The explicit control law for hybrid systems via parametric programming

An algorithm is presented for the derivation of the explicit optimal control policy for linear dynamical systems that also involve (i) logical decisions and (ii) constraints on process inputs and outputs. The control actions are usually computed by solving at regular time intervals an on-line optimization problem based on a set of measurements that specify the current process state. The approach presented in the paper derives the optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimization problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.