Minimal Actuator Placement with Bounds on Control Effort
Vasileios Tzoumas, Mohammad Amin Rahimian, George Pappas, Ali Jadbabaie

Citation
Vasileios Tzoumas, Mohammad Amin Rahimian, George Pappas, Ali Jadbabaie. "Minimal Actuator Placement with Bounds on Control Effort". submitted to IEEE Transactions on Control of Network Systems (TCNS), 2014.

Abstract
We address the problem of minimal actuator placement in a linear system subject to an average control energy bound. First, following the recent work of Olshevsky, we prove that this is NP-hard. Then, we prove that the involved control energy metric is supermodular. Afterwards, we provide an efficient algorithm that approximates up to a multiplicative factor of O(logn), where n is the size of the system, any optimal actuator set that meets the same energy criteria. This is the best approximation factor one can achieve in polynomial-time, in the worst case. Next, we focus on the related problem of cardinality-constrained actuator placement for minimum control effort, where the optimal actuator set is selected so that an average input energy metric is minimized. While this is also an NP-hard problem, we use our proposed algorithm to efficiently approximate its solutions as well. Finally, we run our algorithms over large random networks to illustrate their efficiency.

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Citation formats

• HTML

  Vasileios Tzoumas, Mohammad Amin Rahimian, George Pappas,
  Ali Jadbabaie. <a
  href="http://www.terraswarm.org/pubs/384.html"
  >Minimal Actuator Placement with Bounds on Control
  Effort</a>, <i>submitted to IEEE Transactions on
  Control of Network Systems (TCNS)</i>,  2014.

• Plain text

  Vasileios Tzoumas, Mohammad Amin Rahimian, George Pappas,
  Ali Jadbabaie. "Minimal Actuator Placement with Bounds
  on Control Effort". <i>submitted to IEEE
  Transactions on Control of Network Systems (TCNS)</i>,
   2014.

• BibTeX

  @article{TzoumasRahimianPappasJadbabaie14_MinimalActuatorPlacementWithBoundsOnControlEffort,
      author = {Vasileios Tzoumas and Mohammad Amin Rahimian and
                George Pappas and Ali Jadbabaie},
      title = {Minimal Actuator Placement with Bounds on Control
                Effort},
      journal = {submitted to IEEE Transactions on Control of
                Network Systems (TCNS)},
      year = {2014},
      abstract = {We address the problem of minimal actuator
                placement in a linear system subject to an average
                control energy bound. First, following the recent
                work of Olshevsky, we prove that this is NP-hard.
                Then, we prove that the involved control energy
                metric is supermodular. Afterwards, we provide an
                efficient algorithm that approximates up to a
                multiplicative factor of O(logn), where n is the
                size of the system, any optimal actuator set that
                meets the same energy criteria. This is the best
                approximation factor one can achieve in
                polynomial-time, in the worst case. Next, we focus
                on the related problem of cardinality-constrained
                actuator placement for minimum control effort,
                where the optimal actuator set is selected so that
                an average input energy metric is minimized. While
                this is also an NP-hard problem, we use our
                proposed algorithm to efficiently approximate its
                solutions as well. Finally, we run our algorithms
                over large random networks to illustrate their
                efficiency.},
      URL = {http://terraswarm.org/pubs/384.html}
  }
  

Posted by Vasileios Tzoumas on 2 Oct 2014.
Groups: terraswarm