Minimum time state feedback control with constrained inputs and states

A state feedback control law that brings the system from a known initial state towards zero in minimum time is proposed. The control law is applicable to linear state space systems with constraints on both the control signals and the states. The type of constraints include bounds on both the input signals and the states, and their derivatives. The proposed method can produce an almost perfect minimum-time control law by feeding back the state vector through precalculated gains. The method contains two design parameters. Depending on the required performance, these two parameters can be tuned in order to trade off computational complexity with time-optimality. Numerical simulations that support the ideas are also given