Finite-horizon multi-objective generalized [formula omitted] control with transients

Abstract

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 L∞ norm in response to uncertain initial states and the external disturbance with a bounded energy. This induced operator norm is named the generalized H2 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 H2 norm with transients for a given output. It is shown that Pareto optimal controls minimizing the generalized H2 norms with transients for several outputs turn out to be the generalized H2 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 H2 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.