Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

/pdf/linear-matrix-inequalities-in-system-and-control-theory-2q5cf0pqm2.pdf

Linear Matrix Inequalities in System and Control Theory

Optimal consumption and portfolio policies when asset prices follow a diffusion process

We prove that if the second-order sufficient condition and constraint regularity hold at a local minimizer of a nonlinear programming problem, then for sufficiently smooth perturbations of the constraints and objective function the set of local stationary points is nonempty and continuous; further, if certain polyhedrality assumptions hold (as is usually the case in applications), then the local minimizers, the stationary points and the multipliers all obey a type of Lipschitz condition.

Generalized equations and their solutions, part II: Applications to nonlinear programming

The use of dissolved nutrients and carbon for photosynthesis in the euphotic zone and the subsequent downward transport of particulate and dissolved organic material strongly affect carbon concentrations in surface water and thus the air–sea exchange of CO2. Efforts to quantify the downward carbon flux for the whole ocean or on basin-scales are hampered by the sparseness of direct productivity or flux measurements. Here, a global ocean circulation, biogeochemical model is used to determine rates of export production and vertical carbon fluxes in the Southern Ocean. The model exploits the existing large sets of hydrographic, oxygen, nutrient and carbon data that contain information on the underlying biogeochemical processes. The model is fitted to the data by systematically varying circulation, air–sea fluxes, production, and remineralization rates simultaneously. Use of the adjoint method yields model property simulations that are in very good agreement with measurements. In the model, the total integrated export flux of particulate organic matter necessary for the realistic reproduction of nutrient data is significantly larger than export estimates derived from primary productivity maps. Of the 10,000 TgC yr −1 (10 GtC yr −1 ) required globally, the Southern Ocean south of 30°S contributes about 3000 TgC yr −1 (33%), most of it occurring in a zonal belt along the Antarctic Circumpolar Current and in the Peru, Chile and Namibia coastal upwelling regions. The export flux of POC for the area south of 50°S amounts to 1000±210 TgC yr −1 , and the particle flux in 1000 m for the same area is 115±20 TgC yr −1 . Unlike for the global ocean, the contribution of the downward flux of dissolved organic carbon is significant in the Southern Ocean in the top 500 m of the water column. Comparison with satellite-based productivity estimates (CZCS and SeaWiFS) shows a relatively good agreement over most of the ocean except for the Southern Ocean south of 50°S, where the model fluxes are systematically higher than the satellite-based values by factors between 2 and 5. This discrepancy is significant, and an attempt to reconcile the low satellite-derived productivity values with ocean-interior nutrient budgets failed. Too low productivity estimates from satellite chlorophyll observations in the polar and sub-polar Southern Ocean could arise because of the inability of the satellite sensors to detect frequently occurring sub-surface chlorophyll patches, and to a poor calibration of the conversion algorithms in the Southern Ocean because of the very limited amount of direct measurements.

/pdf/carbon-export-fluxes-in-the-southern-ocean-results-from-322gtgscxk.pdf

Carbon export fluxes in the Southern Ocean: results from inverse modeling and comparison with satellite based estimates

Second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by closed convex cones. The necessary conditions are an immediate generalization of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as shown by a counterexample. Modified sufficient conditions are developed for the infinite-dimensional case.

Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems

Optimization theory: the finite dimensional case, by Magnus R. Hestenes. Pp xiii, 447. £14. 1976. SBN 0 471 37471 7 (Wiley)

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Optimization theory: the finite dimensional case, by Magnus R. Hestenes. Pp xiii, 447. £14. 1976. SBN 0 471 37471 7 (Wiley)