Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

Contents......Page 14
1. Introduction......Page 18
1.1 Historical Perspective on Nonlinear H∞-Control......Page 19
1.2 General Set-Up for Nonlinear H∞-Control Problems......Page 21
1.2.1 Mixed H2/H∞-Control Problem......Page 29
1.2.2 Robust H∞-Control Problem......Page 31
1.2.3 Nonlinear H∞-Filtering......Page 32
1.2.4 Organization of the Book......Page 33
1.3.1 Notation......Page 35
1.3.2 Stability Concepts......Page 37
1.4 Notes and Bibliography......Page 43
2.1 Dynamic Programming Principle......Page 44
2.2 Discrete-Time Nonzero-SumDynamic Games......Page 47
2.2.1 Linear-Quadratic Discrete-Time Dynamic Games......Page 49
2.3 Continuous-Time Nonzero-Sum Dynamic Games......Page 51
2.3.1 Linear-Quadratic Continuous-Time Dynamic Games......Page 53
2.4 Notes and Bibliography......Page 57
3. Theory of Dissipative Systems......Page 60
3.1 Dissipativity of Continuous-Time Nonlinear Systems......Page 61
3.1.1 Stability of Continuous-Time Dissipative Systems......Page 68
3.1.2 Stability of Continuous-Time Dissipative Feedback-Systems......Page 69
3.2 L2-Gain Analysis for Continuous-Time Dissipative Systems......Page 71
3.3 Continuous-Time Passive Systems......Page 73
3.4 Feedback-Equivalence to a Passive Continuous-Time Nonlinear System......Page 79
3.5 Dissipativity and Passive Properties of Discrete-Time Nonlinear Systems......Page 82
3.6 L2-Gain Analysis for Discrete-Time Dissipative Systems......Page 86
3.7 Feedback-Equivalence to a Discrete-Time Lossless Nonlinear System......Page 89
3.8 Notes and Bibliography......Page 94
4.1 The Hamiltonian Formulation of Mechanics......Page 96
4.2 Canonical Transformation......Page 99
4.2.1 The Transformation Generating Function......Page 101
4.2.2 The Hamilton-Jacobi Equation (HJE)......Page 103
4.2.3 Time-Independent Hamilton-Jacobi Equation and Separation of Variables......Page 104
4.3 The Theory of Nonlinear Lattices......Page 105
4.3.1 The G2-Periodic Toda Lattice......Page 108
4.4.1 Characteristics for Quasi-Linear Equations......Page 109
4.4.2 Characteristics for the General First-Order Equation......Page 111
4.4.3 Characteristics for the Hamilton-Jacobi Equation......Page 113
4.5 Legendre Transformand Hopf-Lax Formula......Page 114
4.5.1 Viscosity Solutions of the HJE......Page 116
4.6 Notes and Bibliography......Page 118
5.1 State-Feedback H∞-Control for Affine Nonlinear Systems......Page 120
5.1.1 Dissipative Analysis......Page 128
5.1.2 Controller Parametrization......Page 132
5.2 State-Feedback Nonlinear H∞ Tracking Control......Page 133
5.3 Robust Nonlinear H∞ State-Feedback Control......Page 136
5.4 State-Feedback H∞-Control for Time-Varying Affine Nonlinear Systems......Page 142
5.5 State-Feedback H∞-Control for State-Delayed Affine Nonlinear Systems......Page 144
5.6 State-Feedback H∞-Control for a General Class of Nonlinear Systems......Page 148
5.7 Nonlinear H∞ Almost-Disturbance-Decoupling......Page 149
5.8 Notes and Bibliography......Page 153
6.1 Output Measurement-Feedback H∞-Control for Affine Nonlinear Systems......Page 154
6.1.1 Controller Parameterization......Page 164
6.2 Output Measurement-Feedback Nonlinear H∞ Tracking Control......Page 168
6.3 Robust Output Measurement-Feedback Nonlinear H∞-Control......Page 170
6.3.1 Reliable Robust Output-Feedback Nonlinear H∞-Control......Page 172
6.4 Output Measurement-Feedback H∞-Control for a General Class of Nonlinear Systems......Page 175
6.4.1 Controller Parametrization......Page 179
6.5 Static Output-Feedback Control for Affine Nonlinear Systems......Page 183
6.5.1 Static Output-Feedback Control with Disturbance-Attenuation......Page 186
6.6 Notes and Bibliography......Page 190
7.1 Full-Information H∞-Control for Affine Nonlinear Discrete-Time Systems......Page 192
7.1.1 State-Feedback H∞-Control for Affine Nonlinear Discrete-Time Systems......Page 199
7.1.2 Controller Parametrization......Page 201
