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Mathematical way of attaining a desired output from a dynamic system
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective
Optimal_control
Variables Control
In optimal control theory, a control is a variable chosen by the controller or agent to manipulate state variables, similar to an actual control valve
Control (optimal control theory)
Control_(optimal_control_theory)
Hypothesis in neuroscience
problem – to movement trajectories. Active inference is related to optimal control by replacing value or cost-to-go functions with prior beliefs about
Free_energy_principle
Numerical method for solving optimal control problems
Pseudospectral optimal control is a numerical technique for solving optimal control problems. These problems involve finding the best way to control a dynamic
Pseudospectral optimal control
Pseudospectral_optimal_control
Advanced method of process control
for this reason MPC is also called receding horizon control. Although this approach is not optimal, in practice it has given very good results. Much academic
Model_predictive_control
Mathematics concept
unscented optimal control combines the notion of the unscented transform with deterministic optimal control to address a class of uncertain optimal control problems
Unscented_optimal_control
Necessary condition for optimality associated with dynamic programming
the optimal policy in the last time period is specified in advance as a function of the state variable's value at that time, and the resulting optimal value
Bellman_equation
Binary feedback controller
In optimal control problems, it is sometimes the case that a control is restricted to be between a lower and an upper bound. If the optimal control switches
Bang–bang_control
Function used in optimal control theory
The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of
Hamiltonian_(control_theory)
Study of mathematical algorithms for optimization problems
a cost function where a minimum implies a set of possibly optimal parameters with an optimal (lowest) error. Typically, A is some subset of the Euclidean
Mathematical_optimization
Multiple ways for multi-joint objects to realize a movement
the natural outcome of an adaptive optimal control process. Optimal control is a way of understanding motor control and the motor equivalence problem,
Degrees_of_freedom_problem
Experimental design that is optimal with respect to some statistical criterion
same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends
Optimal_experimental_design
Branch of engineering and mathematics
and the control strategy chosen. List of the main control techniques Optimal control is a particular control technique in which the control signal optimizes
Control_theory
Control loop feedback mechanism
the three control terms of proportional, integral and derivative influence on the controller output to apply accurate and optimal control. The block
PID_controller
Principle in optimal control theory for best way to change state in a dynamical system
Bellman's principle of optimality, a related approach to optimal control problems which states that the optimal trajectory remains optimal at intermediate points
Pontryagin's maximum principle
Pontryagin's_maximum_principle
Linear optimal control technique
In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Techniques to maintain quantum coherence
pulse with a varying frequency in time. Optimal control as applied in coherent control seeks the optimal control field for steering a quantum system to
Coherent_control
The PROPT MATLAB Optimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters
PROPT
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
Stochastic_control
Optimization algorithm for artificial neural networks
backpropagation appeared in optimal control theory since 1950s. Yann LeCun et al credits 1950s work by Pontryagin and others in optimal control theory, especially
Backpropagation
Field of machine learning
In machine learning and optimal control, reinforcement learning (RL) is concerned with how an intelligent agent should take actions in a dynamic environment
Reinforcement_learning
Python package
optimization and optimal control problems. GEKKO is used for advanced control in the Temperature Control Lab (TCLab) for process control education at 20
Gekko_(optimization_software)
Optimality condition in optimal control theory
sufficient conditions for optimality of a control with respect to a loss function. Its solution is the value function of the optimal control problem which, once
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
Use of various control systems for operating equipment
