Name
Abstract | ||
|---|---|---|
The focal point of this paper is the probabilistically constrained linear program (PCLP) and how it can be applied to control system design under risk constraints. The PCLP is the counterpart of the classical linear program, where it is assumed that there is random uncertainty in the constraints and, therefore, the deterministic constraints are replaced by probabilistic ones. It is shown that for a wide class of probability density functions, called log-concave symmetric densities, the PCLP is a convex program. An equivalent formulation of the PCLP is also presented which provides insight into numerical implementation. This concept is applied to control system design. It is shown how the results in this paper can be applied to the design of controllers for discrete-time systems to obtain a closed loop system with a well-defined risk of violating the so-called property of superstability. Furthermore, we address the problem of risk-adjusted pole placement. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S1052623403430099 | SIAM Journal on Optimization |
Keywords | Field | DocType |
deterministic constraint,probabilistically constrained linear programs,convex program,well-defined risk,discrete-time system,equivalent formulation,probabilistic constraints,system design,convexity,linear program,risk constraint,risk-adjusted controller design,closed loop system,classical linear program,risk-adjusted controller,probability density function,convex programming,pole placement | Focal point,Convexity,Mathematical optimization,Control theory,Full state feedback,Measurement uncertainty,Regular polygon,Linear programming,Probabilistic logic,Probability density function,Mathematics | Journal |
Volume | Issue | ISSN |
15 | 3 | 1052-6234 |
Citations | PageRank | References |
20 | 2.19 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Constantino M. Lagoa | 1 | 164 | 25.38 |
| Xiang Li | 2 | 158 | 47.86 |
| Mario Sznaier | 3 | 656 | 56.66 |