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Probabilistic optimal control
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or
Stochastic_control
Randomly determined process
Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος (stókhos) 'target, aim, guess') is the property of being well-described by a random probability distribution
Stochastic
one of the fundamental principles of stochastic control theory, which states that the problems of optimal control and state estimation can be decoupled
Separation principle in stochastic control
Separation_principle_in_stochastic_control
approaches used in stochastic control theory. Regrettably the simple adaptation of the deterministic schemes for matching up to stochastic models such as
Markov chain approximation method
Markov_chain_approximation_method
Stochastsic differential equations with terminal condition
various applications such as stochastic control, mathematical finance, and nonlinear Feynman–Kac formula. Backward stochastic differential equations were
Backward stochastic differential equation
Backward_stochastic_differential_equation
Branch of engineering and mathematics
small modeling errors. Stochastic control deals with control design with uncertainty in the model. In typical stochastic control problems, it is assumed
Control_theory
Linear optimal control technique
separation principle is a special case of the separation principle of stochastic control which states that even when the process and output noise sources are
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
controller designed to minimize a quadratic cost, is optimal for the stochastic control problem with output measurements. When process and observation noise
Separation_principle
Optimality condition in optimal control theory
Optimal Control. Athena Scientific. Pham, Huyên (2009). "The Classical PDE Approach to Dynamic Programming". Continuous-time Stochastic Control and Optimization
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
Approach to controller design that explicitly deals with uncertainty
A central theme of control theory is feedback regulation--the design a feedback controller to achieve stability and a level of performance for a given
Robust_control
British mathematician (1945–2020)
London. He made fundamental contributions to the theory of stochastic processes, stochastic control and mathematical finance. After completing his BA degree
Mark_H._A._Davis
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables
Stochastic_process
Problem in continuous-time finance
solved by Davis and Norman in 1990. It is one of the few cases of stochastic singular control where the solution is known. For a graphical representation,
Merton's_portfolio_problem
Mathematical model for sequential decision making under uncertainty
outcomes are uncertain. It is a type of stochastic decision process, and is often solved using the methods of stochastic dynamic programming. Originating from
Markov_decision_process
Generalization of a Markov decision process
Cassandra, A.R. (1998). "Planning and acting in partially observable stochastic domains". Artificial Intelligence. 101 (1–2): 99–134. doi:10.1016/S0004-3702(98)00023-X
Partially observable Markov decision process
Partially_observable_Markov_decision_process
Russian-Israeli mathematician (1936–2019)
contributions to the theory and applications of stochastic processes, in particular to martingales, stochastic control and nonlinear filtering. Liptser was born
Robert_Liptser
Mathematical way of attaining a desired output from a dynamic system
Sliding mode control SNOPT Stochastic control Trajectory optimization Ross, Isaac (2015). A primer on Pontryagin's principle in optimal control. San Francisco:
Optimal_control
French applied mathematician
1959) is a French applied mathematician whose research topics include stochastic control, jump diffusion, and mathematical finance. Sulem earned a Ph.D. in
Agnès_Sulem
Hungarian mathematician
of stochastic differential equations, stochastic partial differential equations and their applications to nonlinear filtering and stochastic control. Recently
István_Gyöngy
Canadian physicist (1934–2023)
control theorist and professor at the University of Toronto. He focused on multi-variable geometric control theory, stochastic control and stochastic
W._M._Wonham
Class of mathematical problems
Markov decision process Optional stopping theorem Prophet inequality Stochastic control Sequential analysis Chow, Y.S.; Robbins, H.; Siegmund, D. (1971).
