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Closed‐form solution to finite‐horizon suboptimal control of nonlinear systems
Author(s) -
Heydari Ali,
Balakrishnan S. N.
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3222
Subject(s) - riccati equation , mathematics , linear quadratic regulator , optimal control , nonlinear system , algebraic riccati equation , partial differential equation , control theory (sociology) , controller (irrigation) , horizon , differential equation , mathematical analysis , control (management) , mathematical optimization , computer science , physics , geometry , quantum mechanics , artificial intelligence , agronomy , biology
Summary Finite‐horizon optimal control of input‐affine nonlinear systems with fixed final time is considered in this study. It is first shown that the associated Hamilton–Jacobi–Bellman partial differential equation to the problem is reducible to a state‐dependent differential Riccati equation after some approximations. With a truncation in the control equation, a near optimal solution to the problem is obtained, and the global onvergence properties of the closed‐loop system are analyzed. Afterwards, an approximate method, called Finite‐horizon State‐Dependent Riccati Equation (Finite‐SDRE), is suggested for solving the differential Riccati equation, which renders the origin a locally exponentially stable point. The proposed method provides online feedback solution for controlling different initial conditions. Finally, through some examples, the performance of the resulting controller in finite‐horizon control is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.