6.5 x 10.5 long title - Assets - Cambridge University...

Index

χ, 55, 3472-counter machine, 13420-sim, 55, 329, 346, 358

ABACUSS, 329, 346, 353ABS, see anti-lock braking systemabstraction, 62, 71, 72, 193, 228, 424, 443

a. refinement, 286discrete a., 43, 230

abstraction-based control, 224, 413abstraction-based modeling, 218accumulation point, 176, 179, 202activation duration, 27, 235active damping, 449active index set, 152active suspension, 453activity, 15activity function, 59adaptive cruise control, 453adjoint pair, 80affine dynamics, 36agent, 473

autonomous a., 474aggregation, 414air traffic control, 276air traffic management, 250airpath control, 454algebraic loop, 363algebraic optimization, 411algebraic procedure, 104AMPL, 299, 354analysis, 130

controllability a., 52, 166

observability a., 52reachability a., 64, 249, 264, 299, 308,

312stability a., 52, 72, 121, 299

anti-lock braking system, 441anti-windup, 391, 406application

air traffic control, 276boost converter, 384DC-DC converter, 379Diesel engine, 221electricity distribution, 393Lake Mead, 287, 295mining ventilation, 495multiproduct batch plant, 419power network, 393solar air conditioning system, 502

approximation, 458discrete-time a., 399robust affine a., 386

architecture-specific format, 321, 324ASCET, 444asynchronous communication, 442automatic gearbox, 22automatic voltage regulator, 396automaton

differential a., 55cyclic linear a., 236deterministic a., 178discrete hybrid a., 300finite a., 228gain a., 72hybrid a., 59

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Cambridge University Press978-0-521-76505-3 - Handbook of Hybrid Systems Control: Theory, Tools, ApplicationsEdited by Jan Lunze and Francoise Lamnabhi-LagarrigueIndexMore information

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554 Index

interchange a., 365stochastic a., 213, 264stopwatch a., 64timed a., 40, 368

AUTOSTAR initiative, 441auxiliary variables, 300average model, 440average spectral radius, 133AVR, see automatic voltage regulator

BARON, 436barrier certificate, 274, 275BaSiP, 55, 329, 346, 358batch plant, 419Bayesian procedure, 102, 104BDC, see bottom dead centerbehavior, 225

behavioral framework, 224chaotic b., 203complete b., 226Zeno b., 45

behavioral relation, 219bisimulation, 62, 368

timed b., 64block diagram, 329, 444Bohl function, 162Bohl-type input, 162Boolean optimization, 304Boolean variable, 300bottle filling system, 370bottom dead center, 461bottom-up design, 417bounded-error procedure, 103, 105branch-and-bound search, 433branch-and-bound technique, 429Brockett’s model, 55buffer, 159bumpless transfer, 25

CAPE-OPEN initiative, 327Carathéodory solution, 51, 161, 181cardinality, 207

minimal c., 213causal, 416causal modeling, 331CCM, see continuous conduction modeCDD, 304certainty equivalence principle, 53

CFTOC, see constrained finite time-optimalcontroller

chaotic behavior, 203, 208characteristic multiplier, 240charge stratification, 463Charon, 346chattering, 332CheckMate, 347Chi, see χChurch-Turing thesis, 130CI, see compression ignitionCIF, see compositional interchange formatcircuit theory, 160CITOC, see constrained infinite time-optimal

controlclassification, 96, 97clock, 63clock-driven, 235closed orbit, 238CLP, 304clustering, 101clustering-based procedure, 101, 104, 316clutch, 447CMTOC, see constrained minimum

time-optimal controlco-state variable, 388collision avoidance, 477collocation-based technique, 352communication, 472communication constraint, 197, 204communication network, 5, 442complementarity condition, 151complementarity system, 151, 152, 177

linear c. s., 151switched cone c. s., 154

complete behavior, 226complete model, 218, 220complexity, 4, 50, 130, 209, 231, 433complexity reduction, 307component, 363compositional interchange format, 347, 362compression ignition, 461compression ratio, 461compression stroke, 461computation tree logic, 62computer science, 5computer-automated multi-paradigm

modeling, 327conditional equation, 332






Index 555

cone, 153configuration

nonblocking c., 479safe c., 479

conflict management, 474consensus problem, 473consistency-based diagnosis, 220constrained finite optimal control, 383constrained finite time-optimal control, 303,

