access icon free Exact tracking control of uncertain non-linear systems with additive disturbance

© The Institution of Engineering and Technology
Received 16/10/2013, Accepted 23/09/2014, Revised 08/09/2014, Published 19/03/2015

This study deals with adaptive control of non-linear systems in the strict-feedback form with parametric uncertainties and additive disturbance. The disturbance in the systems is assumed to be bounded. No knowledge of the uncertain parameters, an upper bound of the uncertain parameter vector, a bound of unknown disturbance and the differentiability of the external disturbance is required. Under the weakened assumptions, two continuous robust adaptive control schemes are proposed. In the first control scheme, a modified adaptive backstepping design procedure is proposed to remove overparameterisation. A novel damping term with the estimate of unknown disturbance bound and a positive time-varying integral function are introduced in the control law to counteract the destabilising effects of the external disturbance. In the second scheme, an alternative continuous adaptive controller is designed. Instead of the estimate of the disturbance bound, an adaptive parameter is incorporated into the control design. In both of the two control schemes, the design parameters are freely chosen to improve the control performance. It is proved that the proposed two adaptive control schemes can guarantee that the closed-loop signals are bounded and the output tracking error converges to zero asymptotically in spite of the disturbance. Finally, a numerical example is included to show the effectiveness of the presented control methods.

Inspec keywords: uncertain systems; feedback; control system synthesis; adaptive control; continuous systems; closed loop systems; robust control; nonlinear control systems

Other keywords: disturbance bound estimation; strict-feedback form; adaptive backstepping design procedure; external disturbance; uncertain nonlinear systems; damping term; parametric uncertainties; positive time-varying integral function; closed-loop signals; exact tracking control; continuous robust adaptive control schemes; destabilising effects; output tracking error; alternative continuous adaptive controller design; adaptive parameter; additive disturbance

Subjects: Nonlinear control systems; Control system analysis and synthesis methods; Self-adjusting control systems; Stability in control theory

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