Finite-horizon multi-objective generalized H2 control with transients

This paper presents a variational approach to computing the finite-horizon gain of a linear time varying (LTV) system which characterizes the worst-case peak value of a multiple output measured by the generalized Lco norm in response to uncertain initial states and the external disturbance with a bounded energy. This induced operator norm is named the generalized H-2 norm with transients and is determined in terms of the solution to some Lyapunov differential matrix equation and inequality. By using discretization, a semi-definite program is derived to compute the optimal control minimizing the generalized H-2 norm with transients for a given output. It is shown that Pareto optimal controls minimizing the generalized H-2 norms with transients for several outputs turn out to be the generalized H-2 controls with transients with respect to a single multiple artificial output consisting of the parameterized outputs. As a byproduct, necessary and sufficient conditions in terms of the generalized H-2 norm with transients are provided for a LTV system to be finite-time bounded in a modified formulation. The efficiency of the approach proposed is demonstrated on some problems of optimal protection from shock and vibration. (C) 2019 Elsevier Ltd. All rights reserved.