(1961), navigation (1960), optimal control and estimation theory (1962), nonlinear control theory (1969), digital control and filtering theory (1974)
Automation
In forestry, the optimal rotation age is the growth period required to derive maximum value from a stand of timber. The calculation of this period is
Optimal_rotation_age
Process of developing trajectory performance
optimization is a technique for computing an open-loop solution to an optimal control problem. It is often used for systems where computing the full closed-loop
Trajectory_optimization
Branch of applied mathematics
systems. The problem of finding optimal functions for such changes is studied in variational calculus and in optimal control theory. Before the Second World
Mathematical_economics
American electrical engineer, academic and researcher
including Optimal Control, Optimal Estimation, Aircraft Control and Simulation, Applied Optimal Control and Estimation, and Robot Manipulator Control. Lewis
Frank_L._Lewis
Topics referred to by the same term
regulations on trade Internal control, a process to help achieve specific goals typically related to managing risk Control (optimal control theory), a variable
Control
Probabilistic problem-solving algorithm
"Estimation and nonlinear optimal control: Particle resolution in filtering and estimation". Studies on: Filtering, optimal control, and maximum likelihood
Monte_Carlo_method
Concept in game theory
control of moving systems. Differential games are related closely to optimal control problems. In an optimal control problem there is single control u
Differential_game
Problem optimization method
solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have optimal substructure
Dynamic_programming
Method to solve constrained optimization problems
the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value
Lagrange_multiplier
Engineering discipline that deals with control systems
included developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s
Control_engineering
Local boundary-limited electrical grid
Tertiary control is the last (and the slowest) control level, which considers economical concerns in the optimal operation of the microgrid (sampling time
Microgrid
Problem in mathematical optimisation
navigation problem, proposed in 1931 by Ernst Zermelo, is a classic optimal control problem that deals with a boat navigating on a body of water, originating
Zermelo's_navigation_problem
General-purpose MATLAB software
"GPOPS 2") is a general-purpose MATLAB software for solving continuous optimal control problems using hp-adaptive Gaussian quadrature collocation and sparse
GPOPS-II
Linear optimal control technique
The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set
Linear–quadratic_regulator
British electronic engineer (1930–2024)
Journal of Control, 9(5):547--559, 1966. D. Q. Mayne, Differential Dynamic Programming---a Unified Approach to Optimal Control, in Advances in Control Systems
David_Mayne
Maximized objective function of an optimization problem
on the parameters of the problem. In a controlled dynamical system, the value function represents the optimal payoff of the system over the interval [
Value_function
Mathematical model for sequential decision making under uncertainty
solve the equation to find the optimal value function V ∗ {\displaystyle V^{*}} , which in turns yield the optimal control at any time t {\displaystyle
Markov_decision_process
variables. They are one of the necessary conditions for optimality infinite-horizon optimal control problems without an endpoint constraint on the state
Transversality_condition
Control paradigm in which errors are measured before they can affect a system
Engineering, 1987. Alberts, T.E., Sangveraphunsiri, V. and Book, Wayne J., Optimal Control of a Flexible Manipulator Arm: Volume I, Dynamic Modeling, MHRC Technical
Feed_forward_(control)
linear. Witsenhausen obtained the following results: An optimum exists (Theorem 1). The optimal control law of the first controller is such that E ( x 1 )
Witsenhausen's_counterexample
Dynamic system property
problems, obtaining optimal control strategies, or, simply prescribing an input that has a desired effect on the state. Controllability and observability
Controllability
Mathematical concept
f(x^{*})} ) is called Pareto optimal if there does not exist another solution that dominates it. The set of Pareto optimal outcomes, denoted X ∗ {\displaystyle
Multi-objective_optimization
and open source symbolic framework for automatic differentiation and optimal control. Automatic differentiation JModelica.org "Optimization in Engineering
CasADi
