ABSTRACT
This chapter addresses the time-optimal control system, where the performance measure is the minimization of the transition time from initial state to any target or desired state. It also addresses fuel-optimal control (FOC) system, where the performance measure is minimization of a quantity proportional to fuel consumed by the process or plant. The FOC arise often in aerospace systems where the vehicles are controlled by thrusts and torques. These inputs like thrusts are due to the burning of fuel or expulsion of mass. The chapter provides the energy-optimal control system. It considers a plant with some constraints on their states. The chapter examines the problem of minimizing the time taken for the system to go from an initial state to the desired final state of a linear, time-invariant system. The slack variable approach, often known as Valentine's method, transforms the given inequality state constraint into an equality state constraint by introducing a slack variable.
