Barrier Function-Based Asymptotic Tracking Control of Uncertain Nonlinear Systems With Multiple States Constraints

Abstract

This technical note focus on the tracking control problem of uncertain nonlinear systems with multiple states constraints. Based on the Barrier Lyapunov function and backstepping technology, a new continuous smooth control solution can be ultimately synthesized to realize asymptotic tracking control in presence of multiple states constraints and modeling uncertainties. Firstly, the modeling uncertainties are divided into periodic and un-periodic components and Fourier expansion technology is employed to translate the periodic disturbance into the form which can be easily compensated. Then the Barrier Lyapunov function are flexibly utilized to design the virtual control law of every step and the final controller, which can guarantee the specified states within certain bounds regardless of the amplitude of system output. Meanwhile, a novel nonlinear control technology is introduced to each design step to realize the final asymptotic tracking control despite the matched and mismatched uncertainties. By analyzing the choice of the control parameters, the backstepping cross-term is skillfully dealt with and the stability of the whole system is proved rigorously. Finally, the simulation results on a three-order nonlinear hydraulic system demonstrate the satisfactory performance of the proposed control method.

High Precision Motion Control of Electro-Mechanical Launching Platform with Modeling Uncertainties: A New Integrated Error Constraint Asymptotic Design

“…(1) OCAR-ARC: This is the controller proposed in this research. The detailed controller structure can be found in ( 17) and (19). To facilitate the experiment, the number of the Fourier expansion in ( 7) is taken as m = 2.…”

“…Schematic diagram of the electro-mechanical launching platform shown in Figure 1, which includes pitch and azimuth subsystems and, for each subsystem, the servo motor is driven by the drivers to rotate the inertial launching load. As in [3,7,14,17,19], the current loop dynamic will be ignored for its response is faster than the mechanical response. We take the azimuth subsystem as the research object, then, considering the coupling disturbance between the two motion axes, the dynamics equation can be described as…”

“…In the aforementioned existing literature, the RISE controller utilizes a continuous robust integral term to achieve asymptotic control, but the design structure of RISE is slightly complicated and it may accompany the farfetched assumption that the second derivative of disturbance needs to be bounded [13,14]. Another effective method to realize asymptotic control is SMC [9,10], however the possible jittery control signal may arouse the un-modelled dynamic of the launching platform and weaken the expected performance [19], while, for the novel nonlinear continuous asymptotic control in the presence of uncertain disturbance proposed in [20] for nonlinear systems, it is easy to retrofit the design and convenient to be integrated with other control structures. In addition, for systems with strong parameter uncertainties, the transient tracking performance is also worthy of attention.…”

Quasi-Adaptive Sliding Mode Motion Control of Hydraulic Servo-Mechanism With Modeling Uncertainty: A Barrier Function-Based Method

“…the external disturbance, nonlinear friction and input nonlinearities always exist. More researchers focus on dealing with the unstructured uncertainties [10,11]. Yao et al successively proposed the adaptive robust control [12] and the integrated indirect/direct adaptive robust control [13], which can achieve excellent motion control performance in both of structured and unstructured modeling uncertainties [14].…”

Adaptive Neural Path Following Control of Underactuated Surface Vessels With Input Saturation

“…Besides input saturation, another challenge of path following problem is the model uncertainties, which is a common problem in engineering application [22], [23]. In order to deal with the model uncertainties, the neural network (NN) was used to approximate a nonlinear function based on the universal approximation property in [24].…”