A randomized approximation algorithm for the minimal-norm static-output-feedback problem

Peretz, Y.

doi:10.1016/j.automatica.2015.10.001

Cited by 40 publications

(57 citation statements)

References 32 publications

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“…, n) uses the Ray-Shooting Method in order to find an approximation of the global minimum of the function σ max (K) over S (0) α -the portion of S α bounded in the cone D (0) . The proof of convergence in probability of the inner-loop and its complexity (under the above mentioned assumption) can be found in [16] (see also [22]). In the inner-loop, we choose a search direction by choosing a point F in R ∞ ( )-the base of the cone D (0) .…”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

“…Assume that K (0) ∈ int (S α ) was found by the RS algorithm (see [16]) or by any other method (see [19][20][21]). Let h > 0 and let U (0) be a unit vector w.r.t.…”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

“…where Vo denotes the volume of the related set and M g , m g are the essential-supremum and essential-infimum of g over D (0) , respectively (see [16] …”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

“…The probabilistic and randomized methods for the constrained SOF problem and robust stabilization via SOFs (among other hard problems) are discussed in [12][13][14][15]. The Ray-Shooting Method was recently introduced in [16], where it was utilized to derive the Ray-Shooting (RS) randomized algorithm for the minimal-gain SOF problem with regional pole-assignment, where the region can be non-convex and unconnected. For a survey of the SOF problem see [17] and for a recent survey of the robust SOF problem see [18].…”

Section: Introductionmentioning

confidence: 99%

“…The suggested algorithm is based on the Ray-Shooting Method (see [16]), which, as opposed to smooth optimization methods, has the potential of finding a global optimum of continuous functions over compact non-convex and unconnected regions. 2.…”

Section: Introductionmentioning

confidence: 99%

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On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

Peretz¹

2018

Algorithms

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Abstract:In this article we suggest a randomized algorithm for the LQR (Linear Quadratic Regulator) optimal-control problem via static-output-feedback. The suggested algorithm is based on the recently introduced randomized optimization method called the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over compact non-convex unconnected regions. The algorithm presented here is a randomized algorithm with a proof of convergence in probability. Its practical implementation has good performance in terms of the quality of controllers obtained and the percentage of success.

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Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

“…Assume that K (0) ∈ int (S α ) was found by the RS algorithm (see [16]) or by any other method (see [19][20][21]). Let h > 0 and let U (0) be a unit vector w.r.t.…”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

“…where Vo denotes the volume of the related set and M g , m g are the essential-supremum and essential-infimum of g over D (0) , respectively (see [16] …”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

Peretz¹

2018

Algorithms

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From static output feedback to structured robust static output feedback: A survey

Sadabadi

Peaucelle

2016

Annual Reviews in Control

209

137

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This paper reviews the vast literature on static output feedback design for linear time-invariant systems including classical results and recent developments. In particular, we focus on static output feedback synthesis with performance specifications, structured static output feedback, and robustness. The paper provides a comprehensive review on existing design approaches including iterative linear matrix inequalities heuristics, linear matrix inequalities with rank constraints, methods with decoupled Lyapunov matrices, and non-Lyapunov-based approaches. We describe the main difficulties of dealing with static output feedback design and summarize the main features, advantages, and limitations of existing design methods.

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Algorithms for joint sensor and control nodes selection in dynamic networks

et al. 2019

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The problem of placing or selecting sensors and control nodes plays a pivotal role in the operation of dynamic networks. This paper proposes optimal algorithms and heuristics to solve the simultaneous sensor and actuator selection problem in linear dynamic networks. In particular, a sufficiency condition of static output feedback stabilizability is used to obtain the minimal set of sensors and control nodes needed to stabilize an unstable network. We show the joint sensor/actuator selection and output feedback control can be written as a mixed-integer nonconvex problem. To solve this nonconvex combinatorial problem, three methods based on (1) mixed-integer nonlinear programming, (2) binary search algorithms, and (3) simple heuristics are proposed. The first method yields optimal solutions to the selection problem-given that some constants are appropriately selected. The second method requires a database of binary sensor/actuator combinations, returns optimal solutions, and necessitates no tuning parameters. The third approach is a heuristic that yields suboptimal solutions but is computationally attractive. The theoretical properties of these methods are discussed and numerical tests on dynamic networks showcase the trade-off between optimality and computational time.

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A randomized approximation algorithm for the minimal-norm static-output-feedback problem

Cited by 40 publications

References 32 publications

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

From static output feedback to structured robust static output feedback: A survey

Algorithms for joint sensor and control nodes selection in dynamic networks

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