A Youla–Kučera parameterization approach to output feedback relatively optimal control

This paper presents a continuous time solution to the problem of designing a relatively optimal control, precisely, a dynamic control which is optimal with respect to a given initial condition and is stabilizing for any other initial state. This technique provides a drastic reduction of the complexity of the controller and successfully applies to systems in which (constrained) optimality is necessary for some “nominal operation” only. The technique is combined with a pole assignment procedure. It is shown that once the closed-loop poles have been fixed and an optimal trajectory originating from the nominal initial state compatible with these poles is computed, a stabilizing compensator which drives the system along this trajectory can be derived in closed form. There is no restriction on the optimality criterion and the constraints. The optimization is carried out over a finite-dimensional parameterization of the trajectories. The technique has been presented for state feedback. We propose here a technique based on the Youla–Kučera parameterization which works for output feedback. The main result is that we provide conditions for solvability in terms of a set of linear algebraic equations.