Software

Sparsity-Promoting Linear Quadratic Regulator

lqrsp.m is a Matlab function for the design of sparse and block sparse state-feedback gains that minimize the variance amplification (i.e., the ${cal H}_2$ norm) of distributed systems. Our long-term objective is to develop a toolbox for sparse feedback synthesis. This will allow users to identify control configurations that strike a balance between the performance and the sparsity of the controller and to examine the influence of different control configurations on the performance of distributed systems.

The design procedure consists of two steps:

Identification of sparsity patterns by incorporating sparsity-promoting penalty functions into the optimal control problem.
Optimization of feedback gains subject to structural constraints determined by the identified sparsity patterns.

Leader selection in stochastically forced consensus networks

leaders.m provides a Matlab implementation of algorithms that quantify suboptimality of solutions to two combinatorial network optimization problems. For undirected consensus networks, these problems arise in assignment of a pre-specified number of nodes, as leaders, in order to minimize the mean-square deviation from consensus.

We develop efficient algorithms that quantify performance bounds on the global optimal values. Specifically, we obtain lower bounds by solving the corresponding convex relaxations and we obtain upper bounds using a simple but efficient greedy algorithm.