Robust Control via Sequential Semidefinite ... - Pierre Apkarian
quential Quadratic Programming (SQP) known in nonlinear optimization. ...... d o conclude the proof, let us multiply equation ( 3 ) above by x X ax, and divide by.
bilinear constraints can be formulated as the minimization of a concave functional ... constraints (see e.g. [20, 9]) which are very hard nonconvex optimization.
resentation) uncertain systems depending on a time-varying parameter uncertainty. .... As concave programming is the best studied class of problems in global ...... problem by the introduction of one extra variable, whereas the simplicical ...
where Q is a L x L symmetric matrix, qT Ñ (RL) and p Ñ R. Ñ denotes a hyper-rectangle in the positive ...... 0 .04321 9 - 0 .010111 0 .1441 9 5 6 8. Pi = 10 -5 '.
Sep 13, 1994 - This paper is concerned with the robust control problem of plants ... It alternates analysis phases and synthesis phases both ..... N o w the characteriz ation in ( 1 8 ) - (жР0) is a con v ex feasibility program in the v ariables 7
robust synthesis problem shown schematically in Fig. 1. In sec- tion III we discuss ...... In Table II the results of inner relaxation from algorithm. 1, hybrid approach ...
Feb 20, 2012 - Results in terms of achieved HÑ objectives and running times are displayed .... AC13. 28/7/110. 120.94. 29.56. 157.38. 156.33. AC14. 40/0/12.
A comparative graphical view of the achieved objective values as well as execution times for both techniques is given in figure 1. The top plots in figure. 1 shows ...
approaches to control law design.ба number of different nonlinear tech- ..... conservative for three reasons ¢ that ¢ is treated as a complex number, that.
as quadratic functionals in and by a Schur's com- ... Again, rewriting the left-hand side of (36) as a quadratic functional in .... Equation (9). (10): Rewrite (10) as.
number of decision variables, the proposed techniques o ff er a valuable alternative to S ... F and C denotes the sets of real and complex numbers, respectively.
Email: {s3shung, tuan, n-tatsuo}@toyota-ti.ac.jp. ââ ... proach is due to the non-trivial step of identifying convex or concave ... 2 addresses the adaptive backstepping problem for the system (1) in .... tive controller for system (1) with a new
For Hermitian or symmetric matrices, X â» Y means that. X â Y is ... is used to denote its adjoint operator on the appropriate space. ... 1 Introduction ... number of innovative techniques and heuristics for structured control have been proposed i
classical linear fractional transformation (LFT) representations. ... in scaling variables, while those of [12] are in the form of exact LMIs. ... discrete-time systems.
regions, a class of convex regions of the complex plane that embraces most practically .... R and C denote the sets of real and complex numbers, respectively.
(1). whereÐУ andGЦ are real matrices such thatgУШ Xd У . The matrix- valued function. h i ... the LMI regionХР, if and only if there exists a symmetric. matrixI such that. Ц ..... withstand neglected dynamics and1fl exible modes. ⢠Maximu
AbstractâThe Power Oscillation Damping (POD) controllers implemented in the two ..... is represented by the standard form description (u â Rm2 and y â Rp2 ) ...
trix inequality (LMI) optimization formulations for un- certain NFT discrete systems with performance crite- ria based on generalized H2 and Hâ norm constraints.
answers even for IQC analysis, because we optimize without Lyapunov variables. ... order systems this leads to a significant reduction of the number of unknowns. .... A special case of program (10) is robustness analysis, where K is held fixed. .....
At a closer look, it is fairly easy to generate examples where the conditional gradient ..... mP be the solution so obtained. P ossibly use the previous iterate x. Ы.
as Linear Ð atrix I nequalities ( L ÐI) optimiвб ation problems [7, 10], which are then ... to our definitions, the pairw7ym Y lm @ is the gain-scheduling channel. ...... [5] J .- Ð . Ð iannic and P. Ap arian, Missile Autopilot Design via a mod
Convex quadratic constraints can be rewritten. (Ax + b). â² .... convert family of constrained quadratic inequalities ..... Easily computed by solving linear equation.
