Adaptive control of time‐delay nonlinear HOFA systems with unmodeled dynamics and unknown dead‐zone input

Abstract

This paper focuses on the control problem of time-delay nonlinear high-order fully actuated (HOFA) systems with unmodeled dynamics and unknown dead-zone input. The primary objective of this paper is to design an adaptive controller by using the HOFA systems approach. To do so, we need to tackle some technical obstacles. Firstly, in order to deal with unmodeled dynamics in the HOFA systems, the technique of changing the supply rate is combined with the HOFA systems approach. Secondly, an adaptive dead-zone inverse is constructed to compensate for the influence of the unknown asymmetrical dead-zone input nonlinearity. Then, the controller is designed by the HOFA systems approach, and it is proved that all states of the systems converge to a bounded region based on the Lyapunov-Krasovskii functions. Finally, the simulation results demonstrate the effectiveness of the designed adaptive controller. K E Y W O R D Sadaptive controller designs, dead-zone input, fully actuated nonlinear systems, time-delay systems, unmodeled dynamics INTRODUCTIONIn recent years, the HOFA systems approach has received much attention, 1-7 which has been proven to be very effective and simple in dealing with the analysis and control problems of second-order or higher-order nonlinear systems such as Lagrangian systems, angular momentum, inverted pendulum systems, and so forth. A significant advantage of this approach is that a linear constant closed-loop system with an arbitrary assignable eigenstructure can be obtained, and all the design degrees of freedom existing in the closed-loop system are provided. Therefore, the feature helps to deal with many nonlinear system control problems, such as robust control, 3 adaptive control, 4 robust adaptive control, 5 disturbance attenuation 6 and disturbance decoupling. 7 On the basis of the study above, Liu 8 investigated the control problem of HOFA nonlinear systems with time-varying delays in the discrete-time domain. The problem of adaptive control for a class of time-delay systems was studied by the HOFA systems approach, 9 and a continuous adaptive controller was designed for the system. However, among the above results, it should be pointed out that there is still content for development based on the HOFA systems approach to deal with nonlinear problems such as nonlinear time-delay, unmodeled dynamics and dead-zone input, and so forth. It is well known that time-delay is widespread in the practical control systems, such as electrical power systems, communication systems, teleoperation systems, chemical reactor systems, and so forth. [10][11][12] Besides, as we all know, many systems cannot be accurately modeled due to certain factors when dealing with the control problems of practical physical systems, so we often encounter nonlinear systems with unmodeled dynamics. The existence of time-delay

Decentralized model reference adaptive control for interconnected systems with time‐varying delays and unknown dead‐zone inputs

“…A smooth dead‐zone inverse function was proposed in Reference 24 to deal with the problem of output tracking when there is a time delay and a dead‐zone input in the system. In Reference 25, the system state in the nonlinear time‐delay system was obtained for convergence to a bounded region by creating the dead‐zone inverse function and numerous adaptive laws. In terms of systems covering time delays and dead zones, a precise tracking adaptive control scheme was proposed in Reference 26.…”

“…Due to the skillful construction of Lyapunov–Krasovskii functionals with two integrals and absolute values of unknown parameters, it is easy to solve the positive definite matrices used in this paper through the Lyapunov equation, thus reducing the processing effort required to calculate the LMIs. The gains of the decentralized controller are accurately expressed and used in the gains of the adaptive laws. There are certain inequality criteria that must be satisfied by the suggested controller gains (see (7) in Reference 25, (7)–(9) in Reference 28, and (6) in Reference 31), which may be hard to achieve in some cases. The gain function of the controller is explicitly expressed in this paper, which is easy to implement in practice.…”

“…The tracking errors in References 24 and 32 converged to a bounded region using the proposed dead‐zone inverse function and four designed adaptive laws. When the dead‐zone inverse function and independent controller compensation are adopted to solve the system control problem, the controller will be inevitably more complicated (see, e.g., Reference 25). Furthermore, the controller structures suggested in References 33 and 34 consist of standard model reference adaptive controllers as well as additional independent compensation controllers.…”

“…The gains of the decentralized controller are accurately expressed and used in the gains of the adaptive laws. There are certain inequality criteria that must be satisfied by the suggested controller gains (see (7) in Reference 25, (7)–(9) in Reference 28, and (6) in Reference 31), which may be hard to achieve in some cases. The gain function of the controller is explicitly expressed in this paper, which is easy to implement in practice.…”

Weak disturbance decoupling of high‐order fully actuated nonlinear systems

“…The problems of robust control, adaptive control and robust adaptive control for HOFA nonlinear systems were solved with a HOFA control method in References 24, 25 and 26. Reference 27 focuses on the control problem of time‐delay nonlinear HOFA systems with unmodeled dynamics and unknown dead‐zone input. Reference 28 presents an observer‐based fault‐tolerant controller framework for time‐varying HOFA systems.…”