• Corpus ID: 237532154

Causal State Feedback Representation for Linear Quadratic Optimal Control Problems of Singular Volterra Integral Equations

@inproceedings{Han2021CausalSF,
  title={Causal State Feedback Representation for Linear Quadratic Optimal Control Problems of Singular Volterra Integral Equations},
  author={Shuo Han and Ping-Zong Lin and Jiongmin Yong},
  year={2021}
}
This paper is concerned with a linear quadratic optimal control for a class of singular Volterra integral equations. Under proper convexity conditions, optimal control uniquely exists, and it could be characterized via Fréchet derivative of the quadratic functional in a Hilbert space or via maximum principle type necessary conditions. However, these (equivalent) characterizations have a shortcoming that the current value of the optimal control depends on the future values of the optimal state… 

References

SHOWING 1-10 OF 47 REFERENCES
An elementary proof of the maximum principle for optimal control problems governed by a Volterra integral equation
An elementary proof of the maximum principle for optimal control problems whose states are governed by Volterra integral equations is given. Our proof is motivated by the work of Michel (Ref. 7) and
Causal Feedback Optimal Control for Volterra Integral Equations
The optimal control problem for Volterra integral equations with respect to quadratic criteria is studied by a projection causality approach. The work features a synthesis result where the optimal
Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equations for Fractional-Order Systems
  • M. Gomoyunov
  • Computer Science, Mathematics
    SIAM J. Control. Optim.
  • 2020
TLDR
It is proved that this functional introduced as a functional in a suitable space of histories of motions satisfies the dynamic programming principle and is associated with a Hamilton-Jacobi-Bellman equation.
Optimal processes governed by integral equations
Abstract We consider a control process governed by an integral equation with an integral constraint. We derive optimality conditions using relaxed controls. Existence of optimal pairs is automatic.
First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations
TLDR
The order of a running state constraint is defined in the setting of integral dynamics, and the conditions of optimality are given by the description of the set of Lagrange multipliers.
Controlled Singular Volterra Integral Equations and Pontryagin Maximum Principle
  • P. Lin, J. Yong
  • Mathematics, Computer Science
    SIAM J. Control. Optim.
  • 2020
TLDR
A Pontryagin's type maximum principle is established for optimal controls of controlled singular Volterra integral equations, by using a Liapounoff's type theorem and the spike variation technique for optimal control problem.
Fractional Optimal Control Problems with Several State and Control Variables
In many applications, fractional derivatives provide better descriptions of the behavior of dynamic systems than other techniques. For this reason, fractional calculus has been used to analyze
A new method for optimal control of Volterra integral equations
  • S. Belbas
  • Mathematics, Computer Science
    Appl. Math. Comput.
  • 2007
TLDR
A new method for solving optimal control problems for systems governed by Volterra integral equations and a novel type of dynamic programming in which the Hamilton–Jacobi function is parametrized by the control function (rather than the state) is formulated and analyzed.
Necessary Conditions for Optimal Terminal Time Control Problems Governed by a Volterra Integral Equation
We prove the maximum principle for optimal terminal time control problems with the state governed by a Volterra integral equation and constraints depending on the terminal time and the state. We use
A reduction method for optimal control of Volterra integral equations
  • S. Belbas
  • Mathematics, Computer Science
    Appl. Math. Comput.
  • 2008
TLDR
A novel method based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential equations is presented, which can be solved by dynamic programming methods for ODE controlled systems.
...
1
2
3
4
5
...