We develop in this thesis four sufficiency criteria for the generalized problem of Bolza. These results represent a unification, in the sense that they can be applied to both the calculus of variations and to optimal control problems, as well as to problems with nonsmooth data. The first criterion, "point convexity", extends the convexity approach of Rockafellar. However, we derive a "Hamiltonian-Jacobi" approach which can be applied when the point convexity assumption fails to be satisfied. The method employed for this criterion brings to light a new point of view concerning the Jacobi condition in the classical calculus of variations. The latter can be considered as a condition which guarantees the existence of a canonical transformation transforming the original Hamiltonian to a locally concave-convex Hamiltonian. The third sufficiency criterion is an extension of the Hamilton-Jacobi approach from optimal control to the generalized problem of Bolza. This result gives rise to another sufficiency criterion in terms of a certain inequality. Our theorems on sufficient conditions are closely related. We prove that under certain assumptions the last three approaches can be unified. By this we mean that their hypotheses are equivalent. However, the point convexity, and hence the convexity, criterion turns out to have the most restrictive hypotheses of the four. The generality of the theorems proven stems to a great extent from the fact that not only non-differentiable but even infinite- valued functions are allowed in the treatment. The utility of using such functions appears when we apply these theorems to optimal control problems. / Science, Faculty of / Mathematics, Department of / Graduate

Note:

Hu Guoqiang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 87-93). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Nonlinear Control Systems --- p.2 / Chapter 1.2 --- Output Regulation --- p.5 / Chapter 1.3 --- Semiglobal Stabilization --- p.7 / Chapter 1.4 --- A Benchmark Nonlinear Control Problem --- p.8 / Chapter 1.5 --- Contribution of this Thesis --- p.10 / Chapter 2 --- Semiglobal Robust Output Regulation of a Class of Nonlinear Systems via Output Feedback Control --- p.12 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.2 --- Semiglobal Backstepping Technique --- p.16 / Chapter 2.3 --- Output Regulation Converted to Stabilization --- p.18 / Chapter 2.4 --- Solvability of the Semiglobal Robust Stabilization Problem via Partial State Feedback --- p.23 / Chapter 2.5 --- Design of the Output Feedback Regulator --- p.35 / Chapter 2.6 --- An example --- p.39 / Chapter 2.7 --- Concluding Remarks --- p.46 / Chapter 3 --- Disturbance Rejection of the RTAC system --- p.50 / Chapter 3.1 --- Disturbance Rejection Problem Formulated into Output Regulation Problem --- p.51 / Chapter 3.2 --- Solvability of the Output Regulation Problem via Measurement Output Feedback Control --- p.53 / Chapter 3.3 --- Parameters Design and Simulation Results --- p.57 / Chapter 3.4 --- Concluding Remarks --- p.58 / Chapter 4 --- Robust Disturbance Rejection of the RTAC System --- p.63 / Chapter 4.1 --- Introduction --- p.63 / Chapter 4.2 --- A General Framework for Robust Output Regulation --- p.64 / Chapter 4.3 --- Robust Asymptotic Disturbance Rejection of the RTAC System --- p.69 / Chapter 4.4 --- Algorithms to Design and Optimize the Parameters Kx and L --- p.73 / Chapter 4.5 --- Parameters design and Simulation Results --- p.75 / Chapter 4.6 --- Concluding Remarks --- p.76 / Chapter 5 --- Conclusions --- p.86 / Biography --- p.87 / Bibliography --- p.88 / Appendix A. ITAE Prototype Design --- p.94

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 160-164).

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Thesis (Ph. D.)--Lehigh University, 2002. / Includes vita. Includes bibliographical references (leaves 203-206).

Thesis made openly available per email from author, 5-26-2016.

published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

No description available.