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Index

1-D actuation, 120 1-D sensing, 120 2-D sensing, 120

actuator limitations, 38, 83, 109 a-level set, 9 [a, 13]-sublevel set, 9 amplitude saturation, 83, 109 asymptotically stable, 10 attractive, 10 axial compressors, 61

backstepping control, 2 backstepping controller, 77 Barbashin-Krasovskii-LaSalle, 7 Bernouilli equation, 64 bounded trajectory, 10 bounding function, 51

centrifugal compression system, 97 circumferential averaged flow, 71 compression systems, 59 compressor aerodynamic instabilities,

59 - rotating stall, 59 - surge, 59 compressor characteristic map, 74 compressor efficiency, 59, 101 compressor performance, 59 compressor pressure-flow map, 59 connected set, 8 conservation of angular momentum,

104 conservation of mass, 63, 98 conservation of momentum, 63, 100 control law, 24 control rate saturation constraints, 38

Davidenko differential equation, 37 deep surge, 97 derived cost functional, 40 differential geometric control, 1

discrete-time dynamical systems, 18, 46 disturbance rejection, 118 domain of attraction, 11, 26 dynamic programming, 2

equilibria-dependent Lyapunov functions, 4, 21, 26, 52

equilibrium manifold, 24 equilibrium point, 23 Extended Optimal Switching Control .

Problem, 40, 111

feedback control law, 24 feedback linearization, 1 Filippov, 9 fixed-order dynamic compensator, 37

gain scheduled control, 3, 8 gain scheduled systems, 7 generalized invariant set theorems, 8,

12 generalized Lyapunov function, 8, 12 generalized Lyapunov function

candidate, 12, 29 generalized Lyapunov theorem, 4 generalized stability theorems, 11 globally asymptotically stable, 10

Hamilton- Jacobi-Bellman, 2 hierarchical adaptive control, 119 hierarchical homotopic feedback

controllers, 40 hierarchical robust control for

propulsion systems, 87 hierarchical robust nonlinear controller,

49 hierarchical robust switching controller

algorithm, 56 hierarchical switching control algo-

rithm, 38 hierarchical switching control for axial

flow compressors, 80

132 Index

hierarchical switching control for centrifugal compression systems, 107

hierarchical switching controller, 4, 21, 26, 31

high-speed axial flow compression systems, 120

homotopy map, 37 hybrid control, 22 hybrid systems, ? hysteresis, 60

Implicit Function Theorem, 24 incompressible flow, 64 invariance principle, 7 invariant set, 10 invariant set theorem, 4 inverse optimal switching control, 39,

111 inverse optimality, 2, 45 irrotational flow, 64 isentropic efficiency, 101, 103 isentropic efficiency lines, 103

Laplace equation, 67 linear parameter-varying, 3 local set point designs, 25, 26, 105 lower semicontinuous function, 8, 11, 29 lower semicontinuous Lyapunov

function, 4 lower-level subcontrollers, 21 Lyapunov, 7 - Lyapunov function, 7 - Lyapunov stability theory, 25 - Lyapunov stable, 10 - Lyapunov's direct method, 7

maximum isentropic efficiency, 103 Moore-Greitzer model, 61, 75 moving system equilibria, 21, 26

negatively invariant set, 10 nominal controlled system, 48 nominal equilibrium manifold, 47 nominal system, 49 nominal system equilibria, 49, 52 nonexpansivity, 118 nonlinear dynamic compensation, 35 nonlinear-nonquadratic cost functional,

44

parameterization set, 24 parameterized equilibrium manifold, 21 parameterized system equilibria, 24,

105 parametric stability, 24, 25 positive limit point, 10 positive limit set, 10 positively invariant set, 10 potential function, 27, 52, 53, 111, 113 pressure-flow/angular velocity map,

102 propulsion systems, 59

rate saturation, 83, 109 robust globally asymptotically stable,

49 robust nonlinear control, 47 robust stability, 49 robust stabilization, 5, 47 robust stabilization of axial flow

compressors, 84 robust switching controllers, 47 robustly asymptotically stable, 49 robustly attractive, 49 robustly Lyapunov stable, 49 rotating stall, 59

semi-group property, 9 set-valued map, 27 sliding mode, 22, 35 spool dynamics, 104 stable limit cycle, 60 stagnation density, 103 stagnation temperature, 103 stress tensor, 64 supervisory switching controller, 4, 21 surge, 59 surge margin, 60 switching function, 29, 53 switching function dynamics, 37 switching nonlinear feedback controller,

3O switching set, 27, 34, 52, 82, 93, 108

trajectory, 9

uncertain dynamical system, 48 uncertain pressure-flow maps, 84 unstable, 10, 49

Optimal Switching Control Problem, variable structure control, 4 40 viable switching set, 29, 53

Lecture Notes in Control and Information Sciences

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1997-2000 Published Titles:

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