Controllability of switched linear systems and the optimal control of nonlinear systems

In this thesis, the controllability of switched linear systems and the optimal control of a class of nonlinear systems are studied. Results in the controllability for switched linear systems are presented using the definition of the cone generated by the system matrices. Several necessary conditions and sufficient conditions for the controllability are given. In the second part of the thesis, a geometric approach is used to transform a nonlinear optimal control problem to a linear quadratic optimization problem. Necessary and sufficient conditions are given for the state space transformations and static state feedback which include a nonlinear change of coordinates for accomplishing both the linearization of the system dynamics and transforming the nonlinear cost function to a linear quadratic form.