Characterization of Upper Bound on Cost for Linear Quadratic Problems With a Norm‐Bounded Gain Matrix

ABSTRACT This work proposes a new technique to characterize the suboptimality of stabilizing control laws for the infinite‐horizon linear quadratic regulation problem, wherein the norm of the state feedback gain matrix is conditioned to be lesser than a given bound. In contrast to existing techniques where the upper bound on the cost is pre‐specified, this work proposes to compute an upper bound associated with the suboptimal control law(s). To derive the norm‐bounded state feedback gain matrix, sufficient conditions of Krotov global optimal control framework are analyzed for the constrained linear quadratic problem, which typically renders the optimal control problem non‐convex. To address this issue, suitable convex optimization problems are formulated to compute the upper bound independent of initial conditions. The effectiveness of the proposed technique and its comparison with state‐of‐the‐art methods are demonstrated through numerical examples.