Robust adaptive control for a class of cascaded nonlinear systems with applications to space interception

Abstract

SUMMARYThis paper proposes a robust H ∞ ‐based adaptive backstepping control scheme for the output stabilization of a special class of cascaded nonlinear systems. This kind of systems possess the feature that the first sub‐equation is a linear perturbed system, whereas the rest ones perform a general semi‐strict feedback form. Different from the conventional backstepping design approach, the special cascaded structure ensures to introduce the H ∞ technique to the backstepping procedure such that both the robust performance and the robust stability can be simultaneously guaranteed. Within the Lyapunov framework, the proposed control scheme is proved to guarantee (i) the uniformly ultimate boundedness of the system signals with a bound that can be made arbitrarily small by suitably choosing control parameters; (ii) asymptotic output stabilization as long as the uncertain nonlinearities and external disturbances vanish; and (iii) scriptL2‐performance of the closed‐loop system. A space interception scenario is utilized to demonstrate the effectiveness of the proposed control scheme. Copyright © 2013 John Wiley & Sons, Ltd.

Adaptive sliding‐mode control for spacecraft relative position tracking with maneuvering target

“…Remark To ensure that the mass estimate stays in a closed domain, the common projection function is defined as follows: Obviously, the projection function has the jump discontinuity at the points and . On the contrary, the proposed projection function is continuous and has the nice properties (Equation ); we can guarantee that if we choose the initial mass guess inside the set , the mass estimate can always stay inside the set .…”

“…where > 0 and Φ = s T B (q) . Define the setΩm ch = {m ch ∶ m min − ≤m ch ≤ m max + }; it can be easily concluded that the projection-based adaptive law (27) has the following nice properties:…”

“…However, this method needs the prior knowledge of disturbance bound. To inherit the both advantages of the adaptive law in the works of Huang et al and Lee and Utkin, a switching gain‐adaption law was derived from coupling of the methods in previous works in the work of Plestan et al Meanwhile, the projection‐type adaptive law has been proposed to deal with the parameter uncertainty such as mass parameter uncertainty or inertia matrix uncertainty in the works of Xu and Yao and Zhang et al Then, Yoon et al proposed a modified smooth projection algorithm. Summarizing the above works, it can be concluded that the switching gain‐adaption law in the work of Plestan et al and smooth projection algorithm in the work of Yoon and Agrawal fit well for dealing with the great disturbance and parameter uncertainty in this problem.…”

“…Based on the established LOS relative position model, such problem is formulated as the ASMC problem for a class of second‐order mechanical system without prior knowledge of disturbance bound and mass parameter, which makes it convenient to use some useful physical properties and provide a nice basis in the control law design (for details, please see Remarks and ). In the context of control theory, by integrating the smooth‐projection algorithm in the work of Yoon and Agrawal and equivalent‐control‐dependent gain method in the works of Lee and Utkin and Plestan et al a modified ASMC law is proposed to deal with both the disturbance and uncertain mass parameter. Compared with the works of Zhu et al and Zhang et al, the proposed projection‐based adaptive law is smooth and can force the mass estimate to remain in a desired domain (for details, please see Remarks and ). Besides, this paper generalizes the single‐input situation in the work of Plestan et al to the second‐order mechanical system, and note that the equivalent‐control‐dependent gain method can only weaken chattering phenomenon; the hyperbolic tangent function is used to take place of the sign function to eliminate the effects of chattering, and the boundedness of the closed‐loop system is discussed (for detail, please see Remarks and ).…”

Tracking and parameter identification for model reference adaptive control

“…While usually dependent on some structural properties of the system, adaptive control is valuable because of its ability to solve tracking problems for a wide range of possible values of the unknown model parameters including higher‐order systems. One area where adaptive control is important is in aerospace problems . In basic adaptive control for some classes of control systems (such as linear systems), one can often use nonstrict (or weak) Lyapunov functions to ensure that tracking objectives are realized, and then achieve parameter identification (ie, convergence of the parameter estimates to the true parameter values) provided that a persistency of excitation (PE) condition is also satisfied.…”