Fixed-Time Output Stabilization of a Chain of Integrators

International audienceA solution to the problem of global fixed-time output stabilization of a chain of integrators is proposed. A nonlinear state feedback and a dynamic observer are designed in order to guarantee both fixed-time estimation and fixed-time control. Robustness with respect to exogenous disturbances and measurement noises is established. The performance of the obtained control and estimation algorithms are illustrated by numeric experiments

Finite-and Fixed-Time Nonovershooting Stabilizers and Safety Filters by Homogeneous Feedback

International audienceNon-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to systems with deterministic and stochastic disturbances, has been solved by the second author and his coauthors. In this paper we develop homogeneous feedback laws for fixed-time nonovershooting stabilization for nonlinear systems that are input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of 'fixed-time safety filters' (FxTSf filters) which keep the system within the closed safe set for all time but, in the case where the user's nominal control commands approach to the unsafe set, allow the system to reach the boundary of the safe set no later than a desired time that is independent of nominal control and independent of the value of the state at the time the nominal control begins to be overridden

Homogeneous Nonovershooting Stabilizers and Safety Filters Rejecting Matched Disturbances

International audienceNon-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to systems with deterministic and stochastic disturbances, has been solved by the second author and his coauthors. In this paper we develop homogeneous feedback laws for fixed-time nonovershooting stabilization for nonlinear systems that are input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of 'fixedtime safety filters' (FxTSf filters) which keep the system within the closed safe set for all time but, in the case where the user's nominal control commands approach to the unsafe set, allow the system to reach the boundary of the safe set no later than a desired time that is independent of nominal control and independent of the value of the state at the time the nominal control begins to be overridden

Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations

The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the "uniform tangent decay flow" and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.Comment: 13 pages, 4 figures, Comments welcom

Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems

The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly reduced compared to classical CLFs, which makes \emph{flexible CLFs} more suitable for stabilization of constrained discrete-time nonlinear systems and real-time control. The purpose of this overview is to highlight the potential of flexible CLFs for real-time control of fast mechatronic systems, with sampling periods below one millisecond, which are widely employed in aerospace and automotive applications.Comment: 2 figure

Hybrid stabilizing control on a real mobile robot

To establish empirical verification of a stabilizing controller for nonholonomic systems, the authors implement a hybrid control concept on a 2-DOF mobile robot. Practical issues of velocity control are also addressed through a velocity controller which transforms the mobile robot to a new system with linear and angular velocity inputs. Experiments in the physical meaning of different controller components provide insights which result in significant improvements in controller performanc

Further Results on Active Magnetic Bearing Control with Input Saturation

We study the low-bias stabilization of active magnetic bearings (AMBs) subject to voltage saturation based on a recently proposed model for the AMB switching mode of operation. Using a forwarding-like approach, we construct a stabilizing controller of arbitrarily small amplitude and a control-Lyapunov function for the AMB dynamics. We illustrate our construction using a numerical example.Comment: 9 pages, 2 figures. IEEE Transactions on Control Systems Technology, accepted for publication in January 200

On the Design of Voltage-Controlled Sinusoidal Oscillators Using OTA's

A unified systematic approach to the design of voltage-controlled oscillators using only operational transconductance amplifiers (OTA's) and capacitors is discussed in this paper. Two classical oscillator models, i.e., quadrature and bandpass-based, are employed to generate several oscillator structures. They are very appropriate for silicon monolithic implementations. The resulting oscillation frequencies are proportional to the transconductance of the OTA and this makes the reported structures well-suited for building voltage controlled oscillators (VCO's). Amplitude stabilization circuits using both automatic gain control (AGC) mechanisms and limitation schemes are presented which are compatible with the transconductance amplifier capacitor oscillator (TACO). Experimental results from bipolar breadboard and CMOS IC prototypes are included showing good potential of OTA-based oscillators for high frequency VCO operation.Comisión Interministerial de Ciencia y Tecnología ME87-000