Optimal_stopping
Aspect of control theory
theory, the Mabinogion sheep problem or Mabinogian urn is a problem in stochastic control introduced by David Williams (mathematician) in 1991, who named it
Mabinogion_sheep_problem
French mathematician (born 1944)
stochastic control theory and mathematical finance. Her contributions focused on the mathematical theory of stochastic control, backward stochastic differential
Nicole_El_Karoui
Optimization algorithm
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e
Stochastic_gradient_descent
Czech-American mathematician (born 1930)
mathematician known for his contributions to the theory of stochastic processes, queueing theory and control theory, as well as the design of telecommunications
Václav_E._Beneš
Method of quality control
displaying short descriptions of redirect targets Stochastic control – Probabilistic optimal control Total quality management – Approach to business improvement
Statistical_process_control
Optimization method
Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions
Stochastic_optimization
and a control option for individuals for interactions with the society. A (discrete-time) resource-dependent branching process is a stochastic process
Resource-dependent branching process
Resource-dependent_branching_process
figure below, is a deceptively simple toy problem in decentralized stochastic control. It was formulated by Hans Witsenhausen in 1968. It is a counterexample
Witsenhausen's_counterexample
German mathematician (born 1971)
her research include harmonic analysis, several complex variables, stochastic control, and elliptic partial differential equations. Petermichl studied at
Stefanie_Petermichl
Electrical engineer
decentralized information systems and stochastic control. Demosthenis Teneketzis’ research is on Stochastic Control, Decentralized Decision-Making with
Demosthenis_Teneketzis
Russian mathematician
from 1963) he, in collaboration with Dynkin, worked on nonlinear stochastic control theory, making advances in the study of convex, nonlinear partial
Nikolay Krylov (mathematician, born 1941)
Nikolay_Krylov_(mathematician,_born_1941)
Macroeconomics term
time lags in the effects of policy actions exist. In this dynamic stochastic control context with multiplier uncertainty, a key result is that the "certainty
Multiplier_uncertainty
French mathematician (1928–2001)
contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John von Neumann Lecture
Jacques-Louis_Lions
1957 technique for modelling problems of decision making under uncertainty
stochastic dynamic programming is a technique for modelling and solving problems of decision making under uncertainty. Closely related to stochastic programming
Stochastic dynamic programming
Stochastic_dynamic_programming
Theory of laying bets
regret, regardless of the final outcome or the gambler's strategy. Stochastic Control: Some models treat the arrival of bets as a Poisson process. The bookmaker
Mathematics_of_bookmaking
Stationary process Stochastic calculus Itô calculus Malliavin calculus Semimartingale Stratonovich integral Stochastic control Stochastic differential equation
List of stochastic processes topics
List_of_stochastic_processes_topics
Greek-American electrical engineer
2002 to 2016. His research specializes in control theory, with an emphasis on stochastic and robust control. He made contributions to the development
Tryphon_T._Georgiou
Concept in control theory
Richard (1958-09-01). "Dynamic programming and stochastic control processes". Information and Control. 1 (3): 228–239. doi:10.1016/S0019-9958(58)80003-0
Sequential_decision_making
Pardoux and Peng in 1990 and have since become essential tools in stochastic control and financial mathematics. In the 1990s, Étienne Pardoux and Shige
Deep backward stochastic differential equation method
Deep_backward_stochastic_differential_equation_method
French mathematician (born 1948)
on geometry. Bismut's early work was related to stochastic differential equations, stochastic control, and Malliavin calculus, to which he made fundamental
Jean-Michel_Bismut
role and use of the stochastic linear-quadratic-Gaussian problem in control system design". IEEE Transactions on Automatic Control. AC-16 (6): 529–552
Optimal_projection_equations
Overview of and topical guide to control engineering
control Neural control Nonlinear control Optimal control Real-time control Robust control Stochastic control Complex analysis Differential equations Linear
Outline of control engineering
Outline_of_control_engineering
Mathematical relation assigning a probability event to a cost
because it results in linear first-order conditions. In the context of stochastic control, the expected value of the quadratic form is used. The quadratic loss
Loss_function
interests are in mathematical finance, contract theory, stochastic control theory, and stochastic differential equations. From 1992 to 1999 he was an Assistant
Jakša_Cvitanić
Mathematical model for state estimation
In the theory of stochastic processes, filtering describes the problem of determining the state of a system from an incomplete and potentially noisy set
Filtering problem (stochastic processes)
Filtering_problem_(stochastic_processes)
