Distributed Synthesis of State-Dependent Switching Control

Abstract

Abstract. We present a correct-by-design method of state-dependent control synthesis for linear discrete-time switching systems. Given an objective region R of the state space, the method builds a capture set S and a control which steers any element of S into R. The method works by iterated backward reachability from R. More precisely, S is given as a parametric extension of R, and the maximum value of the parameter is solved by linear programming. The method can also be used to synthesize a stability control which maintains indefinitely within R all the states starting at R. We explain how the synthesis method can be performed in a distributed manner. The method has been implemented and successfully applied to the synthesis of a distributed control of a concrete floor heating system with 11 rooms and 2 11 = 2048 switching modes.

An improved algorithm for the control synthesis of nonlinear sampled switched systems

“…A first approach is the use of compositionality, which permits to split the system in two (or more) sub-systems, and to perform control synthesis on these sub-systems of lower dimensions. This approach has been successfully applied in [36] to a system of dimension 11, and we are currently working on applying this approach to the more general context of contract-based design [37]. A second approach is the use of Model Order Reduction, which allows to approximate the full-order system (1) with a reduced-order system, of lower dimension, on which it is possible to perform control synthesis.…”

“…Another advantage is that we do not require a homogeneous discretization of the state space. We can thus tile large parts of the state space using only few boxes, and this often permits to consider much fewer states than with discretization methods, especially in higher dimensions (see [36]).…”

Distributed Control Synthesis Using Euler’s Method

“…From a certain point of view, this method is along the lines of [6] and [11] which are inspired by small-gain theorems of control theory (see, e.g., [9]). In the future, we plan to apply our distributed Euler-based method to significant examples such as the 11-room example treated in [12,14].…”

Control of nonlinear switched systems based on validated simulation

“…Another advantage is that we do not require a homogeneous discretization of the state space. We can thus tile large parts of the state-space using only few boxes, and this often permits to consider much less symbolic states than with discretization methods, especially in high dimensions (see [22]).…”