Optimal control obtains a control law for a dynamic system, guaranteeing close loop stability, as well as minimizing a cost function on states and inputs. Analytical solution of an optimal control problem in nonlinear systems results in a partial differential equation, known as Hamilton-Jacobi-Bellman (HJB), which is complex or impossible to solve except in special problems. So researchers have looked for control laws using some simplifying assumptions. One of these methods is inverse optimal control in which a cost function is made according to a stabilizing control law. Meanwhile, there are always some limitations on inputs of physical systems, such as upper or lower bounds. Neglecting input limitations in a control strategy may lead to instability of close loop system. Therefore, in this thesis, an inverse optimal control strategy is proposed for quadratic nonaffine systems with bounded inputs based on a stabilizing control law. Control lyapunov function (CLF) is used to design the stabilizing control law. Although control lyapunov function has been applied to affine systems, it has been rarely considered in nonaffine systems. Since quadratic nonaffine systems consist of vast and important kinds of nonlinear systems, this thesis is focused on quadratic nonaffine systems with bounded inputs. First, designing methods of control lyapunov function to stabilize quadratic nonaffine system are investigated. Then some techniques are proposed to overcome the drawbacks of those methods. Specially, to find a continuous stabilizing control law for general quadratic nonaffine systems with bounded inputs, a new method is proposed which is based on control lyapunov function and coordinates rotation. Next, inverse optimal problem in quadratic nonaffine systems is addressed. The required conditions on inputs are declared and then it is shown that proposed stabilizing control law for quadratic nonaffine systems can also solve an inverse optimal control problem. At last, to prove the proposed method in practice, a continuous stabilizing control law is designed for a laboratory magnetic levitation system, which is a single input quadratic nonaffine system. The designed control law is verified and compared with some other controllers through simulation and experimental implementation. Keywords: Quadratic nonaffine systems, Bounded inputs, Control lyapunov function, Inverse optimal control, Magnetic levitation system