306constrained finite time-optimal controller,

487constrained infinite time-optimal control,

304, 306constrained minimum time-optimal control,

306constraint, 67, 287, 434constraint satisfaction, 304continuous conduction mode, 27, 244, 379continuous dynamics, 7, 59continuous evolution, 60, 252continuous input, 18continuous state variable, 19continuous-to-discrete interface, 34continuous-valued signal, 8control

abstraction-based c., 413cooperative c., 472decentralized c., 472distributed c., 472embedded c., 4finite optimal c., 383finite time-optimal c., 303, 306hierarchical c., 414high-level c., 423hybrid c., 223, 506infinite time-optimal c., 304, 306low-level c., 414, 423model-predictive c., 52, 381, 397, 452multirate c., 442nonlinear model-predictive c., 427optimal c., 211, 303, 418, 434optimal state-feedback c., 383periodic c., 243PI c., 23, 427receding-horizon c., 305rule-based c., 450spatially decentralized c., 475supervisory c., 227

control code, 452control engineering, 5control mode, 59control parametrization, 351control software, 406control switch, 59control system, 442Control System Toolbox, 305control validation, 443controllability, 52, 166controllability analysis, 52controlled Markov chain, 263controlled switching, 18controller

deadbeat c., 210discrete-event c., 231predictive logic c., 507qdb-c., 210sequential c., 406

controller synthesis, 67convex hull operator, 71convex optimization, 386cooperative control, 472coordination, 473core dynamics, 151cost function, 400, 418, 423cost matrix, 158counter, 76Cplex, 309crank angle, 461crankshaft sensor management, 449cruisable graph, 474cruise control, 449, 453current-mode control, 245cut-off control, 441, 449cyclic process, 27cylinder pressure, 464

DAE, see differential-algebraic equationDASSL, 331, 398data interchange format, 320DC-DC converter, 26, 379DCM, see discontinuous conduction modedead zone, 389deadbeat controller, 210decentralized control, 472decentralized hysteresis controller, 426decidability, 62, 63decision problem, 130






556 Index

delay, 472density, 207dependency graph, 363derivative design, 444DES, see discrete-event systemdesign flow, 442detectability, 52determinism, 179DHA, see discrete hybrid automatondiagnosis, 213

consistency-based d., 220diagnostic algorithm, 214, 449diagnostic tool, 448difference equation, 300differential equation with discontinuous

right-hand side, 156differential inclusion, 41, 63, 64, 174, 176,

185impulse d. i., 188linear d. i., 70, 115

differential index, 331differential-algebraic equation, 327, 350,

398diffusion process, 257diffusion term, 271direct injection stratified charge engine, 455discontinuous conduction mode, 28discontinuous differential equation, 91discontinuous dynamical system, 35discontinuous model, 93discrete approximation, 413discrete dynamics, 7, 59discrete evolution, 252discrete hybrid automaton, 300discrete input, 18discrete sensor, 18, 197discrete state, 19discrete successor, 65discrete-event quantized system, 215discrete-event simulation, 55discrete-event system, 223, 332discrete-time hybrid system, 299discrete-time piecewise affine system, 41,

322discrete-time quantized system, 215discrete-time stochastic hybrid system, 261,

275discrete-time system, 130discrete-to-continuous interface, 34

discrete-valued signal, 8discretely controlled continuous system, 39,

90, 231discretization, 352distinguishability, 109distributed control, 472disturbance, 234disturbance attenuation, 241drift term, 271drive-by-wire, 454driveline, 445, 447dtPWA, see discrete-time piecewise affine

systemDTSHA, see discrete-time stochastic hybrid

automatondual cone, 153duration calculus, 55duty cycle, 27, 381dwell time, 76, 107, 126, 235Dymola, 354dynamical programming, 275, 386dynamical time scale, 416dynamics

continuous d., 7discrete d., 7, 59

EcosimPro, 347, 365ECU, see electronic control unitEECI, see European Embedded Control

