Robust resilient control for parametric strict feedback systems with prescribed output and virtual tracking errors

Abstract

Summary This paper investigates the robust resilient control problem for a class of parametric strict feedback nonlinear systems with prescribed output and virtual tracking errors performance. The resilience is governed by a continuously nonlinear control gains function, which endows the virtual and actual controllers with self‐adjusting abilities with respect to transformed error surfaces. The proposed control scheme is adaptation, estimation, and approximation‐free in the presence of unknown parameters and nonlinearities, and only a number of control gains, which is equal to the relative degree of the considered plants, need to be selected in applications. It is proved by rigorous analysis that the output tracking errors are confined in predefined prescribed performance functions under some nonrestrictive initial conditions, and the bounds of states are obtained characterized as control gains and systemic function‐associated constants. Finally, comparative illustrative examples are given to demonstrate the effectiveness of the proposed control scheme.

Prescribed performance control approaches, applications and challenges: A comprehensive survey

“…And, the research on control designing for such systems can provide a significant guidance for control system developing for a lot of practical systems. Due to the high-order strict-feedback formulation, a common approach is the combination of back-stepping and PPC [143][144][145][146], which stabilizes all system states and guarantees system outputs with satisfactory predefined performance. Dead-zone inputs, unknown control directions and actuator failures are very common problems which widely exist in dynamic systems.…”

Extended prescribed performance control with input quantization for nonlinear systems

“…23 A robust resilient control for parametric strict feedback system is proposed with prescribed output and virtual tracking errors. 24 From the perspective of computationally inexpensive control, it is shown that linearly parameterized approximators, which require large volume of computing resources in practice, can be reduced to robust partial-state feedback. 25 With this point kept in mind, a low-complexity global approximation-free PPC (LC-PPC) is proposed for unknown pure feedback systems to provide a further simplified control scheme at the utmost possibility, 26 the merits of LC-PPC are twofold: (i) the PPC problem isolates the output performance boundary from chosen control gains in both virtual and actual control signals, and (ii) the complexity problem is circumvented without resorting to filtering.…”

“…25 With this point kept in mind, a low-complexity global approximation-free PPC (LC-PPC) is proposed for unknown pure feedback systems to provide a further simplified control scheme at the utmost possibility, 26 the merits of LC-PPC are twofold: (i) the PPC problem isolates the output performance boundary from chosen control gains in both virtual and actual control signals, and (ii) the complexity problem is circumvented without resorting to filtering. Improved versions of LC-PPC has been following reported, concerning output feedback for switched system, 23 fault-tolerant with unknown control direction, 27 deadzone input, 28 robust resilient control, 24 and other applications. [29][30][31][32] Despite the merits of LC-PPC, from another point of view, it is known that the description of "PPC problem isolates the output performance boundary from chosen control gains" is equivalent to "bounds of tracking errors are not controlled by control gains directly," which is, of course, a non-ideal result to users in some sense.…”

“…1. On comparison with the pioneering PPC framework, 23,24,[26][27][28][29][30][31][32] the proposed extended PPC (E-PPC) scheme relaxed the necessary condition that ultimate value of PPF 𝜌 ∞ is chosen as small as possible, the first feature of proposed E-PPC is that state tracking errors can be constrained by boundary functions characterizing by PPFs and control gains simultaneously. While, state tracking errors are constrained by boundary PPFs only.…”

Approximation-free Quantitative Prescribed Performance Control of Unknown Strict-feedback Systems

“…In the last several years, lots of PPC-based control researches of strict-feedback systems have been reported [2]- [3], [22]- [23]. Unfortunately, all of them cannot quantitatively set prescribed performance (i.e., overshoot and convergence time) for control errors.…”