Index

a

  • Adaptive control  2, 25
  • Advanced process control (APC)  2, 297
  • Aggregation, equivalent  284–90
    • algorithms  287, 290
    • unconstrained case  284–7
    • zero terminal constraint case  287–90
  • Aggregation, quasi equivalent  291–4
    • with input/state constraints  292
    • with terminal set constraints  291
  • Aggregation of optimization variables  281–94
    • aggregation matrix, variable  282
    • input decaying strategy  283–4
    • linear aggregation transformation  282
    • relationship with input parameterization  283
  • Air separation unit (ASU)  346–50
    • controlled variables (CVs)  346
    • manipulated variables (MVs)  346
    • step response  348
    • zone control technique  347
  • Angle servo system  339
  • Application fields, extension  313–18
    • advanced manufacturing  314
    • automobiles  316
    • autonomous vehicles  317
    • buildings  315
    • critical infrastructure systems (CIS)  315–16
    • medical treatment systems  317
    • power electronics  314–15
    • power networks  316
  • Associated variable (AV)  310–12
  • Automatic train operation (ATO)  323–8
    • black box  324
    • brake control system  324
    • multi model strategy  327
    • operation command  324
    • traction control system  324

b

  • Back propagation (BP) network  249
    • back propagation of error  251
    • gradient method  251
    • hidden node layer  250
    • input bias  250
    • Sigmoid function  250
    • weighting coefficient  250
  • Black box technique  320
  • Blocking technology  277–9, 308
    • average blocking strategy  278
    • horizontal blocking strategy  278
    • layered blocking strategy  278

c

  • CARIMA (Controlled auto‐regressive integrated moving average) model  25
    • backward shift operator  25
    • differencing operator  25
    • random disturbance  25
  • Cascade predictive control  262–6
    • control structure  264
    • disturbance rejection  262
    • generalized plant  263
    • inner loop (secondary loop)  263–4
    • intermediate variable  263
    • layered structure  263
    • outer loop (major loop)  263–4
    • secondary disturbance  263
  • Coefficient mapping of open/closed‐loop characteristic polynomials  81–9
    • coefficient mapping, GPC  85
    • coefficient mapping, DMC  88
    • relationship of model parameters and step response  83
  • Constrained multi‐objective multi‐degrees of freedom optimization (CMMO)  270–7, 302
    • constraints  273–4
    • hard/soft requirements  273
    • performance index  273–4
    • priority of user’s requirements  273
  • Constrained optimization, DMC  123–32
  • Constraint violation  292, 301, 306
  • Constraints  123, 273–4, 307
  • Controlled variable (CV)  302, 310
  • Conversion section of synthetic ammonia production  265
  • CSTR (Continuously stirred tank reactor)  246

d

  • Deadbeat property  60, 79–81, 93–4
  • Decentralized predictive control  140–3
    • feedback correction  142
    • non‐causal prediction methods  142
  • Decomposition of online optimization, multivariable DMC  132–46
    • comparison of three decomposition algorithms  143–6
      • information structure  143–4
      • optimal control law  144
      • optimization scheme  143–4
    • three decomposition strategies  133–43
  • Definition of process variables  302, 305
  • Diophantine equation  26
    • recursive calculation  27–8
  • Direct digit control (DDC)  302
  • Distributed predictive control  137–40
    • convergence of iteration  139
    • information architecture  140
    • Nash optimal solution  138 (see also Nash optimization)
    • prediction and iteration  139
  • Disturbance variable (DV)  302
  • DMC algorithm, state space framework  21–5
    • correspondence with DMC  24
    • predictive state  23
    • realization condition  23
    • separation principle  24
    • state feedback control with state observer  24
    • state space realization with step response  23
  • DMC algorithm, unconstrained case  15–21, 115–22
    • algorithmic structure  20, 120
    • online computation chart  22
  • DMC controller in IMC structure  47, 48–55
    • stability  48–53
    • transfer function  47
  • DMC filter in IMC structure  47, 56–62
    • robust stability  60–62
    • transfer function  56–8
  • DMC optimization for time delay systems  54–5
  • DMC‐PID cascade control  262–6 (see also Cascade predictive control)
  • Dual mode control  170, 191, 199, 207, 224
  • Dynamic constraint control, requirements from industrial users  270–4
    • adjustable hard/soft requirements  273
    • hard, requirements  273
    • priority of requirements  273, 306
    • soft requirements  273
  • Dynamic constraint control, role in industrial hierarchy  300–2
    • boundary control  301
    • economic profits  301
    • steady‐state operating point  301
  • Dynamic matrix control (DMC)  2, 297

