Invariant semidefinite programs
نویسندگان
چکیده
1 Laboratoire A2X, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, France [email protected] 2 CWI and Department of Mathematics, Leiden University; Centrum voor Wiskunde en Informatica (CWI), Sciencepark 123, 1098 XG Amsterdam, The Netherlands [email protected] 3 CWI and Department of Mathematics, University of Amsterdam; Centrum voor Wiskunde en Informatica (CWI), Sciencepark 123, 1098 XG Amsterdam, The Netherlands [email protected] 4 Delft Institute of Applied Mathematics, Technical University of Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands [email protected]
منابع مشابه
On Structured Semidefinite Programs for the Control of Symmetric Systems
In this paper we show how the symmetry present in many linear systems can be exploited to significantly reduce the computational effort required for controller synthesis. This approach may be applied when controller design specifications are expressible as a semidefinite program. In particular, when the overall system description is invariant under unitary coordinate transformations of the stat...
متن کاملStructured semidefinite programs for the control of symmetric systems
In this paper we show how the symmetry present in many linear systems can be exploited to significantly reduce the computational effort required for controller synthesis. This approach may be applied when controller design specifications are expressible via semidefinite programming. In particular, when the overall system description is invariant under unitary coordinate transformations of the s...
متن کاملSymmetry in Semidefinite Programs
This paper is a tutorial in a general and explicit procedure to simplify semidefinite programming problems which are invariant under the action of a group. The procedure is based on basic notions of representation theory of finite groups. As an example we derive the block diagonalization of the Terwilliger algebra in this framework. Here its connection to the orthogonal Hahn and Krawtchouk poly...
متن کاملOutput Variance–Constrained LQG Control of Discrete-Time Systems
The constrained infinite-horizon LQG control problem can be solved via semidefinite programming if the state-control constraints are given by variance-bounds on linear functions of the state and control input. Given a nonzero initial state covariance matrix, each suboptimal dynamic output feedback controller is initially time-varying but reaches time-invariance after a finite number of time ste...
متن کاملFinding Polynomial Loop Invariants for Probabilistic Programs
Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle’s Positivstellensatz and a transformation to a sum-of-squ...
متن کاملProving Program Invariance and Termination by Parametric Abstraction, Lagrangian Relaxation and Semidefinite Programming
In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstractio...
متن کامل