.title | On the Stability Regions of Nonlinear Control Systems | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | Chemical Engineering | en_US |
dc.description.degreetype | Thesis | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
dc.description.layabstract | In this thesis, advances in the theory of stabilization of control systems are reported. A control system explains how a physical system evolves in time and how this evolution can be influenced through the use of manipulable inputs. Accordingly, we consider the problem of determining what sequence of inputs must be used in order for the system to converge to a desired state. The first contribution provides a controller design for systems that contain states that cannot be directly measured and must be actively inferred from the changes in measurable states: a situation which is occurs frequently in practice. In this work, theoretical arguments about the region in which stability can be guaranteed are used to establish the odds of stabilizing certain systems afflicted by unpredictable random disturbances, even in the presence of uncertainty caused by estimation of the unmeasured states. The second contribution to this problem is to efficiently determine all of the states of a system that can be stabilized to any given setpoint, termed the null controllable region (NCR). In this direction, two solutions are brought fourth based on completely different principles. The third contribution is to use the geometry of the NCR to indicate the input that must be used to induce stabilization. In this direction, several examples are used to illustrate the efficacy of the technique, including a chemical reactor example. These are the main contributions of the thesis. A final contribution considers optimal control problems: steering systems in a lowest cost manner with respect to a given metric. The article explains how knowledge of the boundary of the NCR simplifies the procedure for solving optimal control problems and how this solution reveals how to stabilize the system. | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Homer_Tyler_G_2019January_PHD.pdf | 1.78 MB | Adobe PDF | View/Open |
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