Instituteego, 410EGR, see exhaust gas recirculationELC, see extended linear complementarity

systemelectronic control unit, 441electronic throttle, 454embedded control, 4embedded controller, 7, 204, 440embedded logic, 427embedded map, 235

controlled e. m., 241embedded simulation, 410emission control, 449energy management, 378engaged gear identification, 447engine control, 440engine start-up, 448entry point, 73equilibrium, 72, 74, 114, 199, 233, 388






Index 557

equivalence ratio, 462, 463ESPRESSO, 304ETAS, 444European Embedded Control Institute, xvevaporation system, 407, 425, 430event, 34

threshold e., 144event function, 234event generator, 34, 232, 300event-driven sampling, 224event-driven switching, 235example

automatic gearbox, 22, 84boost converter, 26, 153, 233, 244bottle filling system, 370bouncing ball, 45flying ball, 173Leontiev economy, 157moving agent, 204quantized tank system, 215reset oscillator, 12tank system, 10thermostat, 7, 254two-tank system, 17, 61, 81, 154, 354user-ressource model, 158

execution, 107, 175, 235, 252, 258, 262finite e., 179infinite e., 179maximal e., 179periodic e., 238sampled e., 238stable e., 239synchronous e., 363

exhaust gas recirculation, 221, 449, 454, 462exhaust stroke, 461exhaust valve control, 448expansion stroke, 461expressiveness, 327extended linear complementarity system,

168extensible markup language, 321, 364extensible markup language document, 323extremal point, 73

fault, 397, 401, 449fault detection

f.d. of quantized system, 221fault diagnosis, see diagnosisfault identification

f.i. of quantized system, 221fault probability, 220fault tolerance, 449, 472feasible subsystem, 95feature vector, 101feedback linearization, 458Filippov solution, 51, 189finite automaton, 228finite-state automaton, 299, 335finite-state machine, 106, 445, 505finiteness property, 132first-principle modeling, 92fixpoint, 240flow function, 63flow set, 40flowsheet, 407forbidden region, 67forced transition, 257, 262, 275forward solution, 161, 189fuel injection, 448functional development, 442functional integration, 443

gain, 72gain automaton, 72GAMS, 354GBT, 304gear-box control, 449Geometric Bounding Toolbox, 304glcDirect, 410GLPK, 304gOPT, 353gPROMS, 328, 338, 353guard, 34, 60, 489guard set, 234

HA, see hybrid automatonHamiltonian, 79, 81

port control H., 388port-H., 154

HCCI, see homogeneous charge compressionignition

HCCI engine, 461heat release, 464HHARX model, see hinging-hyperplane

ARX modelhierarchical connection, 369hierarchical control, 414hierarchical process, 508, 509






558 Index

high-level control, 423high-level supervisor, 414H∞-synthesis, 384hinging-hyperplane ARX model, 318HMP, see hybrid maximum principlehomogeneous charge compression ignition,

461HW/SW components, 442HW/SW testing, 443hybrid automaton, 15, 17, 35, 59, 63, 145,

251, 407network of h.a., 362rectangular h.a., 63regular h.a., 74

hybrid control, 223hybrid decoupling constraint, 100hybrid decoupling polynomial, 100hybrid dynamical phenomenon, 9hybrid flow, 74hybrid identification, 316Hybrid Identification Toolbox, 316, 320hybrid inclusion, 177hybrid jump, 275hybrid maximum principle, 80hybrid model parameter, 100hybrid model-predictive control, 452hybrid state, 59, 106hybrid state observer, 106hybrid state space, 59hybrid switch point, 235hybrid system, 4, 31

autonomous h. s., 8continuous-time h. s., 151phenomena of h. s., 9structure of h. s., 33

Hybrid System Interchange Format, 362hybrid system theory, 4hybrid time basis, 107hybrid time set, 252hybrid time trajectory, 175Hybrid Toolbox, 308, 320, 322, 459HyBrSim, 348HYCON, xivhyperplane, 72HYSDEL, 299, 458HyTech, 55, 286, 368HyVisual, 367