e

  • Efficient robust predictive control (ERPC)  216–20
    • additional input variables (perturbations)  217
    • algorithm, offline/online  220
    • fixed feedback control law  217
    • input constraint handling  218
    • invariant set in augmented state space  218–9
    • invariant set in original state space  217
    • set projection from augmented to original state space  218–9
  • Embedded implementation, predictive controller  335–50
    • digital signal processor (DSP)  343–50
    • field programmable gate array (FPGA)  335–43
  • Extended prediction self‐adaptive control (EPSAC)  3

f

  • Feasibility, CMMO  274–6
    • definition  274
    • judgment/adjustment  274–5
    • LP formulation  275
    • steady‐state gain matrix  274
  • Feedback correction, DMC  19–20, 119
    • correction vector, also correction parameter  19–21, 119
    • output feedback  304
    • shift matrix  20, 63, 119
  • Feedback correction, GPC  31
    • control law adaption  31
    • parameter estimation  31
    • reference trajectory  31
  • Feedback correction, state space MPC  35
    • state observer with measurable outputs  36
  • Feedback correction strategies  56–60
    • attenuation correction  57
    • equal‐value correction  56
    • increasing correction  57
  • Feedback linearization  235–8 (see also Input‐output linearization)
  • Feedforward‐feedback structure  259–62
    • causal information  260
    • control scheme  261
    • feedback correction  260
    • feedforward compensation  260
    • non‐causal prediction  260
    • uncontrollable inputs with known variation rules  260
    • unknown disturbance  260
  • Finite impulse response (FIR)  304
  • Finite step response (FSR)  304
  • First order inertia plant with time delay  98–103, 264, 325
  • Fuzzy satisfactory clustering (FSC)  242–5
    • cluster center  243
    • data sample set  242
    • fuzzy rules  242
    • generalized input vector  242, 245
    • membership degree  242
    • membership matrix  243

g

  • Gas transportation network  318–23
    • closed‐loop optimization  321
    • demand forecasting  321
    • hierarchical decomposition  323
    • model transformation  320
    • observer technology  321
    • partial differential equations  319
    • software package GANESI  318
  • Generalized predictive control (GPC)  3, 25–32
  • GPC controller in IMC structure  81–6
  • Gustafson and Kessel (GK) algorithm  243

h

  • Hammerstein model  253
    • dynamic linear model  254
    • input nonlinearity  254
    • intermediate variable  254
    • static nonlinear component  254
  • Hierarchical predictive control  133–7, 328–35
    • convergence  136–7
    • coordination variable (factor)  133, 135
    • decomposition‐coordination  133–5
    • goal coordination method  133
    • gradient algorithm  135
    • interaction balance relationship  133, 135
    • optimality of the solution  136
    • strong duality theorem  133
    • two level optimization  134
  • Hierarchical structure of industrial processes  300, 310
    • basic dynamic control  301
    • dynamic constraint control  300
    • global economic optimization  300
    • local economic optimization  300
  • Historical trajectory of predictive control  5
  • Holding process, injection molding machine  342
  • Homogeneous linear equations  285
    • base of null solution space  288
    • linear independence of column vectors  285
    • particular solution  288
  • Hydrocracking reactor, QDMC application  308–13
    • energy saving mode  310
    • profile control mode  310

