Pointwise-Sparse Actuator Scheduling for Linear Systems with Controllability Guarantee

TL;DR

This paper develops a method for designing sparse actuator schedules in linear systems that guarantees controllability while minimizing control effort, using greedy algorithms and randomized optimization techniques.

Contribution

It introduces a novel approach for sparse actuator scheduling that ensures controllability and reduces control effort, combining greedy algorithms with MCMC-based optimization.

Findings

Greedy algorithm guarantees controllability with sparse actuator schedules.

MCMC-based randomized optimization improves schedule performance.

Proposed method effectively balances control effort and actuator sparsity.

Abstract

This paper considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization