146 research outputs found
Uniform global asymptotic stability of a class of adaptively controlled nonlinear systems
We give a new explicit, global, strict Lyapunov function construction for the error dynamics for adaptive tracking control problems, under an appropriate persistency of excitation condition. We then allow time-varying uncertainty in the unknown parameters. In this case, we construct input-to-state stable Lyapunov functions under suitable bounds on the uncertainty, provided the regressor also satisfies an affine growth condition. This lets us quantify the effects of uncertainties on both the tracking and the parameter estimation. We illustrate our results using Rössler systems. © 2009 IEEE
A nonparametric learning framework for nonlinear robust output regulation
This paper proposes a nonparametric learning solution framework for a generic
internal model design of nonlinear robust output regulation. The global robust
output regulation problem for a class of nonlinear systems with output feedback
subject to a nonlinear exosystem can be tackled by constructing a linear
generic internal model, provided that a continuous nonlinear mapping exists. An
explicit continuous nonlinear mapping was constructed recently in [1] under the
assumption that the steady-state generator is linear in the exogenous signal.
We further relax such an assumption to a relaxed assumption that the
steady-state generator is polynomial in the exogenous signal. A nonparametric
learning framework is proposed to solve a linear time-varying equation to make
the nonlinear continuous mapping always exist. With the help of the proposed
framework, the nonlinear robust output regulation problem can be converted into
a robust non-adaptive stabilization problem for the augmented system with
integral Input-to-State Stable (iISS) inverse dynamics. Moreover, a dynamic
gain approach can adaptively raise the gain to a sufficiently large constant to
achieve stabilization without requiring any a priori knowledge of the
uncertainties appearing in the dynamics of the exosystem and the system. We
further apply the nonparametric learning framework to globally reconstruct and
estimate multiple sinusoidal signals with unknown frequencies without using
adaptive techniques. An explicit nonlinear mapping can directly provide the
estimated parameters, which will exponentially converge to the unknown
frequencies. As a result, a feedforward control design is proposed to solve the
output regulation using our nonparametric learning framework.Comment: 15 pages; Nonlinear control; iISS stability; output regulation;
parameter estimation; Non-adaptive contro
Consensus and Flocking under Communication Failures for a Class of Cucker-Smale Systems
In this paper, we study sufficient conditions for the emergence of asymptotic consensus and flocking in a certain class of non-linear generalised Cucker-Smale systems subject to multiplicative communication failures. Our approach is based on the combination of strict Lyapunov design together with the formulation of a suitable persistence condition for multi-agent systems. The latter can be interpreted as a lower bound on the algebraic connectivity of the time-average of the interaction graph generated by the communication weights, and provides quantitative decay estimates for the variance functional along the solutions of the system
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