Abstract
Drawing upon Lyapunov stability theories and online adaptive dynamic programming (ADP) technique, we propose a novel optimal control scheme for the nonlinear time delay system. Our contribution is twofold. First, we investigate the asymptotical stability problem and obtain a generalized stability condition in terms of linear matrix inequalities (LMIs). An explicit, easy-computing delay bound is presented by virtue of Gronwall's inequality. Second, we propose the neural network (NN)-based optimal control strategy by utilizing two approximate NNs. The NN-based optimal control law converges to the real optimal control law since that the estimation errors of NNs weights converge to zero. Numerical examples are presented to illustrate our results.
Highlights
For various control systems and communication networks, time delays are widely existed and may cause bad performance, poor robustness, and even task failure
For linear systems with constant time delay, it is readily available to the necessary and sufficient conditions on stability in terms of linear matrix inequalities (LMIs) from time-domain theories [4] and small gain theorem from frequency-domain techniques [5], to name a few
The stability on nonlinear systems subject to constant time delays is mainly investigated based on sliding mode control theories [6], H∞ optimization method [7], LMI techniques [8], neural networkds (NNs) and adaptive control maneuver [9], etc
Summary
For various control systems and communication networks, time delays are widely existed and may cause bad performance, poor robustness, and even task failure. It is of fundamental significance to analyze the stability and control problems on systems subject to time delays. Time delay systems are analyzed either by time-domain or frequency-domain approach (see [1]–[3], and the references therein). For linear systems with constant time delay, it is readily available to the necessary and sufficient conditions on stability in terms of linear matrix inequalities (LMIs) from time-domain theories [4] and small gain theorem from frequency-domain techniques [5], to name a few. The stability on nonlinear systems subject to constant time delays is mainly investigated based on sliding mode control theories [6], H∞ optimization method [7], LMI techniques [8], neural networkds (NNs) and adaptive control maneuver [9], etc. The past work, sheds few lights on the development of nonlinear time delay system theories, and leaves it an open problem yet up to now
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