I/-behavior, 226

I/S-machine, 225identification, 54, 92

actual engaged gear i., 451set-membership i., 103

if-then rule, 144, 299implicit description, 173impulse differential inclusion, 188inclusion, 131inequality constraint, 153, 400initial state probability, 219injector, 34input

Bohl-type i., 162continuous i., 8, 18discrete i., 8, 18quantized i., 214

input quantizer, 199input/output model, 93input/output pair, 95

spurious i/o p., 218input/output system, 152intake stroke, 461intake throttle valve control, 441integer optimization problem, 507integral-partial-differential-algebraic

equation, 327integration and testing flow, 442intensity, 269interchange architecture, 321interchange format, 41, 362

compositional i.f., 362interface, 34interval region, 73invariant, 60, 287

i. hypercubes, 210i. property, 76

IPDAE, see integral-partial-differential-algebraic equation

Jacobian, 399joint spectral radius, 122, 131jump, 10, 287jump function, 61jump rate, 269jump set, 12, 40

KRONOS, 55

l-complete approximation, 228






Index 559

l-completeness, 228labeling function, 60Lagrangian, 77language-equivalence relation, 62LaSalle’s invariance principle, 74LCP, see linear complementarity problemleast squares, 104least squares fitting, 382LHA, see linear hybrid automatonlifting representation, 385limit cycle, 203, 238linear classifier, 317linear complementarity model, 37linear complementarity problem, 151, 159linear complementarity system, 152, 168linear constraint, 300linear dynamical system, 299linear hybrid automaton, 62, 286, 322linear hybrid system, 63linear matrix inequality, 52, 117linear passive system, 160linear programming, 288, 304linear quadratic regulator, 142linear saturation system, 183linear switched system, 106, 107linear temporal logic, 62Lipschitz continuity, 257live-lock, 178liveness, 107LMI, see linear matrix inequalityload shedding, 397local regression, 101local stability, 206location, 15, 59, 287location observability, 110locational optimization, 208logic constraint, 301logic controller, 406low complexity setup, 306low-level control, 414, 423low-level plant model, 423LQR, see linear quadratic regulatorLTL, see linear temporal logicLyapunov function, 114, 205, 307

common L.f., 116, 388control L.f., 207multiple L.f., 119piecewise linear L.f., 120poly-quadratic L.f., 123

quasi-quadratic L.f., 120weak L.f., 121

Lyapunov stability theory, 114Lyapunov’s indirect method, 75Lyapunov-like function, 120

magnetic actuators, 455Markov chain, 264, 487Markov parameter, 189Markov property, 218

M.p. of quantized system, 218mathematical programming, 152max-min-plus-scaling system, 169mean-value model, 449measurement aggregation, 416MILP, see mixed-integer linear programmingminimax optimization, 304MINLP, see mixed-integer nonlinear

programmingMIQP, see mixed-integer quadratic

programmingmixed discrete-continuous dynamical

program, 423mixed logical dynamical model, 37, 506mixed logical dynamical system, 37, 145,

168, 299, 305, 458mixed switching, 235mixed-integer linear programming, 148, 304mixed-integer linear sequence, 312mixed-integer nonlinear optimization

problem, 436mixed-integer nonlinear programming, 351,

427mixed-integer programming, 96, 303, 308,

398mixed-integer quadratic programming, 148MLD, see mixed logical dynamical systemMMPS, see max-min-plus-scaling systemmode

active m., 145mode of operation, 152, 445mode selector, 145mode sequence, 232model

average m., 43complete m., 218decisive power, 41discrete-event m., 196, 218input/output form, 93






560 Index

modeling power, 41nondeterministic m., 217sampled-data m., 384

model checker, 275, 286model checking, 54, 274model integration, 327Model Predictive Control Toolbox, 308model-based design, 444model-predictive control, 52, 211, 353, 397,

