Adaptive saturation compensation for strict‐feedback systems with unknown control coefficient and input saturation

Abstract

Summary This work presents an adaptive saturation compensation scheme for the strict‐feedback uncertain systems with unknown control coefficient and input saturation. An adaptive saturation dynamic filter that does not require the a priori information of the completely unknown control coefficient is incorporated to correct position errors online to reduce the saturation effect. A Nussbaum‐type function is employed to handle the unknown control coefficient and avoid the control singularity. The adaptive command‐filtered backstepping is employed to derive the adaptive controller. The repeated differential operations of stabilizing functions required in the traditional backstepping are obviated due to command filters. It is analyzed that the designed adaptive controller achieves the system output tracking and the closed‐loop uniform ultimate stability. A simulation example is provided to validate the scheme.

Event‐triggered disturbance rejection tracking for surface ships under stochastic disturbances and actuator saturation

“…where 𝜉 1 and 𝜉 2 denote the state vectors produced by the auxiliary dynamic filter. 33 K 1 = K T 1 and K 2 = K T 2 represent the 3 × 3 positive-definite design matrices and Δ𝜏 = 𝜏 − 𝜏 c represents the control derivation vector induced by actuator saturation (15). The signals 𝜉 1 and 𝜉 2 are the filtered versions of the saturation effects on the variables being controlled.…”

“…To address the actuator saturation effects, the following auxiliary filer is constructed by $$$$ \kern0.3em d{\xi}_1\kern0.5em =-{K}_1{\xi}_1 dt+J\left(\psi \right){\xi}_2 dt $$$$ $$$$ d{\xi}_2\kern0.5em =-{M}^{-1}{K}_2{\xi}_2 dt+{M}^{-1}\Delta \tau dt $$$$ where $$$ {\xi}_1 $$$ and $$$ {\xi}_2 $$$ denote the state vectors produced by the auxiliary dynamic filter 33 . $$$ {K}_1={K}_1^{\mathrm{T}} $$$ and $$$ {K}_2={K}_2^{\mathrm{T}} $$$ represent the $$$ 3\times 3 $$$ positive‐definite design matrices and $$$ \Delta \tau =\tau -{\tau}_c $$$ represents the control derivation vector induced by actuator saturation (15).…”

Toward Resilience in Mixed Critical Industrial Control Systems: A Multi-Disciplinary View

“…Hence, the problem formulation of model-based adaptive control is meaningful for resilient control. In general, if system (2) has the lower-triangular form, or strict-feedback form, then backstepping designs originating from [51], [52] are very fruitful not only for the case of ordinary differential equations [53], but also for other classes such as stochastic systems [54], etc.…”

Command filter‐based adaptive control of flexible‐joint manipulator with input saturation and output constraints

“…With the help of the auxiliary dynamic signal, approximation-based adaptive control was proposed for uncertain nonaffine plants in Zhang and Gao [17]. An auxiliary system was constructed to compensate the effect of the input saturation in Olofsson and Nielsen [18]; the same tactics were presented in earlier studies [19,20]. Besides, the Gaussion error function was employed to handle with estimating the model along with an error bound in Si and Dong [21].…”