i

  • Identification of impulse/step response  303–4, 310–11
    • data acquisition  303–4
    • PRBS‐like stepping signal  304
      • least square method  304
    • Pseudo Random Binary Signal (PRBS)  304, 310
      • correlation analysis method  304
  • Identity of DMC/GPC controller  86
  • IHO approximated by FHO  152–4
    • terminal constraint set  153
    • terminal cost function  153
    • terminal equality constraint  153
    • zero terminal constraint  153
  • IMC properties  42–4
    • dual stability criterion  42
    • perfect controller  42
    • zero offset  43
  • IMC structure, DMC algorithm  44–8
    • block diagram transformation  44–7
    • transfer functions of blocks  47–8
  • Impulse response  303–4
  • Industrial MPC software  298–9, 303
    • common properties  303
    • Connoisseur (control and identification package)  299
    • DMC‐plus  299
    • HIECON (Hierarchical Constrained Control)  299
    • IDCOM (IDentification and COMmand)  270, 297–8
    • IDCOM‐M  299
    • PFC (Predictive Functional Control)  299
    • QDMC (Quadratic Dynamic Matrix Control)  299, 308–13
    • RMPCT (Robust Model Predictive Control Technology)  299
    • SMCA (Setpoint Multivariable Control Architecture)  299
    • SMOC (Shell Multivariable Optimizing Controller)  299
  • Input parametrization  277–81, 308
  • Input‐output (I‐O) linearization  235–7
    • decoupled SISO linear system  237
    • Lie derivative  236
    • MIMO affine nonlinear system  235
    • relative degree  236
  • Internal model control (IMC)  3, 41–8, 81–6
  • Invariant set  157–60

k

  • Kleinman controller  77

l

  • Linear matrix inequality (LMI)  160–3
    • input constraint satisfaction  161–2
    • output constraint satisfaction  162–3
    • Schur complements  160–1, 184, 188
  • Linear parameter varying (LPV) system  182
  • Linear programming (LP)  268, 274–6, 306
  • Linear quadratic (LQ) control  76, 151, 163, 170
  • Lyapunov function  152, 155, 187–91
    • parameter dependent  187
    • single  187

m

  • Mathematical model  1
  • Maximal admissible set  160
  • Mean level control  51
  • Min‐max optimization  182, 192, 216, 267
  • Minimal form of DMC controller  88
  • Minimum parametric model  3
  • Minimum variance self‐tuning regulator  25
  • Minkowski set addition/subtraction  205
  • Model algorithmic control (MAC)  2
  • Model mismatch  44, 59, 61, 142, 264
  • Model predictive control (MPC), also predictive control  1
  • Model predictive heuristic control (MPHC)  2, 297
  • Modern control theory  1
    • gap with industrial practice  2
  • Multi input multi output (MIMO) system, also multivariable system  115
  • Multi‐step control set  199
    • LMI conditions  200
    • properties  200
  • Multiparameter programming  227
  • Multiple model predictive control  241–8
    • control structure  246
    • divide‐and‐conquer strategy  241
    • integration into MIMO model  245
    • integration mode  241
    • multi‐input single‐output (MISO) system  242
    • switching mode  241
  • Multivariable predictive control  115–46
    • constrained DMC algorithm  123–32
    • unconstrained DMC algorithm  115–22

n

  • Nash optimization  138
    • multi‐person multi‐objective optimization  138
    • Nash optimum  139
  • Neural network predictive control  248–53
    • IMC structure  253
    • multi‐step prediction  251
    • neural network modeling  249–51 (see also Back propagation network)
    • neural network online optimization controller  253
    • one step neural network prediction model  253
  • Nonlinear algebraic equation group (NAEG)  254
    • Newton iteration method  255
  • Nonparametric model  2, 16, 63

o

  • Off line design and online synthesis, RMPC synthesis  220–3
    • combination coefficients  222
    • look‐up table  221
    • off line design steps  221
    • online synthesis steps  221–3
    • a series of ellipsoidal invariant sets/feedback control laws  221
  • One step optimization strategy (OSOS) of DMC  53–4, 121
  • Online optimization problem formulation  152–4
    • finite horizon optimization (FHO)  153
    • infinite horizon optimization (IHO)  152
    • predictive control (PC)  155
  • Optimal control, information requirement /control mechanism  354–5
  • Optimal control, relationship with predictive control  150–2
    • dynamic programming  150
    • infinite horizon optimization  150
    • maximum value principle  150
    • optimal control sequence  150
    • optimal feedback control law  150
    • optimal value function  151
  • Output trajectories  307
    • funnel control  307
    • reference trajectory  307
    • set point control  307
    • zone control  307, 347
      • set point approximation  307