Subfield of machine learning, intelligent control, and control theory
Machine learning control (MLC) is a subfield of machine learning, intelligent control, and control theory which aims to solve optimal control problems with
Machine_learning_control
Double-setpoint control is quite similar to bang–bang control. It is an element of a feedback-loop and therefore evaluated by application of control theory. It
Double-setpoint_control
Optimization for dynamical systems
application to optimal control in queueing networks. Lyapunov optimization refers to the use of a Lyapunov function to optimally control a dynamical system
Lyapunov_optimization
object in question. The search for optimal values for object or system characteristics is carried out by means of optimal change to design, geometrical or
IOSO
Ball for association football produced by Adidas
20-panel synthetic leather, providing a consistent and stable surface for optimal control and accuracy. The Oceaunz is the ninth successive football that Adidas
Adidas_Oceaunz
Lacitignola, Deborah; Tilioua, Mouhcine (2024). "Optimal social distancing through cross-diffusion control for a disease outbreak PDE model". Communications
PDE-constrained_optimization
Surname list
Bryson Jr., American professor of engineering, the "father of modern optimal control theory" Bernarda Bryson Shahn (1903–2004), formerly Bernarda Bryson
Bryson_(surname)
Matrix-valued random variable
uncertainty) the optimal policy with a quadratic loss function coincides with what would be decided if the uncertainty were ignored, the optimal policy may
Random_matrix
Topics referred to by the same term
electrons and nuclei in a molecule Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system Hamiltonian path
Hamiltonian
Artificial-intelligence researcher (born 1971)
and director of the Movement Control Laboratory at the University of Washington. He introduced the use of optimal control as a formal explanatory framework
Emanuel_Todorov
Director of Control and Optimization at the Naval Postgraduate School in Monterey, CA. He has published a highly-regarded textbook on optimal control theory
I._Michael_Ross
Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory. It states that dualization and discretization are, in general
Ross–Fahroo_lemma
NP-hard problem in combinatorial optimization
that, instead of seeking optimal solutions, would produce a solution whose length is provably bounded by a multiple of the optimal length, and in doing so
Travelling_salesman_problem
Indian-American mathematician
arise in optimal control problems that exhibit multiple optimal solutions. A Sethi-Skiba point is an indifference point in an optimal control problem such
Suresh_P._Sethi
Differential calculus on function spaces
developed new mathematical tools for the calculus of variations in optimal control theory. The dynamic programming of Richard Bellman is an alternative
Calculus_of_variations
In optimal control, problems of singular control are problems that are difficult to solve because a straightforward application of Pontryagin's minimum
Singular_control
Konidaris and Leslie Kaelbling and Tomas Lozano-Perez (2012). "LQR-RRT*: Optimal sampling-based motion planning with automatically derived extension heuristics"
Linear-quadratic regulator rapidly exploring random tree
Linear-quadratic_regulator_rapidly_exploring_random_tree
Classification scheme for mathematics
92: Biology and other natural sciences 93: Systems theory; control (including optimal control) 94: Information and communication, circuits 97: Mathematics
Mathematics Subject Classification
Mathematics_Subject_Classification
certain optimal control problems with multiple optimal solutions Legendre–Clebsch condition — second-order condition for solution of optimal control problem
List of numerical analysis topics
List_of_numerical_analysis_topics
Fastest curve descent without friction
problem can be solved using tools from the calculus of variations and optimal control. The curve is independent of both the mass of the test body and the
Brachistochrone_curve
Mathematical optimization algorithm
is that the method is locally optimal in this case, in particular, it does not converge slower than the locally optimal steepest descent method. In both
Conjugate_gradient_method
French mathematical economist
Pintus, Patrick (2012). "On the optimal control of a linear neutral differential equation arising in economics". Optimal Control Applications and Methods. 33
Raouf_Boucekkine
1957 technique for modelling problems of decision making under uncertainty
s t ) {\displaystyle f_{t}(s_{t})} represent the optimal cost/reward obtained by following an optimal policy over stages t , t + 1 , … , n {\displaystyle
