Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics - Softcover
Synopsis
I. Introduction.- 1. Introduction.- 1.1 What Are the Key Concepts?.- 1.2 How Did the Story Start?.- 1.3 What About Complexity?.- 1.4 How is the Book Organized?.- II. Tools.- 2. Interval Analysis.- 2.1 Introduction.- 2.2 Operations on Sets.- 2.2.1 Purely set-theoretic operations.- 2.2.2 Extended operations.- 2.2.3 Properties of set operators.- 2.2.4 Wrappers.- 2.3 Interval Analysis.- 2.3.1 Intervals.- 2.3.2 Interval computation.- 2.3.3 Closed intervals.- 2.3.4 Interval vectors.- 2.3.5 Interval matrices.- 2.4 Inclusion Functions.- 2.4.1 Definitions.- 2.4.2 Natural inclusion functions.- 2.4.3 Centred inclusion functions.- 2.4.4 Mixed centred inclusion functions.- 2.4.5 Taylor inclusion functions.- 2.4.6 Comparison.- 2.5 Inclusion Tests.- 2.5.1 Interval Booleans.- 2.5.2 Tests.- 2.5.3 Inclusion tests for sets.- 2.6 Conclusions.- 3. Subpavings.- 3.1 Introduction.- 3.2 Set Topology.- 3.2.1 Distances between compact sets.- 3.2.2 Enclosure of compact sets between subpavings.- 3.3 Regular Subpavings.- 3.3.1 Pavings and subpavings.- 3.3.2 Representing a regular subpaving as a binary tree.- 3.3.3 Basic operations on regular subpavings.- 3.4 Implementation of Set Computation.- 3.4.1 Set inversion.- 3.4.2 Image evaluation.- 3.5 Conclusions.- 4. Contractors.- 4.1 Introduction.- 4.2 Basic Contractors.- 4.2.1 Finite subsolvers.- 4.2.2 Intervalization of finite subsolvers.- 4.2.3 Fixed-point methods.- 4.2.4 Forward-backward propagation.- 4.2.5 Linear programming approach.- 4.3 External Approximation.- 4.3.1 Principle.- 4.3.2 Preconditioning.- 4.3.3 Newton contractor.- 4.3.4 Parallel linearization.- 4.3.5 Using formal transformations.- 4.4 Collaboration Between Contractors.- 4.4.1 Principle.- 4.4.2 Contractors and inclusion functions.- 4.5 Contractors for Sets.- 4.5.1 Definitions.- 4.5.2 Sets defined by equality and inequality constraints.- 4.5.3 Improving contractors using local search.- 4.6 Conclusions.- 5. Solvers.- 5.1 Introduction.- 5.2 Solving Square Systems of Non-linear Equations.- 5.3 Characterizing Sets Defined by Inequalities.- 5.4 Interval Hull of a Set Defined by Inequalities.- 5.4.1 First approach.- 5.4.2 Second approach.- 5.5 Global Optimization.- 5.5.1 The Moore-Skelboe algorithm.- 5.5.2 Hansen's algorithm.- 5.5.3 Using interval constraint propagation.- 5.6 Minimax Optimization.- 5.6.1 Unconstrained case.- 5.6.2 Constrained case.- 5.6.3 Dealing with quantifiers.- 5.7 Cost Contours.- 5.8 Conclusions.- III. Applications.- 6. Estimation.- 6.1 Introduction.- 6.2 Parameter Estimation Via Optimization.- 6.2.1 Least-square parameter estimation in compartmental modelling.- 6.2.2 Minimax parameter estimation.- 6.3 Parameter Bounding.- 6.3.1 Introduction.- 6.3.2 The values of the independent variables are known.- 6.3.3 Robustification against outliers.- 6.3.4 The values of the independent variables are uncertain.- 6.3.5 Computation of the interval hull of the posterior feasible set.- 6.4 State Bounding.- 6.4.1 Introduction.- 6.4.2 Bounding the initial state.- 6.4.3 Bounding all variables.- 6.4.4 Bounding by constraint propagation.- 6.5 Conclusions.- 7. Robust Control.- 7.1 Introduction.- 7.2 Stability of Deterministic Linear Systems.- 7.2.1 Characteristic polynomial.- 7.2.2 Routh criterion.- 7.2.3 Stability degree.- 7.3 Basic Tests for Robust Stability.- 7.3.1 Interval polynomials.- 7.3.2 Polytope polynomials.- 7.3.3 Image-set polynomials.- 7.3.4 Conclusion.- 7.4 Robust Stability Analysis.- 7.4.1 Stability domains.- 7.4.2 Stability degree.- 7.4.3 Value-set approach.- 7.4.4 Robust stability margins.- 7.4.5 Stability radius.- 7.5 Controller Design.- 7.6 Conclusions.- 8. Robotics.- 8.1 Introduction.- 8.2 Forward Kinematics Problem for Stewart-Gough Platforms.- 8.2.1 Stewart-Gough platforms.- 8.2.2 From the frame of the mobile plate to that of the base.- 8.2.3 Equations to be solved.- 8.2.4 Solution.- 8.3 Path Planning.- 8.3.1 Graph discretization of configuration space.- 8.3.2 Algorithms for finding a feasible path.- 8.3.3 Test case.- 8.4 Lo
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Review
From the reviews:
"Applied Interval Analysis is the right book at the right time to move computing with intervals into the mainstream of engineering, financial, and scientific computing."
G. William Walster, Interval Technology Engineering Manager, Sun Microsystems and Member of the Editorial Board of Reliable Computing
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