p

  • pH neutralization process  246
  • PID Controller  1, 263, 301
  • PID Controller, information requirement/control mechanism  354–5
  • Plants with different degrees of freedom  302
    • “fat” plant, under‐determined  302
    • “square” plant, well posed  302
    • “thin” plant, over‐determined  302
  • Polytopic uncertainty  181, 187, 191–9
    • composite polytope  193
    • convex combination parameters/coefficients  182, 187, 193
    • convex hull/vertices  182, 187, 193, 195–9
    • uncertainty expansion  193, 195–9
      • tree structure of state expansion  195
  • Prediction model, DMC  15–16, 116–17
    • model length  16, 89, 115
    • model vector, also model parameter  16, 20–21, 115, 119
    • output prediction  16, 116
    • step response  15, 115
  • Prediction model, GPC  25–8
    • deterministic input‐output difference model  26
    • discrete time transfer function model  26, 32
    • stochastic linear difference equation  25 (see also CARIMA model)
  • Prediction model, state space MPC  32–4
    • control increment form  35, 326
    • output prediction  33
    • state prediction  32
  • Predictive control  1
  • Predictive control, Hammerstein system  253–6
    • control structure  255
    • desaturation method  254
    • Hammerstein system, , 253 (see also Hammerstein model)
    • nonlinear separation strategy  254
    • two step predictive control strategy  254
  • Predictive control, nonlinear systems  231–56
    • compounded nonlinearity  232–4
    • general description  231–3
    • input‐output model  232
    • nonlinear rolling horizon optimization  234
    • state space model  231
    • strategies and methods  234–5
  • Predictive control, nonlinear systems with I‐O linearization  235–8
    • layered control structure  237
  • Predictive control based on state space model  32–7
  • Predictive functional control (PFC)  279–81, 308
    • base function  279
    • closed‐loop output prediction  280
    • combination coefficients  280
    • control structure  281
    • free model output  280
    • model function output  280
    • reference trajectory  280
    • tuning of design parameters  281
  • Principles of predictive control, basic  6–10, 353
    • feedback correction  7, 353
    • prediction model  6, 353
    • rolling optimization  6, 353
  • Principles of predictive control, generalized  355–8
    • dynamic uncertain environment  356
    • feedback initialization  357
    • general control problems  355
    • rolling window optimization  357
    • scenario prediction  356
  • Proportion and superposition properties  16, 116, 120, 231

q

  • QP implementation in DSP  343–50
    • continuous‐time SDNN for solving QP  344–5
    • discrete time implementation of SDNN  345
    • simplified dual neural network (SDNN)  343
  • QP implementation in FPGA  337–43
    • ECQP (QP with equality constraints) solver  337–8
    • hardware matrix inversion  341
    • hardware matrix multiplier and adder  337
    • S‐ECQP (combination of SPMI and ECQP) solver  341
    • SPMI (symmetric matrix inversion) algorithm  341
    • vector multiplier  337
  • Quadratic programming (QP)  125, 128, 306, 337
    • active set method  129
    • QP with equality constraints (ECQP)  129, 337–8
    • rules for judgment/adjustment  130
    • standard QP form  128
  • Qualitative synthesis theory of predictive control  4, 149–78, 181–227
    • fundamental philosophy  150–7
    • robust predictive controller synthesis  181–227
    • stable predictive controller synthesis  163–78
  • Quantitative analysis in time domain, GPC  76–81
    • deadbeat and stability conditions for GPC  79–81
    • GPC control law in the form of Kleinman controller  79
      • LQ control law of GPC  77
      • realization in state space, GPC  76
      • Riccati iterative formula  77
  • Quantitative analysis in Z domain, DMC and GPC  81–112
    • closed‐loop stability  97
    • deadbeat controller/closed‐loop transfer function  93–5
    • reduced order  94–7
    • solvability  92
    • uniform coefficient mapping of DMC and GPC  88
    • zero coefficient condition  91
  • Quantitative analysis in Z domain, typical systems  98–112
    • close‐loop dynamics  101, 106, 110
    • first order plant  98
    • parameter setting  99, 104
    • second order oscillation plant  104
    • stability  101, 106, 107
    • summary of performance analysis  103, 112
  • Quantitative analysis theory of predictive control  3–4, 75–112, 149

