控制中有哪些亟待解決的問題？

12-29

可以是機器人控制，無人機控制，等等。
可以是控制問題，狀態估計問題，感知問題，等等。
可以是未解決的，也可是解決得不夠好的。

可以是理論上的，也可以是工程中的。

更新（已解決的問題，歡迎補充）

Problem 1.5 Is Monopoli』s model reference adaptive controller correct?

歷時30年被解決，答案是Monopoli"s MRAC controller is wrong. 在某些情況下，自適應增益趨於無窮，但參數誤差呈現出freezing特點，Monopoli的結果是半全局的。 (N. Barahanov et. al. TAC, 2005.)

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幾年前，有學者組織系統地整理系統與控制領域懸而未決的問題，出版了兩本書，分別是Open Problems in Mathematical Systems and Control Theory和Unsolved Problems in Mathematical Systems and Control Theory。目錄如下：

***第一本：Open Problems in Mathematical Systems and Control Theory
1 Uniform asymptotic stability of linear time-varying systems
2 Positive system realizations
3 System approximation in the 2-norm
4 Is it possible to recognize local controllability in a finite number of differentiations?
5 Open problems in sequential parametric estimation
6 Conditions for the existence and uniqueness of optimal matrix scalings
7 Matrix inequality conditions for canonical factorization of rational transfer function matrices
8 Open problems in $ell_1$ optimal control
9 Efficient neural network learning
10 Mechanical feedback control systems
11 Three problems on the decidability and complexity of stability
12 Simultaneous stabilization of linear systems and interpolation
with rational functions
13 Forbidden state control synthesis for timed Petri net mode~
14 On matrix mortality in low dimensions
15 Entropy and random feedback
16 A stabilization problem
17 Spectral factorization of a spectral density with arbitrary
delays
18 Lyapunov exponents and robust stabilization
19 Regular spectral factorizations
20 Convergence of an algorithm for the Riemannian SVD
21 Some open questions related to flat nonlinear systems
22 Approximation of complex J.L
23 Spectral value sets of infinite-dimensional systems
24 Selection of the number of inputs and states
25 Input-output gains of switched linear systems
26 Robust stability of linear stochastic systems
27 Monotonicity of performance with respect to its specification
in $H_infty$ control
28 Stable estimates in equation error identification: An open
problem
29 Elimination of latent variables in real differential algebraic
systems
30 How conservative is the circle criterion?
31 On chaotic observer design
32 The minimal realization problem in the max-plus algebra
33 Input design for worst-case identification
34 Max-pIus-times linear systems
35 Closed-loop identification and self-tuning
36 To estimate the L2-gain of two dynamic systems
37 Open problems in the area of pole placement
38 An optimal control theory for systems defined over finite rings
39 Re-initialization in discontinuous systems
40 Control-Lyapunov functions
41 Spectral Nevanlinna-Pick Interpolation
42 Phase-sensitive structured singular value
43 Conservatism of the standard upper bound test: Is sup(/il J.t)
finite? Is it bounded by 2?
44 When does the algebraic Riccati equation have a negative
semi-definite solution?
45 Representing a nonlinear input-output differential equation
as an input-state-output system
46 Shift policies in QR-like algorithms and feedback control of
self-similar flows
47 Equivalences of discrete-event systems and of hybrid systems
48 Covering numbers for input-output maps realizable by neural
networks
49 A powerful generalization of the Carleson measure theorem?
50 Lyapunov theory for high order differential systems
51 Performance lower bound for a sampled-data signal reconstruction
52 Coprimeness of factorizations over a ring of distributions 281
53 Where are the zeros located?

***第二本：Unsolved Problems in Mathematical Systems and Control Theory
PART 1. LINEAR SYSTEMS 1
Problem 1.1. Stability and composition of transfer functions
Problem 1.2. The realization problem for Herglotz-Nevanlinna functions
Problem 1.3. Does any analytic contractive operator function on the polydisk
have a dissipative scattering nD realization?
Problem 1.4. Partial disturbance decoupling with stability
Problem 1.5. Is Monopoli』s model reference adaptive controller correct?
Problem 1.6. Model reduction of delay systems
Problem 1.7. Schur extremal problems
Problem 1.8. The elusive iff test for time-controllability of behaviors
Problem 1.9. A Farkas lemma for behavioral inequalities
Problem 1.10. Regular feedback implementability of linear differential behaviors
Problem 1.11. Riccati stability
Problem 1.12. State and first order representations
Problem 1.13. Projection of state space realizations