7.2 Output Measurement-Feedback Nonlinear H∞-Control for Affine Discrete- Time Systems......Page 205
7.3.1 Full-Information H∞-Control for a General Class of Discrete-Time Nonlinear Systems......Page 211
7.3.2 Output Measurement-Feedback H∞-Control for a General Class of Discrete-Time Nonlinear Systems......Page 213
7.4 Approximate Approach to the Discrete-Time Nonlinear H∞-Control Problem......Page 214
7.4.1 An Approximate Approach to the Discrete-Time State-Feedback Problem......Page 215
7.4.2 An Approximate Approach to the Discrete-Time Output Measurement- Feedback Problem......Page 218
7.5 Notes and Bibliography......Page 221
8.1 Continuous-Time Nonlinear H∞-Filtering......Page 222
8.1.1 Infinite-Horizon Continuous-Time Nonlinear H∞-Filtering......Page 227
8.1.2 The Linearized Filter......Page 230
8.2 Continuous-Time Robust Nonlinear H∞-Filtering......Page 231
8.3 Certainty-Equivalent Filters (CEFs)......Page 234
8.3.1 2-DOF Certainty-Equivalent Filters......Page 237
8.4 Discrete-Time Nonlinear H∞-Filtering......Page 239
8.4.1 Infinite-Horizon Discrete-Time Nonlinear H∞-Filtering......Page 244
8.4.2 Approximate and Explicit Solution......Page 245
8.5 Discrete-Time Certainty-Equivalent Filters (CEFs)......Page 249
8.5.1 2-DOF Proportional-Derivative (PD) CEFs......Page 252
8.5.2 Approximate and Explicit Solution......Page 254
8.6 Robust Discrete-Time Nonlinear H∞-Filtering......Page 258
8.7 Notes and Bibliography......Page 265
9.1 Singular Nonlinear H∞-Control with State-Feedback......Page 266
9.1.1 State-Feedback Singular Nonlinear H∞-Control Using High-Gain Feedback......Page 269
9.2 Output Measurement-Feedback Singular Nonlinear H∞-Control......Page 271
9.3 Singular Nonlinear H∞-Control with Static Output-Feedback......Page 273
9.4 Singular Nonlinear H∞-Control for Cascaded Nonlinear Systems......Page 275
9.5 H&38734;-Control for Singularly-Perturbed Nonlinear Systems......Page 280
9.6 Notes and Bibliography......Page 285
10.1 ProblemDefinition and Preliminaries......Page 286
10.2 Decomposition Filters......Page 287
10.3 Aggregate Filters......Page 295
10.4 Examples......Page 296
10.5 Notes and Bibliography......Page 297
11.1 Continuous-Time Mixed H2/H∞ Nonlinear Control......Page 298
11.1.1 The Infinite-Horizon Problem......Page 304
11.1.2 Extension to a General Class of Nonlinear Systems......Page 306
11.2 Discrete-Time Mixed H2/H∞ Nonlinear Control......Page 308
11.2.1 The Infinite-Horizon Problem......Page 314
11.3 Extension to a General Class of Discrete-Time Nonlinear Systems......Page 316
11.4 Notes and Bibliography......Page 318
12.1 Continuous-Time Mixed H2/H∞ Nonlinear Filtering......Page 320
12.1.1 Solution to the Finite-Horizon Mixed H2/H∞ Nonlinear Filtering Problem......Page 322
12.1.2 Solution to the Infinite-Horizon Mixed H2/H∞ Nonlinear Filtering......Page 327
12.1.3 Certainty-Equivalent Filters (CEFs)......Page 330
12.2 Discrete-Time Mixed H2/H∞ Nonlinear Filtering......Page 332
12.2.1 Solution to the Finite-Horizon Discrete-Time Mixed H2/H∞ Nonlinear Filtering Problem......Page 334
12.2.2 Solution to the Infinite-Horizon Discrete-Time Mixed H2/H∞ Nonlinear Filtering Problem......Page 338
12.2.3 Approximate and Explicit Solution to the Infinite-Horizon Discrete-Time Mixed H2/H∞ Nonlinear Filtering Problem......Page 340
12.2.4 Discrete-Time Certainty-Equivalent Filters (CEFs)......Page 344
12.3 Example......Page 346
12.4 Notes and Bibliography......Page 348
13.1 Review of Some Approaches for Solving the HJBE/HJIE......Page 350
13.1.1 Solving the HJIE/HJBE Using Polynomial Expansion and Basis Functions......Page 353
13.2 A Factorization Approach for Solving the HJIE......Page 358
13.2.1 Worked Examples......Page 362
13.3.1 Solving the Hamilton-Jacobi Equation......Page 367
13.3.2 Solving the Hamilton-Jacobi Equation for the A2-Toda System......Page 371
A. Proof of Theorem 5.7.1......Page 376
B. Proof of Theorem 8.2.2......Page 380
Bibliography......Page 384