A Neural Network Solution for Fixed-Final Time Optimal Control of Nonlinear Systems

Abstract

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Fixed‐time fault tolerant control for a class of switched nonlinear systems

“…The authors in Reference 15 discovered fixed‐time stability and then the fixed‐time stability was defined in Reference 16. Subsequently, some significant results on fixed‐time control problem for nonlinear systems emerged in References 17‐25. To list a few: a fixed‐time output feedback control for the double integrator systems was designed via homogeneity and Lyapunov techniques in Reference 22.…”

“…To list a few: a fixed‐time output feedback control for the double integrator systems was designed via homogeneity and Lyapunov techniques in Reference 22. The fixed‐time optimal control method had been developed for nonlinear systems with known nonlinear functions in Reference 17. The state feedback fixed‐time control algorithm was developed for the strict‐feedback nonlinear systems with state‐independent external disturbance in Reference 19.…”

“…The fixed‐time tracking control approach was presented for multiagent systems 24 . However, it has to be noticed that one common drawback of References 17‐25 is that the powers of the actual control and virtual control signals are equal to one. Most importantly, the system dynamics in References 17‐25 are nonswitched and the common seen faults have not been taken into account.…”

“…The main contributions of this article are listed as follows:This work first addresses the fixed‐time stability problem for nonstrict‐feedback switched nonlinear systems with unknown functions. Note that the authors in Reference 27 consider the fixed‐time control problem for switched systems, the virtual control input, actual control powers of Reference 27 are one, and fixed‐time convergence has not been considered either. Although References 17‐24 investigated the fixed‐time control problems for nonlinear systems, the fixed‐time stability has been proved that all closed‐loop signals converge to zero in fixed time. Unfortunately, the common feature of the models in References 17‐24 is that the actuator failure has not been taken into consideration. …”

Neural network solution for suboptimal control of non-holonomic chained form system

“…We provide uniform convergence results over a Sobolev space. By Brockett's theorem (Cheng et al, 2005), non-holonomic systems cannot be asymptotically stabilized around a fixed point under any smooth (or even continuous) time-independent state feedback control law. In this paper, a smooth nearly-optimal time-varying control is designed to stabilize the chained form system.…”