Stochastic dynamic programming
Stochastic_dynamic_programming
Greek-American electrical engineer (1942–2026)
"Reinforcement Learning and Optimal Control" (2019), which aims to explore the common boundary between dynamic programming/optimal control and artificial intelligence
Dimitri_Bertsekas
equation Merton's portfolio problem Optimal stopping Malthusian growth model Mean field game theory Optimal rotation age Sovereign debt accumulation
List of named differential equations
List_of_named_differential_equations
Soviet scientist
field of automatic control and fundamental computer science. He is one of the founders of optimal control, and proposed dual control theory in the study
Alexander_Feldbaum
desirable to have an optimal navigation function with respect to a given cost functional J {\displaystyle J} . Formalized as an optimal control problem, we can
Navigation_function
Reciprocating internal combustion engine
the engine are minimized by measures including optimal design of the combustion chambers, optimal control of the intake air motion by means of the cylinder-head
Mitsubishi_4A9_engine
Nonlinear equation which arises on linear optimal control problems
nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati
Algebraic_Riccati_equation
available thrust is limited, the transfer is occasionally posed as an optimal control problem subjected to the required objective and constraints. Relative
Low thrust relative orbital transfer
Low_thrust_relative_orbital_transfer
Software product for solving general-purpose optimal control problems
DIDO (/ˈdaɪdoʊ/ DY-doh) is a MATLAB optimal control toolbox for solving general-purpose optimal control problems. It is widely used in academia, industry
DIDO_(software)
Optimization algorithm
MATLAB/Octave), implemented by Dieter Kraft as part of a package for optimal control, and modified by S. G. Johnson. ALGLIB SQP solver (C++, C#, Java, Python
Sequential quadratic programming
Sequential_quadratic_programming
pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger theory of pseudospectral optimal control, a term coined
Legendre pseudospectral method
Legendre_pseudospectral_method
Topics referred to by the same term
Navier-Stokes equations Kalman filter, an approximating algorithm in optimal control applications and problems Filter (social media), an appearance-altering
Filter
Generalization of a Markov decision process
exact solution to a POMDP yields the optimal action for each possible belief over the world states. The optimal action maximizes the expected reward (or
Partially observable Markov decision process
Partially_observable_Markov_decision_process
Algorithm for trajectory optimization
Differential dynamic programming (DDP) is an optimal control algorithm of the trajectory optimization class. The algorithm was introduced in 1966 by Mayne
Differential dynamic programming
Differential_dynamic_programming
Estimation method
computational framework for Riemann-Stieltjes optimal control. This computational approach is known as unscented optimal control. Uhlmann and Simon Julier published
Unscented_transform
Mathematical relation assigning a probability event to a cost
choose the optimal action under the actual observed data to obtain a uniformly optimal one, whereas choosing the actual frequentist optimal decision rule
Loss_function
Problem of finding the optimal shape under given conditions
optimization is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost
Shape_optimization
Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program (NLP). The Gauss pseudospectral method
Gauss_pseudospectral_method
Weakly optimal allocation of resources
identify a single "best" (optimal) outcome. Instead, it only identifies a set of outcomes that might be considered optimal, by at least one person. Formally
Pareto_efficiency
Algorithm for solving boundary value problems of the Eikonal equation
{\displaystyle x} . The fast marching method takes advantage of this optimal control interpretation of the problem in order to build a solution outwards
Fast_marching_method
Mathematical method
and they are important in the theories of differential inclusions, optimal control, and mathematical economics. Given two sets X and Y, let F be a set-valued
Selection_theorem
bandit#Empirical motivation). Dual control theory was developed by Alexander Aronovich Fel'dbaum in 1960. He showed that in principle the optimal solution can be found
Dual_control_theory
Model". Optimal Control Applications and Methods. 4 (2): 179–184. doi:10.1002/oca.4660040207. S2CID 123673289. Sethi, S.P. (2021). Optimal Control Theory:
Sethi_model
