Nonlinear Control for a Class of Non-Control Affine Systems

The optimal control problem for non-control affine nonlinear systems can usually be solved only exactly with numerical tools. In almost all other cases approximations are needed (also in the numerical formulation the optimization problem is usually treated as sequential quadratic approximations), either in the problem statement or in the solution procedure or in both. This work proposes to map the original problem into a class of special non-control affine systems consisting of a static state dependent part and a dynamic control affine system. By exploiting the available degrees of freedom in the mapping and using converse approaches, it is possible to design the mapping in such a way that the Hamilton Jacobi Bellman equation corresponding to the input affine part is solved.
Since an optimal state feedback controller requires the knowledge of the state of the plant an observer becomes necessary. The most commonly used nonlinear observers are adopted to apply for the proposed system class. Additionally a new reduced order observer is presented which robustly estimates the state of the system. It uses dynamic scaling and filtering to approximately solve a partial differential equation appearing in the design procedure.