Finite-, fixed-, and prescribed-time stabilization and estimation
Full day workshop
58th IEEE Conference on Decision and Control – Nice, France – December 10th, 2109
The design of control and estimation algorithms for dynamical systems is centered around performance metrics which require optimization. A necessary property for these algorithms is stability, which is usually investigated with respect to an invariant mode of the system (e.g., an equilibrium, a desired trajectory or a limit cycle). A related performance metric is the rate of attractivity to the invariant mode, which can occur in infinite time (e.g., asymptotic or exponential convergence) or in finite-time. The latter type of attractivity, coupled with stability, is the focus of this workshop.
We further specialize our presentation to three types of attractivity: finite-, fixed-, and prescribed-time. For finite-time attractivity, we require convergence to the limit mode to occur in a finite, terminal time, which is permitted to depend on the initial condition of the system. A subclass of this is fixed-time attractivity, where the terminal time admits a uniform upper bound. An even more demanding type is that of prescribed-time attractivity, where the terminal time is prescribed independently of initial conditions.
For finite-dimensional models, the system properties and approaches utilized to ensure finite-/fixed-time attractivity include homogeneity, the implicit Lyapunov function method, and nonlinear system discretization tools. For prescribed-time attractivity of certain classes of ODEs, scalings of the state as well as a temporal scaling have proven useful. For some infinite-dimensional systems, time-varying damping and homogeneity can be employed to establish prescribed-time attractivity.
In many applications (e.g., multi-agent rendezvous, ABS braking, missile tactical guidance) ensuring fixed-/finite-/prescribed-time convergence is required; for other applications (e.g., time separation of observer and controller transients in nonlinear systems, fast commutation in switched dynamics) these convergences greatly simplify design and analysis.
The goal of this workshop is to present recent advances on the design and analysis of linear/nonlinear dynamical systems with these accelerated convergence rates.
Location, Time, Date
Palais des Congrès et des Expositions Nice Acropolis, 09:00 AM – 05:00 PM, Tuesday 10 December, 2019
Plan of the workshop
- definitions of stability and convergence rates
- Necessary and sufficient conditions for finite-time and fixed-time stability
- ordinary differential equations, differential inclusions, time-delay systems
- ISS counterparts
- Prescribed-time stabilization
- scaling of state method for ordinary differential equations
- time-varying backstepping for parabolic partial differential equations, observer and output feedback stabilization
- weighted homogeneity for ordinary differential equations
- discrete-time systems
- time-delay and partial differential equations
- Implicit Lyapunov function method
- introduction to the theory
- application for control and estimation
- explicit and implicit Euler method with state depending discretization step
- consistent discretization of controllers
- Denis Efimov, Inria, Lille, France
- Miroslav Krstic, University of California, San Diego, US
- Wilfrid Perruquetti, Centrale Lille, France
- Andrey Polyakov, Inria, Lille, France
- Drew Steeves, University of California, San Diego, US
The on-line registration for the IEEE CDC 2019 is available at PaperPlaza. Please select “Finite-, fixed-, and prescribed-time stabilization and estimation” for registration of the workshop.