3,307 research outputs found
Partial Stability Concept in Extremum Seeking Problems
The paper deals with the extremum seeking problem for a class of cost
functions depending only on a part of state variables of a control system. This
problem is related to the concept of partial asymptotic stability and analyzed
by Lyapunov's direct method and averaging schemes. Sufficient conditions for
the practical partial stability of a system with oscillating inputs are derived
with the use of Lie bracket approximation techniques. These conditions are
exploited to describe a broad class of extremum-seeking controllers ensuring
the partial stability of the set of minima of a cost function. The obtained
theoretical results are illustrated by the Brockett integrator and rotating
rigid body.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019
Exponential Stabilization of Nonholonomic Systems by Means of Oscillating Controls
This paper is devoted to the stabilization problem for nonlinear driftless
control systems by means of a time-varying feedback control. It is assumed that
the vector fields of the system together with their first order Lie brackets
span the whole tangent space at the equilibrium. A family of trigonometric
open-loop controls is constructed to approximate the gradient flow associated
with a Lyapunov function. These controls are applied for the derivation of a
time-varying feedback law under the sampling strategy. By using Lyapunov's
direct method, we prove that the controller proposed ensures exponential
stability of the equilibrium. As an example, this control design procedure is
applied to stabilize the Brockett integrator.Comment: 25 pages, 2 figure
On Exponential Stabilization of Nonholonomic Systems with Time-Varying Drift
A class of nonlinear control-affine systems with bounded time-varying drift
is considered. It is assumed that the control vector fields together with their
iterated Lie brackets satisfy Hormander's condition in a neighborhood of the
origin. Then the problem of exponential stabilization is treated by exploiting
periodic time-varying feedback controls. An explicit parametrization of such
controllers is proposed under a suitable non-resonance assumption. It is shown
that these controllers ensure the exponential stability of the closed-loop
system provided that the period is small enough. The proposed control design
methodology is applied for the stabilization of an underwater vehicle model and
a front-wheel drive car.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019
Partial Stabilization of Stochastic Systems with Application to Rotating Rigid Bodies
This paper addresses the problem of stabilizing a part of variables for
control systems described by stochastic differential equations of the Ito type.
The considered problem is related to the asymptotic stability property of
invariant sets and has important applications in mechanics and engineering.
Sufficient conditions for the asymptotic stability of an invariant set are
proposed by using a stochastic version of LaSalle's invariance principle. These
conditions are applied for constructing the state feedback controllers in the
problem of single-axis stabilization of a rigid body. The cases of control
torques generated by jet engines and rotors are considered as illustrations of
the proposed control design methodology.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019
Approximating a flexible beam model in the Loewner framework
The paper develops the Loewner approach for data-based modeling of a linear
distributed-parameter system. This approach is applied to a controlled flexible
beam model coupled with a spring-mass system. The original dynamical system is
described by the Euler-Bernoulli partial differential equation with the
interface conditions due to the oscillations of the lumped part. The transfer
function of this model is computed analytically, and its sampled values are
then used for the data-driven design of a reduced model. A family of
approximate realizations of the corresponding input-output map is constructed
within the Loewner framework. It is shown that the proposed finite-dimensional
approximations are able to capture the key properties of the original dynamics
over a given range of observed frequencies. The robustness of the method to
noisy data is also investigated.Comment: This is a preprint version of the paper submitted to the 2023
European Control Conference (ECC
Periodic switching strategies for an isoperimetric control problem with application to nonlinear chemical reactions
This paper deals with an isoperimetric optimal control problem for nonlinear
control-affine systems with periodic boundary conditions. As it was shown
previously, the candidates for optimal controls for this problem can be
obtained within the class of bang-bang input functions. We consider a
parametrization of these inputs in terms of switching times. The control-affine
system under consideration is transformed into a driftless system by assuming
that the controls possess properties of a partition of unity. Then the problem
of constructing periodic trajectories is studied analytically by applying the
Fliess series expansion over a small time horizon. We propose analytical
results concerning the relation between the boundary conditions and switching
parameters for an arbitrary number of switchings. These analytical results are
applied to a mathematical model of non-isothermal chemical reactions. It is
shown that the proposed control strategies can be exploited to improve the
reaction performance in comparison to the steady-state operation mode.Comment: Submitted to "Applied Mathematical Modelling
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