Indian electrical engineer and mathematician (born 1954)
Technology, Mumbai. He is known for introducing analytical paradigm in stochastic optimal control processes and is an elected fellow of all the three major Indian
Vivek_Borkar
Wisconsin-Milwaukee. His contributions to research primarily involve stochastic control theory, optimal stopping and mathematical finance. Most notably, alongside
Richard_H._Stockbridge
Vietnamese American aerospace engineer
engineering at the University of New Mexico, he studies topics like stochastic control and satellite communications. He has also helped encourage small business
Khanh_D._Pham
Signal boosting phenomenon using white noise
Stochastic resonance (SR) is a mathematical mechanism and behavior of nonlinear systems (that is, systems in which the change of the output is not proportional
Stochastic_resonance
this method hard to analyze. Dynamic programming Bellman equation Optimal control [No reference provided in original] Keller, Philipp; Mannor, Shie; Precup
Automatic basis function construction
Automatic_basis_function_construction
Academic journal on business and economics
education and training, the effects of unionization, and applications of stochastic control theory to business and economic problems. List of scholarly journals
Journal of Business & Economic Statistics
Journal_of_Business_&_Economic_Statistics
French-Tunisian mathematician
and algebra. He is being known for publications on optimization and stochastic control. Touzi completed his PhD in Applied Mathematics at the Paris Dauphine
Nizar_Touzi
Iranian electrical engineer and computer scientist
engineer and computer scientist who studies networked information, stochastic control, machine learning, hypothesis testing, network optimization, and network
Tara_Javidi
Difference of forecasted and actual values
filtering of diffusion processes a guided tour. In Advances in Filtering and Optimal Stochastic Control (pp. 256-266). Springer, Berlin, Heidelberg. v t e
Innovation (signal processing)
Innovation_(signal_processing)
Random process independent of past history
probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability
Markov_chain
mathematician and control theorist. He has made contributions to the theory of partial realization, stochastic modeling, estimation and control, and moment
Anders_Lindquist
Norwegian mathematician (born 1945)
Norway. His main field of interest is stochastic analysis, including stochastic control, optimal stopping, stochastic ordinary and partial differential equations
Bernt_Øksendal
American applied mathematician
Kushner equation), and for the development of numerical methods for stochastic control problems such as the Markov chain approximation method. He is commonly
Harold_J._Kushner
American control theorist (1940–2022)
the IEEE Control Systems Award, "for outstanding contributions to stochastic and adaptive control and the unification of concepts from control and computer
Pravin_Varaiya
Family of iterative methods
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive
Stochastic_approximation
Optimization algorithm
perturbation stochastic approximation (SPSA) is an algorithmic method for optimizing systems with multiple unknown parameters. It is a type of stochastic approximation
Simultaneous perturbation stochastic approximation
Simultaneous_perturbation_stochastic_approximation
Historic university in France (1150–1970)
differential equations and to stochastic control, among other areas Marc Yor, was a French mathematician well known for his work on stochastic processes, especially
University_of_Paris
Lithography using 13.5 nm UV light
and shorting. Yield requires detection of stochastic failures down to below 1e-12. The tendency to stochastic defects is worse from defocus over a large
EUV_lithography
Control theorist and engineer
real-time, self-learning stochastic optimal control of advanced powertrain systems. His dissertation introduced a learning-based control framework that transforms
Andreas_A._Malikopoulos
its application to control" 1989 Anders Lindquist "For contributions to filtering and estimation, stochastic control, and stochastic theory" 1989 Debasis
List of fellows of IEEE Control Systems Society
List_of_fellows_of_IEEE_Control_Systems_Society
Computing using random bit streams
Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed
Stochastic_computing
Trading strategy
Primbs and W. Wong: "Optimal Pairs Trading: A Stochastic Control Approach". Proceedings of the American Control Conference, 2008. http://www.nt.ntnu
Pairs_trade
Algorithm in queueing theory
November 2003. M. J. Neely, E. Modiano, and C. Li, "Fairness and Optimal Stochastic Control for Heterogeneous Networks," Proc. IEEE INFOCOM, March 2005. A. Stolyar
Backpressure_routing
Type of algorithmic trading
precise modeling of the target market microstructure together with stochastic control techniques. These strategies appear intimately related to the entry
High-frequency_trading
Study of strategic decision making
populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is inspired by mean-field
Mean-field_game_theory
system analysis and control theory. The eminent researchers (born after 1920) include the winners of at least one award of the IEEE Control Systems Award,
