Performance certification of interconnected nonlinear systems using ADMM

Abstract

We present a compositional performance certification method for interconnected nonlinear systems, using dissipativity properties of the subsystems along with the interconnection structure. To select the most relevant dissipativity properties, we formulate a large-scale optimization problem, and solve it with the alternating direction method of multipliers (ADMM). The dissipativity properties are allowed to depend on an unknown equilibrium, enabling us to certify performance without explicit knowledge of the equilibrium for the interconnected system. The effectiveness of the algorithm is demonstrated on two examples, including a model of vehicle platoons.

Compositional performance certification of interconnected systems using ADMM

“…Proposition 1 certified global dissipativity from subsystem dissipativity. The following theorem states that this compositional approach is not overly conservative: for linear systems the existence of a separable quadratic storage function for the interconnection is equivalent to the existence of supply rates satisfying (14). Related results in [7,12] show that, under certain assumptions on the interconnection, passivity of an interconnected system is equivalent to passivity of the subsystems.…”

“…The global constraint set G is unchanged. Proposition 1 is directly applicable to this formulation, thus a feasible solution to (14) with the local constraint sets defined as in (21) implies that the interconnected system is EID with respect to (19).…”

“…The ADMM algorithm [5] allows us to decompose (14) into local subproblems and a global problem involving only the supply rates and interconnection. ADMM is used to solve problems of the form…”

A primal‐dual active‐set method for distributed model predictive control

“…We consider a class of model predictive control (MPC) problems that have quadratic cost, linear dynamics, additive disturbance, and box constraints with dynamics coupled through the control inputs. This class of problems includes large‐scale control problems such as buildings, network flow , or multi‐agent coordination .…”

“…Perhaps the most popular algorithm for distributed optimization today is ADMM. There are numerous publications in the controls, machine learning, and other communities that show that ADMM has gained widespread acceptance and usage . ADMM can be implemented on a star communication network of distributed processors, and in practice, it has better convergence rates than dual decomposition .…”