7,648 research outputs found
Locally optimal controllers and globally inverse optimal controllers
In this paper we consider the problem of global asymptotic stabilization with
prescribed local behavior. We show that this problem can be formulated in terms
of control Lyapunov functions. Moreover, we show that if the local control law
has been synthesized employing a LQ approach, then the associated Lyapunov
function can be seen as the value function of an optimal problem with some
specific local properties. We illustrate these results on two specific classes
of systems: backstepping and feedforward systems. Finally, we show how this
framework can be employed when considering the orbital transfer problem
Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers
Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers
Global Stabilization of Triangular Systems with Time-Delayed Dynamic Input Perturbations
A control design approach is developed for a general class of uncertain
strict-feedback-like nonlinear systems with dynamic uncertain input
nonlinearities with time delays. The system structure considered in this paper
includes a nominal uncertain strict-feedback-like subsystem, the input signal
to which is generated by an uncertain nonlinear input unmodeled dynamics that
is driven by the entire system state (including unmeasured state variables) and
is also allowed to depend on time delayed versions of the system state variable
and control input signals. The system also includes additive uncertain
nonlinear functions, coupled nonlinear appended dynamics, and uncertain dynamic
input nonlinearities with time-varying uncertain time delays. The proposed
control design approach provides a globally stabilizing delay-independent
robust adaptive output-feedback dynamic controller based on a dual dynamic
high-gain scaling based structure.Comment: 2017 IEEE International Carpathian Control Conference (ICCC
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