High-order fully actuated system approaches: Part V. Robust adaptive control

Abstract

A type of high-order fully actuated (HOFA) systems with both nonlinear uncertainties and timevarying unknown parameters is considered, and a direct approach for the designs of robust adaptive stabilising controllers and robust adaptive tracking controllers is proposed based on the Lyapunov stability theory. The established controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed-loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, and the adaptation part adjusts online the controller to suit the effect of the unknown timevarying parameter vector. The proposed controller guarantees that the tracking error of the state to a given signal and the estimation error of the parameter vector finally converge globally into a bounded ellipsoid. Particularly, in the case that the unknown parameter vector is constant, an adaptive scheme that enables global asymptotical tracking is presented. An example demonstrates the effect of the proposed approach.

High-order fully actuated system approaches: part VII. Controllability, stabilisability and parametric designs

“…The fact mentioned in the above Proposition 3.3 has been demonstrated by many examples (see those in Duan, 2020dDuan, , 2020e, 2021aDuan, , 2021bDuan, , 2021cDuan, , 2021d. While in the case where the considered system physical or ( 26) is not controllable, its model appears to be more complicated.…”

“…In the recent two series of papers, Duan (2020aDuan ( , 2020bDuan ( , 2020c, and Duan (2020dDuan ( , 2021aDuan ( , 2021bDuan ( , 2021cDuan ( , 2021d, a different approach other than the state-space approach is proposed, which is termed as the HOFA system approach. In this paper, several aspects of the proposed HOFA approach are further improved and proposed, and by now a relatively more complete general picture of the HOFA system approaches has been roughly sketched.…”

“…Two parametric design approaches for the proposed general HOFA models are proposed, which provide all the degrees of freedom to be further utilised to meet other design performance. Based on the proposed general HOFA models with multiple orders, many other control design problems, such as robust control (Duan, 2021c), adaptive control (Duan, 2021d), robust adaptive control (Duan, 2020d), and disturbance rejection (Duan, 2020e), can also be easily treated and better solved.…”

“…(10) Clearly, in the case of η = 1, the above HOFA model (8), or (10), reduces to the form of (1) with E = I, which is proposed in Duan (2020a) (see, also Duan, 2021a). When nonlinear uncertainties, unknown parameters and disturbances are added to this basic HOFA model, robust and adaptive control as well as disturbance rejection control have been investigated in Duan (2020dDuan ( , 2020e, 2021cDuan ( , 2021d.…”

High-order fully actuated system approaches: Part VIII. Optimal control with application in spacecraft attitude stabilisation

“…As argued in Duan (2020a), Duan (2020b), Duan (2020d) and Duan (2020j), high-order fully actuated (HOFA) models also serve as a general model for dynamical control systems, and are especially convenient and effective in dealing with control problems. The demonstration of this with robust control, adaptive control and disturbance rejection control has been given in Duan (2020f), Duan (2020g), Duan (2020h) and Duan (2020i). A huge advantage of the HOFA models is that their full-actuation feature allows one to cancel the known nonlinearities in the system and hence to convert, to an extent, a nonlinear problem into a linear one.…”