4.7 Article

Convex Computation of the Region of Attraction of Polynomial Control Systems

期刊

IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 59, 期 2, 页码 297-312

出版社

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2013.2283095

关键词

Capture basin; convex optimization; linear matrix inequalities (LMIs); occupation measures; polynomial control systems; reachable set; region of attraction; viability theory

资金

  1. Grant Agency of the Czech Republic [13-06894S]

向作者/读者索取更多资源

We address the long-standing problem of computing the region of attraction (ROA) of a target set (e. g., a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We show that the ROA can be computed by solving an infinite-dimensional convex linear programming (LP) problem over the space of measures. In turn, this problem can be solved approximately via a classical converging hierarchy of convex finite-dimensional linear matrix inequalities (LMIs). Our approach is genuinely primal in the sense that convexity of the problem of computing the ROA is an outcome of optimizing directly over system trajectories. The dual infinite-dimensional LP on nonnegative continuous functions (approximated by polynomial sum-of-squares) allows us to generate a hierarchy of semialgebraic outer approximations of the ROA at the price of solving a sequence of LMI problems with asymptotically vanishing conservatism. This sharply contrasts with the existing literature which follows an exclusively dual Lyapunov approach yielding either nonconvex bilinear matrix inequalities or conservative LMI conditions. The approach is simple and readily applicable as the outer approximations are the outcome of a single semidefinite program with no additional data required besides the problem description. The approach is demonstrated on several numerical examples.(1)

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