4 research outputs found
Stabilizability and Disturbance Rejection with State-Derivative Feedback
In some practical problems, for instance in the control of mechanical systems using
accelerometers as sensors, it is easier to obtain the state-derivative signals than the state
signals. This paper shows that (i) linear time-invariant plants given by the state-space
model matrices {A,B,C,D} with output equal to the state-derivative vector are not observable
and can not be stabilizable by using an output feedback if det(A)=0 and (ii) the
rejection of a constant disturbance added to the input of the aforementioned plants, considering
det(A)≠0, and a static output feedback controller is not possible. The proposed
results can be useful in the analysis and design of control systems with state-derivative
feedback
Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics
In this paper, we propose in a Hilbertian setting a second-order
time-continuous dynamic system with fast convergence guarantees to solve
structured convex minimization problems with an affine constraint. The system
is associated with the augmented Lagrangian formulation of the minimization
problem. The corresponding dynamics brings into play three general time-varying
parameters, each with specific properties, and which are respectively
associated with viscous damping, extrapolation and temporal scaling. By
appropriately adjusting these parameters, we develop a Lyapunov analysis which
provides fast convergence properties of the values and of the feasibility gap.
These results will naturally pave the way for developing corresponding
accelerated ADMM algorithms, obtained by temporal discretization
Stabilizability and stability robustness of state derivative feedback controllers
We study the stabilizability of a linear controllable system using state derivative feedback control. As a special feature the stabilized system may be fragile, in the sense that arbitrarily small modeling and implementation errors may destroy the asymptotic stability. First, we discuss the pole placement problem and illustrate the fragility of stability with examples of a different nature. We also define a notion of stability, called -stability, which explicitly takes into account the effect of small modeling and implementation errors. Next, we investigate the effect on the fragility of including a low-pass filter in the control loop. Finally, we completely characterize the stabilizability and -stabilizability of linear controllable systems using state derivative feedback. In the stabilizability characterization the odd number limitation, well known in the context of the stabilization of unstable periodic orbits using Pyragas-type time-delayed feedback, plays a crucial role