r

  • Receding horizon control (RHC)  4, 151, 155, 175
    • finite horizon optimization  151
    • infinite horizon LQ control  151
  • Recursive feasibility  155–7, 186, 195, 203
    • candidate solution  156
    • feasible solution  156
    • Lyapunov function  155–7
    • optimal control sequence  155, 174
    • optimal state trajectory  155, 174
    • optimal value of performance index  155
    • rolling style implementation  155
  • Region of attraction  209
  • Removal of ill‐conditioning  305
    • input move suppression  305
    • singular value thresholding  305
  • Robot rolling path planning  363–6
    • collision free moving path  363
    • environment map  363
    • local path planning  364
    • obstacle avoidance  365
    • subgoal determination  364
  • RMPC synthesis, contradiction  214–16
    • computational burden  214
    • control performance  215
    • feasible region  214
  • RMPC synthesis, QP method  223–7
    • dual‐mode control strategy  224
    • feedback gain/terminal invariant set solving  224–5
    • polyhedral invariant set calculation  225
    • QP problem formulation  225–6
  • RMPC synthesis, systems with disturbances  205–14
    • based on disturbance invariant set  205–9
      • disturbance invariant set  206
      • disturbed subsystem  207
      • linear and additive character  206
      • nominal subsystem  207
      • properties of the RMPC controller  209
    • based on mixed imagesperformance  209–14
      • imagesperformance  210
      • H2performance  210
      • nominal sub‐state  213
      • sub‐state affected by disturbance  213
    • external disturbance  205
  • RMPC synthesis, systems with polytopic uncertainty  181–205
    • asymptotical stability  186, 203
    • LMI formulation of constraints  183–5
    • LPV system with polytopic uncertainty  181
    • recursive feasibility  186, 195, 203, 213
    • strictly decreasing condition  183, 186, 188, 202
  • Robust model predictive control (RMPC)  181–227
  • Robust predictive control with infinite norm optimization  267–70
    • affine function  269
    • boundary vertexes  269
    • infinite norm  267
    • min‐max optimization  267, 269
    • standard LP problem  268, 270
    • step response with polyhedral uncertainty  268
  • Rolling optimization, DMC  16–18, 117–18
    • analytical control law, unconstrained case  18, 118
    • control horizon  16, 122, 308
    • control vector, also control parameter  18, 20–21, 119
    • control weighting matrix  18, 118, 122
    • dynamic matrix  17, 311
    • error weighting matrix  18, 118, 122
    • optimization horizon, also prediction horizon  16, 122, 307
    • performance index  16, 18, 117
  • Rolling optimization, GPC  28–30
    • control horizon  28
    • control weighting sequence  28
    • long range prediction and optimization  28
    • mathematical expectation  28
    • minimum/maximum optimization horizon  28
    • performance index  28
    • reference trajectory  28, 31
    • step response coefficients  30
  • Rolling optimization, state space MPC  34–5
    • output optimization  34
    • state optimization  34
  • Rolling scheduling, Job Shop  358–63
    • dynamic scheduling  359
    • flexible manufacturing system (FMS)  358
    • job window  359
    • periodic and event driven rolling mechanism  360

s

  • Satisfactory control  276–7, 303
  • Scenario technique  353
  • Sequential quadratic programming (SQP)  132, 331
  • Single input single output (SISO) system  4, 15, 76
  • Stable predictive control, general stability condition  174–7
    • direct method  176
    • monotonicity of optimal value function  175
    • three ingredients  154, 174
      • local stabilizing controller  174
      • terminal constraint set  174
      • terminal cost function  174
  • Stable predictive control, sub‐optimality  177–8
  • Stable predictive control, synthesis  163–73
    • with terminal cost functions  165–70
    • with terminal set constraints  170–3
    • with zero terminal constraints  163–5, 287
  • Steady‐state optimization (SSO)  276, 305
  • Step response  15, 115, 303
    • coefficients of  16, 30, 115
    • truncation of  19, 63

t

  • Takagi‐Sugeno (T‐S) model  242
  • Time series forecasting  142, 260
    • Holt‐Winters approach  142
  • Transparent control, (TC)  266, 302
  • Trend analysis of DMC parameters  53, 75
    • stability  48–53, 75
    • robustness  60–62
  • T‐S modeling algorithm based on FSC  243–4
  • Tuning of DMC parameters, MIMO system  122
  • Tuning of DMC parameters, SISO system  62–8
    • control horizon  65
    • control weighting matrix  66
    • correction parameter  66
    • error weighting matrix  64
    • model length  63
    • optimization horizon  64
    • steps for general plants  67–8

u

  • Urban traffic networks  328–35
    • centralized predictive control  332
    • decentralized predictive control  332
    • fixed‐time control  332
    • macroscopic fundamental diagram (MFD)  329
    • optimal traffic flows between subnetworks  329
    • two level hierarchical predictive control  328–31
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