PART 2. STOCHASTIC SYSTEMS 65
Problem 2.1. On error of estimation and minimum of cost for wide band noise
driven systems
Problem 2.2. On the stability of random matrices
Problem 2.3. Aspects of Fisher geometry for stochastic linear systems
Problem 2.4. On the convergence of normal forms for analytic control systems

PART 3. NONLINEAR SYSTEMS 87
Problem 3.1. Minimum time control of the Kepler equation
Problem 3.2. Linearization of linearly controllable systems
Problem 3.3. Bases for Lie algebras and a continuous CBH formula
Problem 3.4. An extended gradient conjecture
Problem 3.5. Optimal transaction costs from a Stackelberg perspective
Problem 3.6. Does cheap control solve a singular nonlinear quadratic problem?
Problem 3.7. Delta-Sigma modulator synthesis
Problem 3.8. Determining of various asymptotics of solutions of nonlinear time optimal problems via right ideals in the moment algebra
Problem 3.9. Dynamics of principal and minor component flows

PART 4. DISCRETE EVENT, HYBRID SYSTEMS 129
Problem 4.1. L2-induced gains of switched linear systems
Problem 4.2. The state partitioning problem of quantized systems
Problem 4.3. Feedback control in flowshops
Problem 4.4. Decentralized control with communication between controllers

PART 5. DISTRIBUTED PARAMETER SYSTEMS 151
Problem 5.1. Infinite dimensional backstepping for nonlinear parabolic PDEs
Problem 5.2. The dynamical Lame system with boundary control: on the structure
of reachable sets
Problem 5.3. Null-controllability of the heat equation in unbounded domains
Problem 5.4. Is the conservative wave equation regular?
Problem 5.5. Exact controllability of the semilinear wave equation
Problem 5.6. Some control problems in electromagnetics and fluid dynamics

PART 6. STABILITY, STABILIZATION 187
Problem 6.1. Copositive Lyapunov functions
Problem 6.2. The strong stabilization problem for linear time-varying systems
Problem 6.3. Robustness of transient behavior
Problem 6.4. Lie algebras and stability of switched nonlinear systems
Problem 6.5. Robust stability test for interval fractional order linear systems
Problem 6.6. Delay-independent and delay-dependent Aizerman problem
Problem 6.7. Open problems in control of linear discrete multidimensional systems
Problem 6.8. An open problem in adaptative nonlinear control theory
Problem 6.9. Generalized Lyapunov theory and its omega-transformable regions
Problem 6.10. Smooth Lyapunov characterization of measurement to error stability

PART 7. CONTROLLABILITY, OBSERVABILITY 245
Problem 7.1. Time for local controllability of a 1-D tank containing a fluid
modeled by the shallow water equations
Problem 7.2. A Hautus test for infinite-dimensional systems
Problem 7.3. Three problems in the field of observability
Problem 7.4. Control of the KdV equation

PART 8. ROBUSTNESS, ROBUST CONTROL 265
Problem 8.1. H1-norm approximation
Problem 8.2. Noniterative computation of optimal value in H1 control
Problem 8.3. Determining the least upper bound on the achievable delay margin
Problem 8.4. Stable controller coefficient perturbation in floating point implementation

PART 9. IDENTIFICATION, SIGNAL PROCESSING 285
Problem 9.1. A conjecture on Lyapunov equations and principal angles in subspace
identification
Problem 9.2. Stability of a nonlinear adaptive system for filtering and parameter
estimation

PART 10. ALGORITHMS, COMPUTATION 297

Problem 10.1. Root-clustering for multivariate polynomials and robust stability

analysis

Problem 10.2. When is a pair of matrices stable?

Problem 10.3. Freeness of multiplicative matrix semigroups

Problem 10.4. Vector-valued quadratic forms in control theory

Problem 10.5. Nilpotent bases of distributions

Problem 10.6. What is the characteristic polynomial of a signal flow graph?

Problem 10.7. Open problems in randomized μ analysis

CHALLENGES FOR CONTROL RESEARCH

轉自：The Impact of Control Technology 2nd Ed.

