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Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

2010 International Journal of Applied Mathematics and Computer Science  
Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for  ...  We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered.  ...  Acknowledgment The author would like to thank the anonymous referees for very helpful suggestions and comments which improved the quality of this paper.  ... 
doi:10.2478/v10006-010-0048-9 fatcat:h2snmee6evgntgsa3gphxqlo3m

On$H_2$Control of Systems With Multiple I/O Delays

A.A. Moelja, G. Meinsma, J. Kuipers
2006 IEEE Transactions on Automatic Control  
The H optimal control problem of systems with multiple I/O delays is solved. The problem is tackled by first transforming it to what is called the two-sided regulator problem.  ...  The latter is solved using orthogonal projection arguments and spectral factorization.  ...  There, the one-sided problem is transformed to an LQR with input delays, which is solved in time domain using dynamic programming ideas.  ... 
doi:10.1109/tac.2006.878739 fatcat:75paonwxfvbgvisfg4sfcaex64

[IEEE Robotics & Automation Society]

2012 IEEE robotics & automation magazine  
At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems.  ...  to now, there is no descriptor variable observer scheme for implicit rectangular systems.In this paper we propose two different ways for observing the descriptor variable: a descriptor variable observer  ... 
doi:10.1109/mra.2012.2229854 fatcat:rjrxtwk4jbcgjpvjdad6mougsq

IEEE Robotics & Automation Society

2012 IEEE robotics & automation magazine  
At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems.  ...  to now, there is no descriptor variable observer scheme for implicit rectangular systems.In this paper we propose two different ways for observing the descriptor variable: a descriptor variable observer  ... 
doi:10.1109/mra.2012.2230568 fatcat:33actbknxrel3jnag2kx7cncem

IEEE Robotics & Automation Society

2011 IEEE robotics & automation magazine  
At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems.  ...  to now, there is no descriptor variable observer scheme for implicit rectangular systems.In this paper we propose two different ways for observing the descriptor variable: a descriptor variable observer  ... 
doi:10.1109/mra.2011.941112 fatcat:owvu2behc5hulpcae2dp5myigm

IEEE Robotics & Automation Society

2011 IEEE robotics & automation magazine  
At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems.  ...  to now, there is no descriptor variable observer scheme for implicit rectangular systems.In this paper we propose two different ways for observing the descriptor variable: a descriptor variable observer  ... 
doi:10.1109/mra.2011.943480 fatcat:d2wvloyv6jcbzp2yathd52mx2u

A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations [article]

Peter Benner, Zvonimir Bujanović, Patrick Kürschner, Jens Saak
2018 arXiv   pre-print
There are several goals of this manuscript: first, to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them  ...  In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations.  ...  Especially the later were a great asset for developing the implementations used in this study. Additional thanks go to Tony Stillfjord for his careful revision of our final draft.  ... 
arXiv:1811.00850v1 fatcat:csrdnfevbnfulk6apgk4cefmla

2019 Index IEEE Transactions on Automatic Control Vol. 64

2019 IEEE Transactions on Automatic Control  
., +, TAC Jan. 2019 97-110 Analysis and Control of Stochastic Systems Using Semidefinite Programming Over Moments.  ...  ., +, TAC Nov. 2019 4623-4628 Analysis and Control of Stochastic Systems Using Semidefinite Programming Over Moments.  ... 
doi:10.1109/tac.2020.2967132 fatcat:o2hd2t4jz5fbpkcemjt5aj7xrm

2013 Index IEEE Transactions on Automatic Control Vol. 58

2013 IEEE Transactions on Automatic Control  
., +, TAC Sept. 2013 2230-2245 Mathematical programming Design of Polynomial Control Laws for Polynomial Systems Subject to Actuator Saturation.  ...  ., +, TAC Jan. 2013 168-174 Solving Large-Scale Robust Stability Problems by Exploiting the Parallel Structure of Polya's Theorem.  ... 
doi:10.1109/tac.2013.2295962 fatcat:3zpqog4r4nhoxgo4vodx4sj3l4

New optimization methods in predictive control

Amir Shahzad, Eric Kerrigan, George A. Constantinides
2011
Interior point methods (IPMs) have proven to be an efficient way of solving quadratic programming problems. A linear system of equations needs to be solved in each iteration of an IPM.  ...  The ill-conditioning of this linear system in the later iterations of the IPM prevents the use of an iterative method in solving the linear system due to a very slow rate of convergence; in some cases  ...  Interior point methods (IPMs) have proven to be an efficient way of solving quadratic programming problems. A linear system of equations needs to be solved in each iteration of an IPM.  ... 
doi:10.25560/6141 fatcat:p3xfnprmofgqlmgnyta7l3g7eu

Hierarchical and Cooperative Control of Complex Distributed Systems Hierarchical and Cooperative Control of Complex Distributed Systems

Martin Jilg, Martin Jilg
unpublished
The resulting control problem is a structured optimal control problem which can be solved by the help of a semidefinite program: Theorem 3.1.  ...  The design of each control layer can be formulated by means of independent semidefinite programs, which can be solved sequentially.  ...  To this end, a Monte-Carlo-Simulation has been performed. In each simulation run, a random stable discrete-time LTI system P is first generated using the function drss provided by Matlab.  ... 
fatcat:sdigs2tuvndc3cb4ycff5zftyy

Decomposition Strategies for Nonconvex Problems, a Parametric Approach

Jean-Hubert Hours
2016
Algorithm 5 is then applied to solve two AC-OPF problems in rectangular coordinates on distribution networks.  ...  as well as the standard pointwise-in-time state and input constraints, and that can be computed using semidefinite-programming (SDP).  ...  This amounts to solving a linear program, which can be done efficiently by means of interior point methods. In practice, we use the MPT 3.0 function isEmptySet [80] .  ... 
doi:10.5075/epfl-thesis-6875 fatcat:37ev4hlwxbfejng3w625wnsw6q

ICAS 2012 Committee ICAS Advisory Chairs ICAS 2012 Technical Program Committee

St Maarten, Netherlands Antilles, Michael Bauer, Michael Grottke, Bruno Dillenseger, Michael Bauer, Michael Grottke, Bruno Dillenseger, Jemal Abawajy, Javier Alonso, Richard Anthony, Mark Balas (+66 others)
unpublished
These technical challenges led the context-aware system developers to use improved and new concepts for specifying and modeling these systems to ensure quality and to reduce the development effort and  ...  We take here the opportunity to warmly thank all the members of the ICAS 2012 technical program committee as well as the numerous reviewers.  ...  ACKNOWLEDGMENTS This research is supported by the End-to-End Clouds project funded by the Swedish Foundation for Strategic Research, the Complex Service Systems focus project, a part of the ICT-TNG Strategic  ... 
fatcat:ctehnlqxqzfythqddv4uuzepza