Nussbaum gain adaptive backstepping control of nonlinear strict‐feedback systems with unmodeled dynamics and unknown dead zone

Abstract

Summary This paper investigates an adaptive state feedback control problem for a class of single‐input and single‐output nonlinear systems with strict‐feedback form. A novel adaptive control strategy is developed for nonlinear systems with unmodeled dynamics, unknown control directions, dynamic disturbances and unknown dead zone. To stabilize this category of systems, a dynamic signal is introduced to dominate the unmodeled dynamics. Nussbaum gain technique is used to overcome the unknown control directions problem. Nonlinear damping terms are framed to counteract the dynamic disturbances, and the assistant signal is constructed to compensate the influence of symmetric dead zone. The adaptive control approach ensures all signals in the closed‐loop system to be bounded. Finally, a numerical example is used to verify the effectiveness of the theoretical results.

Fault estimation for a class of nonlinear semi‐Markovian jump systems with partly unknown transition rates and output quantization

“…Case 3. i ∈ N i k , N i uk = ∅ In this case, the transition rates are all known. That is, the condition is equivalent to (24). In summary, the condition ofΨ i < 0 can be found in the partly unknown transition probabilities if inequality (12)- (17) holds.…”

“…In practical systems, many kinds of faults always exist and may result to the system being paralyzed. Therefore, detection and estimation of fault are particularly emphasized . Considering the existing fault estimation methods, Liu et al studied estimation and tolerant control of fault for Takagi‐Sugeno (T‐S) fuzzy stochastic systems.…”

“…Therefore, detection and estimation of fault are particularly emphasized. 14,[22][23][24][25][26][27][28][29] Considering the existing fault estimation methods, Liu et al 30 studied estimation and tolerant control of fault for Takagi-Sugeno (T-S) fuzzy stochastic systems. In the work of Jiang and Chowdhury, 31 the actuator fault estimation for a class of multiple-input-multiple-output stochastic systems was reported.…”

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

“…In the past decades, nonlinear control has been paid considerable attention, such as sliding-model control, 1-3 robust control, [4][5][6][7][8] and adaptive control. [9][10][11][12][13] However, stochastic phenomenon always exists in nonlinear systems and effects nonlinear systems' stability.…”

Adaptive stabilization of uncertain nonlinear time‐delay systems with quantized input and output

“…2,3 Therefore, nonlinear control systems without time delay and without quantization have been investigated with various restrictions such as growth rate conditions have been imposed on the unmeasured states (see the works of Qian and Lin, 1 Mazenc and Praly, 4 Astolfi et al, 5 and Marino and Tomei 6 and references therein, if the nonlinearity is known, and the works of Benabdallah et al, 7 Lei and Lin, 8,9 and Yang and Lin, 10 to cite few, if the nonlinear parts of the system are uncertain). For systems with unknown control directions, unknown deadzone, and dynamic disturbances, Nussbaum gain adaptive backstepping control is addressed in the work of Ma et al, 11 and the event-triggered adaptive tracking control problem for multiagent systems with unknown disturbances is studied in the work of Zhang et al 12 Via sampled-data control, adaptive practical stabilization of uncertain nonlinear systems is studied in the work of Mao et al 13 and global stabilization of uncertain switched nonlinear systems is established in the works of Mao et al 14 and Li et al 15 For time-delay systems, many problems are encountered. Such systems can be used to model various processes such as turbojet engines, nuclear reactors, chemical process, and many other physical plants.…”