452, 454dual mode m.p.c., 211explicit m.p.c., 379

model-predictive controller, 308, 406, 507,509

Modelica, 55, 283, 329, 348, 353, 357, 365modeling framework, 31modularity, 326modulation scheme, 493MPC, see model-predictive controlmpQP, see multi-parametric quadratic

programmingMPT, see Multi-Parametric ToolboxMRLP, see multicategory robust linear

programmingMS, see mode selectormulti-agent system, 474multi-controller scheme, 113multi-disciplinary design, 4multi-parametric programming, 303, 383multi-parametric quadratic programming,

308Multi-Parametric Toolbox, 303, 316, 320,

322multi-rate automaton, 54multi-regime system, 157multicategory robust linear programming,

317multiMin, 410multiple shooting, 351, 436multiple state feedback, 389multiple time scales, 416multiple-vehicle system, 478multiproduct plant, 419multirate control, 442MUSCOD, 354

natural gas, 463natural projection, 226NCS, see networked control system

nearest-neighbor quantizer, 207needle variation, 78networked control system, 5, 113, 203, 472,

487networked system, 441NMPC, see nonlinear model-predictive

controlnominal operation, 448nonanticipating system, 226nonblocking, 178, 179noncausal modeling, 329nonconflicting behavior, 227nondeterminism, 216, 250nondeterministic hybrid system, 250nonlinear differential equation, 20nonlinear dynamics, 19, 406nonlinear model-predictive control, 427nonlinear programming, 211, 428nonsmooth mechanics, 6nonsmooth system, 42nonswitching time, 164nontriviality condition, 81NP, 130NP-complete, 131NP-hard, 95, 99, 130, 131NPSOL, 430numerical simulation tool, 329

object-oriented implementation, 324observability, 52, 108, 182

incremental o., 108, 137observer, 53observer design, 451obstacle, 477ODE, see ordinary differential equationOmola, 329, 348on-board diagnosis, 449on/off switch, 300operating point, 399operation mode, 15, 18, 232optimal control, 49, 211, 303, 418, 434optimal state-feedback control, 383Optimica, 354optimization, 350, 410

smooth constrained o., 96Optimization Toolbox, 309optimization-based analysis using simula-

tion, 411optimization-based controller, 307






Index 561

orbital stability, 239ordinary differential equation, 327oscillation, 401output

continuous o., 8discrete o., 8quantized o., 214

output quantizer, 197over-approximation, 67, 437

P, 130P-matrix, 160p-periodic linear system, 243p-periodic state feedback, 243packet loss, 206, 472parallel composition, 362parallel connection, 369particle filtering, 103passivity, 151, 161, 163passivity constraint, 454PCH, see port control Hamiltonianpdf, see probability density functionperformance, 209, 389periodic control, 243periodic solution, 384periodic stationary execution, 238periodic stationary operation, 233perturbation, 74Petri net, 55phase-portrait approximation, 294physical process, 4PI control, 23, 427, 433piecewise affine ARX model, 318piecewise affine autoregressive exogenous

model, 93piecewise affine dynamics, 299piecewise affine feedback, 303, 452piecewise affine model, 453, 454piecewise affine system, 36, 90, 134, 137,

167, 322continuous-time p.a.s., 379discrete-time p.a.s., 121

Piecewise Affine System IdentificationToolbox, 317

piecewise linear Lyapunov function, 120piecewise linear system, 151, 181piecewise smooth system, 35platform, 443platform-based design, 443

platform-dependent language, 321platform-independent format, 324platform-specific format, 321PMP, see Pontryagin’s maximum principlePoisson process, 269polyhedral partition, 93, 308, 383polyhedron, 69, 303polynomial embedding, 99polynomial-time algorithm, 130polytope, 304polytope manipulation, 304Pontryagin’s maximum principle, 78, 85port control Hamiltonian, 388port-Hamiltonian complementarity system,

