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Constrained optimal fitting of threedimensional vector patterns
 IEEE Transactions on Robotics and Automation
, 1998
"... Abstract — This paper addresses the problem of finding whether a given set of threedimensional (3D) vectors (the object) can be brought to match a second set of vectors (the template) by means of an affine motion, minimizing a measure of the mismatch error and satisfying an assigned set of geometr ..."
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Abstract — This paper addresses the problem of finding whether a given set of threedimensional (3D) vectors (the object) can be brought to match a second set of vectors (the template) by means of an affine motion, minimizing a measure of the mismatch error and satisfying an assigned set of geometrical constraints. This problem is encountered in many applications of computer vision, robotics, and manufacturing processes, and has been tackled by several authors in the unconstrained case. Spherical, ellipsoidal and polyhedral constraints are here introduced in the problem, and a solution scheme based on an efficient convex optimization algorithm is proposed. An example of application of the proposed methodology to a manufacturing tolerancing problem is also provided. Index Terms—Absolute orientation, automated tolerancing, computer vision, convex optimization, least squares, visual servo control.
Robust Statefeedback Stabilization of Jump Linear Systems via LMIs
, 1994
"... We consider a linear system subject to Markovian jumps, with a timevarying, unknownbut bounded transition matrix. We derive LMI conditions ensuring various secondmoment stability properties for the system. The approach is then used to generate modedependent statefeedback control laws which stab ..."
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We consider a linear system subject to Markovian jumps, with a timevarying, unknownbut bounded transition matrix. We derive LMI conditions ensuring various secondmoment stability properties for the system. The approach is then used to generate modedependent statefeedback control laws which stabilize the system in the meansquare sense. When the transition matrix is constant and known, our conditions are necessary and sufficient.
Robust Multiobjective Lti Control Design For Systems With Structured Perturbations
, 1996
"... . We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design specifications include robust stability, robust performance (H 2 norm) bounds and timedomain bounds (output and command input peak). We derive sufficient conditions, ..."
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. We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design specifications include robust stability, robust performance (H 2 norm) bounds and timedomain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closedloop system satisfies all specifications simultaneously. These nonconvex conditions can be numerically checked with an efficient LMIbased heuristic. We illustrate our results on a threeparameter mass/spring system. Keywords. Multiobjective robust control, mixed H 2 /H1 , timedomain specification, structured perturbation, quadratic Lyapunov function, linear matrix inequality. 1. INTRODUCTION In a multiobjective robust control problem, one seeks a control law such that the closedloop system satisfies a number of objectives (specifications) despite unkwnonbut bounded perturbations. I...
LMI Optimization for Nonstandard Riccati Equations Arising in Stochastic Control
, 1996
"... We consider coupled Riccati equations that arise in the optimal control of jump linear systems. We show how to reliably solve these equations using convex optimization over linear matrix inequalities (LMIs). The results extend to other nonstandard Riccati equations, that arise e.g. in the optimal co ..."
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We consider coupled Riccati equations that arise in the optimal control of jump linear systems. We show how to reliably solve these equations using convex optimization over linear matrix inequalities (LMIs). The results extend to other nonstandard Riccati equations, that arise e.g. in the optimal control of linear systems subject to statedependent multiplicative noise. Some nonstandard Riccati equations (such as those connected to linear systems subject to both state and controldependent multiplicative noise) are not amenable to the method. We show that we can still use LMI optimization to compute the optimal control law for the underlying control problem, without solving the Riccati equation. Keywords: Jump linear system, multiplicative noise, nonstandard Riccati equation, Linear Matrix Inequality. Research supported in part by DRET under contract 92017BC14. y Author to whom correspondence should be sent. Internet: elghaoui@ensta.fr 1 Notation. For a real matrix A, A ? 0 (r...
Applications of Semide nite Programming
, 1998
"... A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence e ciently solved using recently developed interiorpoint methods. In this paper, we will consider two classes of optimization problems with LMI constraints: The sem ..."
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A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence e ciently solved using recently developed interiorpoint methods. In this paper, we will consider two classes of optimization problems with LMI constraints: The semide nite programming problem, i.e., the problem of minimizing a linear function subject to a linear matrix inequality. Semide nite programming is an important numerical tool for analysis and synthesis in systems and control theory. It has also been recognized in combinatorial optimization as a valuable technique for obtaining bounds on the solution of NPhard problems. The problem of maximizing the determinant of a positive de nite matrix subject to linear matrix inequalities. This problem has applications in computational geometry, experiment design, information and communication theory, and other elds. We review some of these applications, including some interesting applications that are less well known and arise in statistics, optimal experiment design and VLSI. 1 Optimization problems involving LMI constraints We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1) where the matrices Fi = F T i 2 R n n are given, and the inequality F (x) 0 means F (x) is positive semide nite. The LMI (1) is a convex constraint in the variable x 2 R m. Conversely, a wide variety of nonlinear convex constraints can be expressed as LMIs (see the recent