List of people in systems and control
List_of_people_in_systems_and_control
Calculus on stochastic processes
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals
Stochastic_calculus
context of World War 2, defined by people like Norbert Wiener, in (stochastic) control theory, radar, signal detection, tracking, etc. The most common use
Smoothing problem (stochastic processes)
Smoothing_problem_(stochastic_processes)
Swedish control theorist (born 1934)
Engineering for contributions to identification, stochastic, and adaptive control and their incorporation in control engineering practice. Åström was born in
Karl_Johan_Åström
Dutch mathematician
Schuppen, Stochastic realization of a Gaussian stochastic control system, Acta Applicandae Mathematicae 35(1994), 193–212. J.H. van Schuppen, Stochastic realization
Jan_H._van_Schuppen
French mathematician
Advisory Board of Havas Media. As an expert of financial mathematics and stochastic control, Guéant has published several books and articles on liquidity management
Olivier_Guéant
Intelligent control Optimal control Dynamic programming Robust control Stochastic control System dynamics, system analysis Takens' theorem Exponential dichotomy
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
Formula relating stochastic processes to partial differential equations
establishes a link between parabolic partial differential equations and stochastic processes. In 1947, when Kac and Feynman were both faculty members at
Feynman–Kac_formula
stochastic control theory. 1980 Bernard Friedland For contributions to the application of modern control theory in navigation, guidance, and control systems
List of fellows of IEEE Computer Society
List_of_fellows_of_IEEE_Computer_Society
New Zealand mathematician and statistician (1927–2021)
Zealand, working in the fields of stochastic nets, optimal control, time series analysis, stochastic optimisation and stochastic dynamics. From 1967 to 1994
Peter_Whittle_(mathematician)
Greek-American electrical engineer (1942–2026)
John N. Tsitsiklis) A Course in Reinforcement Learning (2023) "Stochastic Optimal Control: The Discrete-Time Case" (1978, co-authored with S. E. Shreve)
Dimitri_Bertsekas
Matrix-valued random variable
the problem is known as one of stochastic control. A key result in the case of linear-quadratic control with stochastic matrices is that the certainty
Random_matrix
solutions using concepts from several control areas such as robust control, optimal stochastic control, model predictive control, fuzzy logic etc. A most critical
Networked_control_system
Principle in optimal control theory for best way to change state in a dynamical system
condition for an optimum, and admits a straightforward extension to stochastic optimal control problems, whereas the maximum principle does not. However, in
Pontryagin's maximum principle
Pontryagin's_maximum_principle
Academic journal
theory and long-term investment Applications of stochastic optimization, stochastic control and stochastic filtering in finance Computational and numerical
International Journal of Theoretical and Applied Finance
International_Journal_of_Theoretical_and_Applied_Finance
Greek-American mathematician
Society for Industrial and Applied Mathematics "for contributions to stochastic control and financial mathematics". She was an invited speaker at the 2014
Thaleia_Zariphopoulou
Israeli-American computer scientist
differentiable reinforcement learning called non-stochastic control, which applies online convex optimization to control. 2002–2006 – Gordon Wu fellowship, Princeton
Elad_Hazan
Use of various control systems for operating equipment
theory (1938), frequency domain analysis (1940), ship control (1950), and stochastic analysis (1941). Starting in 1958, various systems based on solid-state
Automation
Jyeshtharaj Joshi Maharashtra Nuclear science 1992 Vivek Borkar Maharashtra Stochastic control 1993 Dipankar Banerjee West Bengal Metallurgy 1993 Suresh Kumar Bhatia
List of Shanti Swarup Bhatnagar Prize recipients
List_of_Shanti_Swarup_Bhatnagar_Prize_recipients
Engineering discipline that deals with control systems
developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s and
Control_engineering
Random variable with multiple component dimensions
Random Variables and Stochastic Processes (Third ed.). McGraw-Hill. ISBN 0-07-048477-5. Kendrick, David (1981). Stochastic Control for Economic Models
Multivariate_random_variable
Concept in probability theory
theory, the Schramm–Loewner evolution with parameter κ, also known as stochastic Loewner evolution (SLEκ), is a family of random planar curves that have
Schramm–Loewner_evolution
mathematics, from Shandong University in 1985, and M.S. and Ph.D. in control theory and stochastic systems, from Institute of Systems Science (ISS), Chinese Academy
Ji-Feng_Zhang
Mathematical model in optimal trade execution
concession grows sub-linearly in trade size. Continuous-time and stochastic-control formulations. Continuous-time versions of the model have been developed
Almgren–Chriss_model
Study of mathematical algorithms for optimization problems
Press. pp. 57–91. ISBN 9780674043084. A.G. Malliaris (2008). "stochastic optimal control," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract
