Optimal control for switched nonlinear systems with state-dependent switching

A dynamic optimization method is proposed for optimal control of switched systems with fixed switching sequences. The subsystems are activated automatically once the state variable passes through a certain switching surface in the state space. In order to solve this optimal control problem, firstly, the control vector parameterization (CVP) technique is applied to approximate the control input by a piecewise constant function. Second, the partial derivatives of the objective function with respect to parameterized control input are computed in a costate-based formula. Finally, the dynamic optimization method is presented by the gradient-based optimization algorithm.