Terminal command scheme used to transfer data
protocol innovates upon naive "data blaster" protocols through an optimal control-theoretic retransmission algorithm and implementation that achieves
Fast_and_Secure_Protocol
Open source 3D racing simulator
adaptive optimal control. It consists of: a simulation of the physics of cars racing on a track a graphic display of the race a separate control program
RARS_(video_game)
Study of strategic decision making
can be explained by an average agent's optimal control problem. In a mean-field game, an average agent can control their movement α {\displaystyle \alpha
Mean-field_game_theory
Hidden Markov model algorithm
Cassandras. "An improved forward algorithm for optimal control of a class of hybrid systems." Automatic Control, IEEE Transactions on 47.10 (2002): 1735-1739
Forward_algorithm
Mathematical problem solving strategy
direct solution of optimal control problems", Proceedings of the 9th IFAC World Congress, 9th IFAC World Congress: A Bridge Between Control Science and Technology
Direct multiple shooting method
Direct_multiple_shooting_method
slow or fail in solving the problem. Usually they find local optimal instead of the optimal value; however, the values are considered close enough of the
Simulation-based_optimization
Mathematical model for state estimation
part of the solution of an optimal control problem. For example, the Kalman filter is the estimation part of the optimal control solution to the linear-quadratic-Gaussian
Filtering problem (stochastic processes)
Filtering_problem_(stochastic_processes)
French mathematician (born 1974)
optimal; catégorie log-exp en géométrie sous-Riemannienne dans le cas Martinet (Asymptotic study and transcendence of the value function in optimal control;
Emmanuel_Trélat
OPTIMAL CONTROL
OPTIMAL CONTROL
Boy/Male
Tamil
To do something systematically, Optimum utilization of resources
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sikh
Lord Shiva; God's Name; Primal Being
Boy/Male
Indian, Sanskrit
The Primal Head of Religious Sacrifice
Boy/Male
Hindu, Indian, Marathi
The Primal God
Boy/Male
Arabic, Muslim
First; New; Another Name for God; Novel; Primal
Boy/Male
Indian, Sanskrit
One God; The Primal God
Girl/Female
Indian
Optional
Girl/Female
Hindu, Indian
Primal; A Wife of Agni
Boy/Male
Hindu
The primal God
Girl/Female
Tamil
Boy/Male
Hindu, Indian
To do Something Systematically or Optimum Utilization of Resources
Boy/Male
Hindu
To do something systematically, Optimum utilization of resources
Boy/Male
Indian, Sanskrit
The Primal Residue
Boy/Male
Indian, Sanskrit
The Primal Idol
Girl/Female
Hindu, Indian
The Primal Energy
Boy/Male
Tamil
The primal God
Girl/Female
Hindu, Indian, Traditional
The Primal Lakshmi
Girl/Female
Hindu
Girl/Female
Hindu, Indian
The Primal Mother
Boy/Male
Indian, Sanskrit
The Primal Root
OPTIMAL CONTROL
OPTIMAL CONTROL
Boy/Male
American, British, English, French, German, Italian
Protector of Prosperity; Happy Defender; Wealthy Protector
Boy/Male
French
Works in iron.
Boy/Male
Greek
Son of Ares.
Boy/Male
Muslim
Resident of bagh, Baghshur
Girl/Female
English American
Cheerful.
Boy/Male
Hindu, Indian
Weight
Girl/Female
Muslim
Angel, Guard of paradise, Bringer of good news (1)
Female
English
English name derived from Latin blanda, BLANDA means "cherishing."Â
Boy/Male
Indian
Wonder
Girl/Female
Tamil
Conqueror, Victorious, One who is victorious over everyone
OPTIMAL CONTROL
OPTIMAL CONTROL
OPTIMAL CONTROL
OPTIMAL CONTROL
OPTIMAL CONTROL
n.
Government by the nobility.
n.
An optical glass; a telescope.
n.
A nobleman or aristocrat; a chief man in a state or city.
a.
Of or pertaining to the eye; ocular; as, the optic nerves (the first pair of cranial nerves) which are distributed to the retina. See Illust. of Brain, and Eye.
a.
One who deals in optical glasses and instruments.
n.
An optical glass that is convex on both sides.
n.
One of those who stand in the second rank of honors, immediately after the wranglers, in the University of Cambridge, England. They are divided into senior and junior optimes.
a.
Relating to the science of optics; as, optical works.
n.
Collectively, the nobility.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
a.
Of or pertaining to vision or sight.
a.
Alt. of Optical
a.
Of or pertaining to the nobility or aristocracy.
n.
See Elective, n.
n.
The space covered by an optical instrument at one view.
n.
A reflecting optical glass or instrument; a mirror.
adv.
In an optional manner.
n.
An optical toy similar to the phenakistoscope. See Phenakistoscope.
n.
Of or pertaining to the science of vision; optical.
n.
An instrument for showing the optical effects of color.