Adaptive decentralized finite‐time output tracking control for MIMO interconnected nonlinear systems with output constraints and actuator faults

Abstract

In this work, we present a novel adaptive decentralized finite-time fault-tolerant control algorithm for a class of multi-input-multi-output interconnected nonlinear systems with output constraint requirements for each vertex. The actuator for each system can be subject to unknown multiplicative and additive faults.Parametric system uncertainties that model the system dynamics for each vertex can be effectively dealt with by the proposed control scheme. The control input gain functions of the nonlinear systems can be not fully known and state dependent. Backstepping design with a tan-type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, with the use of graph theory, finite-time convergence of the system output tracking error into a small set around zero is guaranteed for each vertex, while the time-varying constraint requirement on the system output tracking error for each vertex will not be violated during operation. An illustrative example on 2 interacting 2-degree-of-freedom robot manipulators is presented in the end to further demonstrate the effectiveness of the proposed control scheme.

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

“…Therefore, substantial research efforts have been devoted to robust control designs for uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems during the past decades. Up to now, a series of successful stories have been reported . By introducing an auxiliary design system, a way to achieve output tracking under input constraints was provided in the works of Chen et al By making use of command filters, the explosion of complexity issue was also evaded in the backstepping procedure.…”

“…By introducing an auxiliary design system, a way to achieve output tracking under input constraints was provided in the works of Chen et al By making use of command filters, the explosion of complexity issue was also evaded in the backstepping procedure. A solution of handling output constraints in the presence of actuator faults was given in the work of Jin, by means of the concept of barrier Lyapunov functions. Moreover, the finite‐time convergence of tracking errors was guaranteed by Jin .…”

“…A solution of handling output constraints in the presence of actuator faults was given in the work of Jin, by means of the concept of barrier Lyapunov functions. Moreover, the finite‐time convergence of tracking errors was guaranteed by Jin . A systematic method to predefine the transient and steady‐state performance regarding the overshoot, convergence rate, and steady‐state error was formulated in other works .…”

“…The first one is associated with the control direction. The methods presented in other works necessitate the a priori known control direction of the system. In some particular cases, the control direction is known in advance.…”

Tracking control of nonlinear systems with improved performance via transformational approach

“…It is well known that tracking a known reference with prespecified performance (including convergence rate/time, overshoot, and given tracking precision) is of great practical importance in a number of applications . For instance, in missile tracking, vehicle self‐parking, and multiagent system formation, etc, it is often required or desired to achieve prescribed control performance, which can be adjustable and predefined for safe and reliable accomplishment, in which transformation technique has been proven useful in signal processing and control, ie, Laplace, time‐varying scaling, error/state transformation, and coordinate transformation in feedback control. For the general nonlinear systems with state‐space equation, especially the strict‐feedback systems, except the coordinate transformation, which is usually used for control design, the other typical and popular transformations are as follows: ➀Constant transformation ζ = γz with γ being a constant scalar or matrix and z being the tracking error or state; ➁Error/State transformation with being the function of z ; ➂Time‐varying scaling transformation ζ = β ( t ) z with β ( t ) being the function of time t . …”