154power conversion, 378power converter, see DC-DC converter,

boost converterpower generation, 378power level, 493power outage, 393power system stabilizer, 396power transmission, 378powertrain control, 454practical stability, 200practically stabilizing controller, 209predicate

convex p., 62deadline p., 367

prediction model, 398predictive logic controller, 507primary controller, 401priority, 367probabilistic safety analysis, 265probability density function, 102probability map, 274programming logic controller, 49propositional logic, 299PSS, see power system stabilizerPtolemy II, 349pulse width modulator, 379PWA, see piecewise affinePWAID, see Piecewise Affine System

Identification ToolboxPWARX, see piecewise affine autoregressive

exogenous modelPWARX model, see piecewise affine ARX

modelPWM, see pulse width modulator






562 Index

qdb-controller, 210QoS, see quality of serviceQP, see quadratic programmingQP solver, 309quadratic optimization problem, 303quadratic programming, 142, 304quality of service, 473quantization, 193, 197, 198

dense q., 203input q., 208output q., 198, 208q. density, 206q. error, 200, 208q. map, 196q. noise, 472, 490q. threshold, 491q. width, 493state q., 198

quantized behavior, 196nondeterminism of the q. b., 216

quantized input, 214quantized model

completeness of q. m., 218, 219quantized output, 214quantized state, 214quantized system, 196

discrete-event q. s., 215discrete-time q. s., 215q. linear s., 196

quantized value, 214quantizer, 214

logarithmic q., 201, 207nearest neighbor q., 199output q., 197state q., 196

quarter car model, 454quasi-quadratic Lyapunov function, 120queue, 159

rapid prototyping, 309raw data classification, 103rbfSolve, 410re-usability, 326reachability, 63, 64, 230, 306reachability analysis, 64, 249reachable space, 69reachable state, 179Real Time Workshop, 307, 309real-time system, 349

real-valued variable, 300receding-horizon control, 304, 305recovery, 449refinement, 103, 229, 443refrigeration system, 426region, 64, 73region estimation, 97, 98region graph, 64region stability, 73regression vector, 93regularity, 55, 273relaxation, 174relay characteristic, 156relay system, 156reliable operation, 393reset, 332reset map, 16, 60residual gas, 462residual signal, 451resolution, 210resource allocation, 212resource utilization, 473return map, 75, 239

controlled r. m., 241RHC, see receding-horizon control, 305right-accumulation point, 46RLP, see robust linear programmingrobust controller, 304robust linear programming, 98robustness, 54, 245roundabout policy, 475rule-based control, 450run, 175, 288

safety, 437, 449probabilistic s., 265

safety analysis, 67, 265, 410sampling

event-driven s., 224time-driven s., 230

sampling period, 206saturated linear system, 135saturation, 37scheduler, 363Scilab, 349scope, 368SeDuMi, 304semantics, 175semi-active suspension, 453






Index 563

semi-analytical approach, 410semi-definite programming, 304semicontinuous, 186semicontinuous function, 186sensor network, 473separation technique, 97sequential controller, 406set-membership identification, 103set-membership test, 303SHIFT, 329, 349shut-down, 406SI, see spark ignitionSiconos, 349simulation, 46, 55, 444

block-diagram-based s., 329simulation tool, 326Simulink, 307, 309, 444single-linkage clustering, 316single-shooting technique, 351slack variable, 400sliding behavior, 47sliding mode, 47, 181small-gain condition, 202small-gain theorem, 211smooth constrained optimization, 96snapshot, 73software engineering, 5solar air conditioning plant, 502solar energy, 393solution, 36, 185

Carathéodory s., 51classical s., 50Filippov s., 51

spark ignition, 448, 461specification, 227, 443spectral radius

generalized s. r., 132SPEEDUP, 338spontaneous transition, 257, 262, 275spurious input/output pair, 218stability, 43, 72, 113, 131, 165

asymptotic s., 114exponential s., 114global asymptotic s., 114input-to-state s., 137local s., 206orbital s., 239practical s., 200, 201region s., 73

stability analysis, 72, 121, 307stabilizability, 52, 166stabilization, 124, 199stabilizing switching law, 124stable system, 114start-up, 406, 433start-up performance, 389start-up time, 434state, 366