Avoiding Pilot-Induced Oscillations in Energy-Efficient Aircraft Designs – D. Acosta, Y. Yildiz, and D. Klyde

Resilient Cyberphysical Systems – S. Amin, G. Schwartz, and S. Sastry

Thermal Control of Manycore and Multicore Processors – A. Bartolini, A. Tilli, and L. Benini

Controlling Modern Radars – J. Cabrera

Discrete-Event Control Theory for Flexible Manufacturing – K. Cai

City Labs for Intelligent Road Transportation Systems – C. Canudas de Wit

Control-Theoretic Approaches in Neuroscience and Brain Medicine – S. Ching

Distributed Control for Turbine Propulsion – D. Culley and S. Garg

Batch Control and Trajectory Optimization in Fuel Ethanol Production – W. Dai and J. Hahn

Actuated Wingsuit for Controlled, Self-Propelled Flight – R. D』Andrea, M. Wyss, and M. Waibel

Control Engineering for Cancer Therapy – A. Datta

Control of Flapping-Wing Micro Air Vehicles – D. Doman and M. Oppenheimer

Biological Oscillators – F. Doyle III

Dynamics and Control for the Artificial Pancreas – F. Doyle III

Human Interactions With Complex Networks – M. Egerstedt

Control for Floating Structures in Offshore Engineering – S. Ge, Y. Choo, B. How, and W. He

Vehicle-to-Vehicle/Vehicle-to-Infrastructure Control – L. Glielmo

Control Challenges in Mobile Telecommunications – G. Goodwin, M. Cea, K. Lau, and T. Wigren

Control of Powered Prosthetic Legs – R. Gregg, L. Hargrove, and J. Sensinger

Management of Complex Water Networks – V. Havlena, P. Trnka, and B. Sheridan

Control for Grid Responsiveness – I. Hiskens

Addressing Automotive Industry Needs with Model Predictive Control – D. Hrovat, H. Tseng, and S. Di Cairano

Design Science for Cyberphysical Systems – X. Koutsoukos and P. Antsaklis

Control of Integrated Gasification Combined Cycle Power Plants with CO2 Capture – F. Lima, D. Bhattacharyya, R. Turton, P. Mahapatra, and S. Zitney

Geoengineering the Earth』s Climate: The World』s Largest Control Problem – D. MacMartin and B. Kravitz

Process Manufacturing Networks – W. Marquardt and K. Frankl

MEMS-Based Nanopositioning for On-Chip Atomic Force Microscopy – S.O. Moheimani

Toward Verifiably Correct Control Implementations – D. Monniaux

Preserving Privacy in Cyberphysical Systems – J. Le Ny and G. Pappas

Opportunities for Control Theory in Stock Trading Research – J. Primbs and B. Barmish

Preview Control of Wind Turbines – D. Schlipf and L. Pao

Supply Chain as a Control Problem – K. Smith, M. Braun, K. Kempf, J. Lu, and D. Morningred

Control for Energy-Efficient Buildings – P. Stluka

Stair-Climbing Assistive Robots – B. Strah and S. Rinderknecht

Lithium-Ion Battery Management – P. Trnka and V. Havlena

Estimating Heavy-Tailed Distributions in Finance – M. Vidyasagar

Modeling Cancer Dynamics and Tumor Heterogeneity – M. Vidyasagar

Control of Tokamak Plasmas – E. Witrant

這是第一版：The Impact of Control Technology

首先回答問題。

高階滑模控制在什麼情況下強於傳統滑模控制？

詳細說明參見我在http://www.zhihu.com/question/41025067里提到的那篇論文。

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以下是吐槽:

最近知乎的控制理論條目下這種大問題好多啊……

「控制理論與工程」是屬於工學門類的國家一級學科，同屬一級學科的有數學、物理學、化學等，我想應該沒人會去問「數學還有哪些沒解決的問題」，或者「化學還有哪些沒解決的問題」吧？

2015年國家自然基金常規面上項目，查詢關鍵詞「控制」有575條記錄，目測每條記錄都夠1-3個博士做畢業的了。我覺得這些項目的申請書都是這個問題的回答，但沒一個是能在知乎寫的下的。

快速而有效的系統建模與辨識方法算一個么