Mathematical_optimization
which will be experienced at the end of the investment period. Given a stochastic model for the market conditions, we consider N {\displaystyle N} of the
Scenario_optimization
Social and ecological concept
Yoichi (2016-06-23). "Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models". PLOS ONE. 11 (6)
Adaptive_capacity
Mathematical model of plan execution
Marzinotto, Alejandro; Ögren, Petter (2014). "Performance analysis of stochastic behavior trees" (PDF). 2014 IEEE International Conference on Robotics
Behavior tree (artificial intelligence, robotics and control)
Behavior_tree_(artificial_intelligence,_robotics_and_control)
Paradox of combining strategies
Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control, Birkhäuser, 2005, ISBN 0-8176-4362-1. Cristel Chandre, Xavier Leoncini
Parrondo's_paradox
STOCHASTIC CONTROL
STOCHASTIC CONTROL
Boy/Male
Hindu
Greek God who controls the winds or west
Boy/Male
Muslim
One who controls her anger
Girl/Female
Tamil
One who can control senses
Girl/Female
Tamil
Self control having complete control on all the senses
Boy/Male
Hindu
Check, Control
Boy/Male
Tamil
Desire, Protector, Lord, Another name for Krishna, Controller
Boy/Male
Tamil
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Controlling all three dimension
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Girl/Female
Hindu
Goddess Durga, Self-respecting, Self-controlled, Wise, Sensible
Girl/Female
Tamil
Indreesha | இநà¯à®¤à¯à®°à®¿à®·à®¾
Having control upon all abilities
Indreesha | இநà¯à®¤à¯à®°à®¿à®·à®¾
Boy/Male
Tamil
Authoritative, Lord, Independent, In control of own passions, Resident of the vindhyas
Boy/Male
Hindu
One who controls senses
Boy/Male
Hindu
Victory or ancient philosopher, One who has control over his heart and mind
Girl/Female
Indian
One who controls, Suppress
Girl/Female
Hindu
Having control upon all abilities
Boy/Male
Hindu
Victory or ancient philosopher, One who has control over his heart and mind
Girl/Female
Tamil
Manasvini | மநஸà¯à®µà®¿à®¨à¯€
Goddess Durga, Self-respecting, Self-controlled, Wise, Sensible
Manasvini | மநஸà¯à®µà®¿à®¨à¯€
Boy/Male
Tamil
Vijitendriya | விஜீதேநà¯à®¤à¯à®°à®¿à®¯Â
Controller of the senses, Lord Hanuman
Vijitendriya | விஜீதேநà¯à®¤à¯à®°à®¿à®¯Â
Boy/Male
Hindu
Controller of the senses
Boy/Male
Hindu
Controller of time
Boy/Male
Tamil
In control of own passions
STOCHASTIC CONTROL
STOCHASTIC CONTROL
Female
Hebrew
(מְ×ִירִי) Variant form of Hebrew Meira, MEIRI means "giving light."
Boy/Male
American, Australian, British, Chinese, English
To Sing
Girl/Female
Tamil
The one who shines, Splendid, Ornamental, Shining
Boy/Male
Arabic, Muslim
Pertaining to Makkah
Boy/Male
Indian, Sanskrit
Lord Shiva
Girl/Female
Indian, Punjabi, Sikh
Master's Word
Boy/Male
Arabic
Smith.
Boy/Male
Hindu
Voice, Audible
Girl/Female
Muslim
Near, Name of a woman scholar
Girl/Female
Arabic, Hindu, Indian, Muslim
Eye; The Beauty of an Eye
STOCHASTIC CONTROL
STOCHASTIC CONTROL
STOCHASTIC CONTROL
STOCHASTIC CONTROL
STOCHASTIC CONTROL
n.
Specifically, a monarch, or other ruler or master, who uses power to oppress his subjects; a person who exercises unlawful authority, or lawful authority in an unlawful manner; one who by taxation, injustice, or cruel punishment, or the demand of unreasonable services, imposes burdens and hardships on those under his control, which law and humanity do not authorize, or which the purposes of government do not require; a cruel master; an oppressor.
v. t.
To treat as a vassal; to subject to control; to enslave.
a.
Not governed or controlled.
a.
Not accountable or responsible; free from control.
a.
Incapable of being controlled; ungovernable; irresistible; as, an uncontrollable temper; uncontrollable events.
n.
Power or authority to check or restrain; restraining or regulating influence; superintendence; government; as, children should be under parental control.
imp. & p. p.
of Control
n.
The office of a controller.
n.
One whose imagination overpowers his reason and controls his judgment; an unpractical schemer; one who builds castles in the air; a daydreamer.
n.
The power or act of controlling; the state of being restrained; control; restraint; regulation; superintendence.
n.
Capability of being controlled.
a.
Acting contrary to the standard of right; not animated or controlled by justice; false; dishonest; as, an unjust man or judge.
a.
Capable of being controlled, checked, or restrained; amenable to command.
p. pr. & vb. n.
of Control
n.
One who, or that which, controls or restraines; one who has power or authority to regulate or control; one who governs.
adv.
In a lower, subject, or subordinate condition; in subjection; -- used chiefly in a few idiomatic phrases; as, to bring under, to reduce to subjection; to subdue; to keep under, to keep in subjection; to control; to go under, to be unsuccessful; to fail.
a.
Conjectural; able to conjecture.
n.
An iron block, usually bolted to a ship's deck, for controlling the running out of a chain cable. The links of the cable tend to drop into hollows in the block, and thus hold fast until disengaged.
n.
Control of one's self; restraint exercised over one's self; self-command.
n.
Capability of being controlled; controllableness.