Distributed Control Synthesis Using Euler’s Method

Abstract

In a previous work, we explained how Euler's method for computing approximate solutions of systems of ordinary differential equations can be used to synthesize safety controllers for sampled switched systems. We continue here this line of research by showing how Euler's method can also be used for synthesizing safety controllers in a distributed manner. The global system is seen as an interconnection of two (or more) subsystems where, for each component, the sub-state corresponding to the other component is seen as an "input"; the method exploits (a variant of) the notions of incremental input-to-state stability (δ-ISS) and ISS Lyapunov function. We illustrate this distributed control synthesis method on a building ventilation example.

Euler’s Method Applied to the Control of Switched Systems

“…These results mainly originate from collaboration with A. Le Coënt, F. De Vuyst, L. Chamoin, J. Alexandre dit Sandretto and A. Chapoutot (see [11,10]).…”

Constructing invariant tori using guaranteed Euler method

“…See [18,17] for details. We now suppose (see [10]) that there exist constants λ ∈ R and γ ∈ R ≥0 such that, for all y 1 , y 2 ∈ S and w 1 , w 2 ∈ W:…”

Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction

“…The main difference with previous work [27,37,19,46,47] is that our method makes use of explicit Euler's algorithm for ODE integration (cf. [32,33]) instead of sophisticated algorithms such as Lohner's algorithm [27] or interval Taylor series methods [44]. This leads us to a simple implementation of just a few hundred lines of Octave (see [31]).…”