continuous s., 8discrete s., 8quantized s., 214

state feedback, 303state jump, 10, 22

autonomous s.j., 12controlled s.j., 14

state machine, see automatonstate observer, 206state quantizer, 196state space

partitioned s. s., 214state transition function, 14state-dependent switching, 157state-event detection, 363stationary operation, 233steady-state operation, 397, 407steepest descent, 389stochastic automaton, 219stochastic hybrid automaton, 256stochastic hybrid model, 55stochastic hybrid system, 249stopping condition, 367stopping time, 257stopwatch automaton, 64strictly passive, 165stroke detection, 448structural stability, 74subharmonic oscillation, 381supervisor, 225

admissible s., 227generically implementable s., 227least restrictive s., 227

supervisory control, 225, 227supervisory control theory, 226support vector machine, 317SVM, see support vector machineswitched affine autoregressive exogenous

model, 93switched circuits, 6






564 Index

switched cone complementarity system, 154switched linear system, 118, 425switched model-predictive controller, 454switched system, 35, 89, 137

autonomous s.s., 90, 112controlled s.s., 89, 112discrete-time s.s., 112linear s.s., 106

switching, 10, 47, 80, 131, 400autonomous s., 10, 17clock-driven s., 235controlled s., 14, 18event-driven s., 10, 235, 241fast s., 124mixed s., 235stabilizing s., 124time-driven s., 10

switching behavior, 363switching condition, 80, 234switching diffusion system, 270switching frequency, 233switching function, 154switching logic, 232switching period, 27switching scheme, 27switching set, 10, 77, 80switching structure, 45switching surface, 47, 90switching system, 90switching time, 77, 80, 164synchronization, 60, 365, 427synthesis, 406synthesis flow, 442system

max-min-plus scaling s., 55chaotic s., 203continuous s., 43discontinuous dynamical s., 35discrete-event s., 43discrete-time stochastic hybrid s., 275hybrid s., 4mixed logical dynamical s., 37passive s., 165piecewise smooth s., 35switching diffusion s., 270switching s., 90timed s., 363

System Identification Toolbox, 305system integration, 441

system specification, 442system testing, 443systems theory, 5

targent vector, 79target region, 434target set, 77TDC, see top dead centertechnological system, 4temporal logic, 62TG, see turbine governortheorem proving, 411thermostat, 7, 254throttle valve control, 448tight over-approximation, 294time scale, 378time-varying linear system, 131time-varying parameter, 128timed automaton, 40, 54, 63, 350, 409timed computation tree logic, 64TOMLAB, 353, 410tool-specific layer, 321top dead center, 461traction control, 453transition function, 234transition intensity, 275transition kernel, 262transition probability, 264transition relation, 59transition system, 59transmission network, 393transversality condition, 81turbine governor, 395Turing machine, 134, 135two-layer architecture, 433two-level control architecture, 414two-level hierarchical solution, 418two-tank system, 17

uncertainty, 304uncertainty set, 131undecidability, 63, 69, 130, 134uniform time scale, 415unilaterally constrained mechanical system,

182uniqueness, 187unsafe set, 264UPPAAL, 55, 283, 329, 347, 349, 368urgency, 363, 366






Index 565

urgency predicate, 367urgent guard semantics, 367usability, 327

valve assembly, 407variable, 141

connected v., 369variable geometry turbine, 221, 454VDC, see vehicle dynamical controlvector field, 59, 60vehicle dynamical control, 441vehicle dynamics, 453verification, 62, 264, 303, 406VGT, 449, 454voltage instability, 393, 397voltage regulation, 381, 393, 396, 397VTG, see variable geometry turbine

Wardrop principle, 158weak Lyapunov function, 121well-defined solution, 173well-formed expression, 175

well-posedness, 36, 46, 173, 178global w., 179initial w., 178local w., 179

Wiener process, 256wind energy, 393wireless communication, 473worst-case analysis, 250

XML, see extensible markup languageXML Toolbox, 321

YALMIP, 302

Zenoleft-Zeno free, 164right-Zeno free, 164Zeno free, 164

ZENO, 45Zeno behavior, 45, 180, 189, 332Zeno phenomenon, 191zero crossing, 46






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