Year: 2020
Type: article
Abstract: We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both inducedL2and terminal Euclidean norm penalties on outputs. Existing computational approaches include the power iteration and the bisection of a Riccati Differential Equation (RDE). The power iteration has low computation time per iteration but overall convergence can be slow. In contrast, the RDE condition provides guaranteed bounds on the induced gain but single RDE integration can be slow. The complementary features of these two algorithms are combined to develop a new algorithm that is both fast and provides provable upper and lower bounds on the induced norm within the desired tolerance. The algorithm also provides a worst-case disturbance input that achieves the lower bound on the norm. We also present a new proof which shows that the power iteration for this problem converges monotonically. Finally, we show a controllability Gramian based simpler computational method for inducedL2-to-Euclidean norm. This can be used to compute the reachable set at any time on the horizon. Numerical examples are provided to demonstrate the proposed algorithm.
Source: IEEE Control Systems Letters
Authors: Jyot Buch, Murat Arcak, Peter Seiler
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G6320102633
OpenAlex ID: W3082158860