Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

Abstract

Summary This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.

Fault Compensation Control of MIMO Nonlinear Systems Subject to Unknown Control Directions

“…where u i (t) is a control input to be designed, λ i (t) and δ i (t) are the time-varying partial loss of effectiveness and the float faults. Assumption 1(See [33], [34]): There exist unknown positive constants λ i , δ i , and d i , such that…”

“…Correspondingly, just as Theodorakopoulos analyzed in [32], the simplification in structure and calculation still made PPC more widely used. For example, [33] focused on solving PPC of SISO strict-feedback nonlinear systems. The error transformation functions were associated with the specific Nussbaum-type functions.…”

“…2) Different from [33][34][35], by introducing the idea of inverse hyperbolic tangent function, an appropriate logarithm-type of error conversion function cooperated with directional function is proposed to realize PPC.…”

Fault compensation control of MIMO nonlinear systems subject to unknown control directions

“…Correspondingly, just as Theodorakopoulos analyzed in [38], the simplification in structure and calculation still made PPC more widely used. For example, [39] focused on solving PPC of SISO strictfeedback nonlinear systems. The error transformation functions were associated with the specific Nussbaumtype functions.…”

“…(2) Based on the idea of inverse hyperbolic tangent function, an appropriate logarithm-type of error conversion function cooperated with directional function is proposed to realize PPC for the MIMO system. This is different from the tan-type commonly used in [39][40][41]. (3) By the programming of the control form, neither the approximation strategies in [27,28] nor the higherorder derivatives of reference signals in [42][43][44] are used.…”