Probability (2nd ed.)
Probabilistic robustness analysis: explicit bounds for the minimum number of samples
Systems & Control Letters
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Survey Research on gain scheduling
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Randomized Algorithms for Analysis and Control of Uncertain Systems: With Applications
Randomized Algorithms for Analysis and Control of Uncertain Systems: With Applications
Brief paper: Guaranteed cost regulator design: A probabilistic solution and a randomized algorithm
Automatica (Journal of IFAC)
A survey of randomized algorithms for control synthesis and performance verification
Journal of Complexity
A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs
Automatica (Journal of IFAC)
Brief paper: Computations of probabilistic output admissible set for uncertain constrained systems
Automatica (Journal of IFAC)
Brief paper: Stochastic ellipsoid methods for robust control: Multiple updates and multiple cuts
Automatica (Journal of IFAC)
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
A randomized approach is considered for a feasibility problem on a parameter-dependent linear matrix inequality (LMI). In particular, a gradient-based and an ellipsoid-based randomized algorithms are improved by introduction of a stopping rule. The improved algorithms stop after a bounded number of iterations and this bound is of polynomial order in the problem size. When the algorithms stop, either of the following two events occurs: (i) they find with high confidence a probabilistic solution, which satisfies the given LMI for most of the parameter values; (ii) they detect in an approximate sense the non-existence of a deterministic solution, which satisfies the given LMI for all the parameter values. These results are important because the original randomized algorithms have issues to be settled on detection of convergence, on the speed of convergence, and on the assumption of feasibility. The improved algorithms can be adapted for an optimization problem constrained by a parameter-dependent LMI. A numerical example shows the efficacy of the proposed algorithms.