Optimal Control of Discrete-time Linear Switched Systems with Dynamical Logic-based Switching

This paper investigates the finite-horizon quadratic optimal control problem of discrete-time switched systems with dynamical logic-based switching, where the switching signal is generated by a dynamical logic decision layer. By using the semi-tensor product of matrices and the vector representation of logic, the logic-state and the continuous-state are merged to a single state vector and the original switched system is transferred into an equivalent ordinary switched system. By using the principle of dynamic programming, both the logic control input for the decision layer and the control for the continuous-state layer are designed to minimize the quadratic cost function. An example is provided to demonstrate the proposed method.