High-order fully actuated system approaches: Part I. Models and basic procedure

Abstract

The state-space approaches have stayed in an absolutely dominant position in the field of systems and control for over a half century. Although a state-space representation is more suitable for deriving the state-response solution and observation (estimation), it does not provide as much convenience as desired for the control problem. In this paper, the concept of high-order fully actuated (HOFA) systems is firstly revisited, and it is pointed out that HOFA systems serve really as models for control systems rather than representing a small portion of physical control systems. Based on the HOFA model, a basic procedure is proposed for control of nonlinear systems satisfying certain conditions, whose first step converts the nonlinear systems into a pseudo strict-feedback system, and the second step establishes the HOFA model of the system. Once an HOFA model is derived, a controller can be immediately designed to make the closed-loop system a constant linear one with a desired eigenstructure. All the design degrees of freedom existing in the closed-loop system are also provided, which can be further utilised to achieve additional system performance. An example demonstrates the design procedure and shows the effect of the proposed HOFA approach.

High-order fully actuated system approaches: Part II. Generalized strict-feedback systems

“…where m ≥ 1 is some integer, x ∈ R n and u ∈ R r are respectively the state and control vectors. It is shown that the system, when n is a multiple of r, can also be converted, under certain conditions, into a similar strict-feedback form of order m (Duan, 2020d), which reduces to the normal SFS form of (10) in the case of m = 1. Such facts indicate, from the theoretical aspect, that SFSs are a type of very common nonlinear systems.…”

“…Very recently, it is pointed out, and also fully evidenced, in Duan (2020aDuan ( , 2020bDuan ( , 2020d) that the commonly used first-order state-space models are, although very convenient for problems of state solutions and observations, not effective enough for nonlinear system control, while the type of HOFA system models, proposed in Duan (2020aDuan ( , 2020d, are more effective and convenient for control design of nonlinear systems. It is shown in Duan (2020aDuan ( , 2020d that, once a HOFA model for a nonlinear system is obtained, the controller can then be immediately written out, which eliminates the nonlinearities in the system, and eventually results in a constant linear closed-loop system.…”

“…Once the HOFA model (6) is obtained, the controller of the system can then be simply designed as (Duan, 2020a(Duan, , 2020d…”

“…State-space approaches for control system analysis and design have remained absolutely dominant for over a half century, yet it is found that statespace models may not be the best choice for dealing with the control of the system, although they are probably the best choice for state solutions (response analysis) and observations (estimations) (see, Duan, 2020aDuan, , 2020bDuan, , 2020cDuan, , 2020d. In contrast, a type of high-order fully-actuated (HOFA) system models behave more powerfully in the control of many nonlinear systems (Duan, 2020a(Duan, , 2020d. This paper is concerned with the derivation of the HOFA models of three types of generalised strict-feedback nonlinear systems.…”

High-order fully actuated system approaches: Part III. Robust control and high-order backstepping

“…It can be used to deal with the control problem of dynamical systems, but is not the best choice. It was the preconceived occurrence which made it so popular, while it does have certain limitations in dealing with the control of dynamical systems (Duan, 2020a(Duan, , 2020b(Duan, , 2020c.…”