The role of the generalised continuous algebraic Riccati equation in impulse-free continuous-time singular LQ optimal control

New results in impulse-free continuous-time cheap LQ optimal control

“…In this paper, we have shown that a fundamental question that remained open in [9], [10] on the connection between the generalised Riccati equation and the singular LQ problem has an affirmative answer, at least in the cheap case. In a forthcoming paper, it is shown that this result holds under a more general framework.…”

“…The recent papers [9], [10], have investigated the connection of the generalised continuous-time algebraic Riccati L.Ntogramatzidis@curtin.edu.au equation -which is defined by substitution of the inverse of R with the pseudo-inverse in the standard algebraic Riccati equation -and the solution of the singular LQ optimal control problem. In these papers it is shown in particular that whenever the generalised Riccati equation admits a symmetric solution, the corresponding singular LQ problem admits an impulse-free optimal control from any initial condition of the system.…”

Generalized Finite-Horizon Linear-Quadratic Optimal Control

“…The corresponding results in continuous time can be obtained along the same lines as the discrete-time case; see Ferrante and Ntogramatzidis (2013b) and references therein.…”