Journal
IEEE ACCESS
Volume 8, Issue -, Pages 47768-47775Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2020.2979068
Keywords
Asymptotic stability; Backstepping; Stability criteria; Nonlinear systems; Lyapunov methods; Numerical stability; Convergence; Finite-time stability; rational-exponent Lyapunov function; backstepping; Lyapunov methods; Bernoulli inequality
Categories
Funding
- Research Council of Norway (RCN) through the Centre for Research-based Innovation on Marine Operations, Centre for Research-based Innovation on Marine Operations (CRI MOVE), through the RCN-project [237929]
Ask authors/readers for more resources
In this paper, we propose a novel state-feedback backstepping control design approach for a single-input single-output (SISO) nonlinear system in strict-feedback form. Rational-exponent Lyapunov functions (ReLFs) are employed in the backstepping design, and the Bernoulli inequality is primarily adopted in the stability proof. Semiglobal practical finite-time stability, or global asymptotically stability, is guaranteed by a continuous control law using a commonly used recursive backstepping-like approach. Unlike the inductive design of typical finite-time backstepping controllers, the proposed method has the advantage of reduced design complexity. The virtual control laws are designed by directly canceling the nonlinear terms in the derivative of the specific Lyapunov functions. The terms with exponents are transformed into linear forms as their bases. The stability proof is simplified by applying several inequalities in the final proof, instead of in each step. Furthermore, the singularity problem no longer exists. The weakness of the concept of practical finite-time stability is discussed. The method can be applied to smoothly extend numerous design methodologies with asymptotic stability with a higher convergence rate near the equilibrium. Two numerical case studies are provided to present the performance of the proposed control.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available