Approximation-Based Adaptive Tracking Control of Pure-Feedback Nonlinear Systems With Multiple Unknown Time-Varying Delays

• Published in: IEEE transaction on neural networks and learning systems 2010-11, Vol.21 (11), p.1804-1816
• Main Authors: Wang, Min, Ge, Shuzhi Sam, Hong, Keum-Shik
• Format: Article
• Language: English
• Subjects: Adaptative systems; Adaptive control; Adaptive systems; Algorithms; Applied sciences; Artificial Intelligence; Artificial neural networks; Backstepping; Computer science; control theory; systems; Computer simulation; Control equipment; Control system analysis; Control system synthesis; Control theory. Systems; Delay; Dynamical systems; Dynamics; Educational institutions; Exact sciences and technology; Feedback; Mathematical analysis; Mathematical Computing; Mathematical models; neural network; Neural Networks (Computer); Nonlinear Dynamics; Nonlinear systems; nonlinear time-delay systems; Pattern Recognition, Automated - methods; pure-feedback systems; Software Design; Studies; System theory; Time Factors; Time varying systems; Tracking control
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2010.2073719

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables as virtual controls , and of the actual control . The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel Lyapunov-Krasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of and . Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.