scholarly journals Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guiling Li ◽  
Weihai Zhang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraint ◽  
Terminal State ◽  
State Feedback Control ◽  
Programming Algorithm ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lq Optimal Control

This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.

Discrete-Time Uncertain LQ Optimal Control with Indefinite Control Weight Costs

2016 ◽  
Vol 20 (4) ◽  
pp. 633-639 ◽  
Author(s):  
Yuefen Chen ◽  
◽  
Liubao Deng ◽  
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Recurrence Equation ◽  
State Feedback Control ◽  
Necessary Condition ◽  
Well Posedness ◽  
Linear Quadratic ◽  
Lq Optimal Control ◽  
Optimal State Feedback ◽  
Lq Problem

This paper deals with a discrete-time uncertain linear quadratic (LQ) optimal control, where the control weight costs are indefinite . Based on Bellman’s principle of optimality, the recurrence equation of the uncertain LQ optimal control is proposed. Then, by using the recurrence equation, a necessary condition of the optimal state feedback control for the LQ problem is obtained. Moreover, a sufficient condition of well-posedness for the LQ problem is presented. Furthermore, an algorithm to compute the optimal control and optimal value is provided. Finally, a numerical example to illustrate that the LQ problem is still well-posedness with indefinite control weight costs.

Multi-Dimension Uncertain Linear Quadratic Optimal Control with Cross Term

2015 ◽  
Vol 19 (5) ◽  
pp. 670-675 ◽  
Author(s):  
Yuefen Chen ◽  
◽  
Bo Li
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Riccati Differential Equation ◽  
Cross Term ◽  
Lq Optimal Control ◽  
Quadratic Optimal Control ◽  
Feedback Optimal Control

In this paper, we consider a multi-dimension uncertain linear quadratic (LQ) optimal control with cross term. With the aid of the equation of optimality of a general multi-dimension uncertain optimal control, we present a necessary and sufficient condition for the existence of optimal linear feedback optimal control which is associated with a Riccati differential equation. Moreover, some properties of the solution for the Riccati differential equation are discussed. Furthermore, the uniqueness of the feedback optimal control for the uncertain linear quadratic optimal control with cross term is proved. Finally, as an application, an example is presented to illustrate the theory obtained.

Optimistic Value Model of Uncertain Linear Quadratic Optimal Control with Jump

2016 ◽  
Vol 20 (2) ◽  
pp. 189-196 ◽  
Author(s):  
Liubao Deng ◽  
◽  
Yuefen Chen ◽  
Keyword(s):  
Optimal Control ◽  
Inventory Problem ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Proposed Model ◽  
Lq Optimal Control ◽  
Existence Of Optimal Control ◽  
Necessary And Sufficient ◽  
Value Model ◽  
Optimistic Value

Based on the optimistic value model of uncertain optimal control model with jump, in this paper, an optimistic value model of uncertain linear quadratic (LQ) optimal control with jump is proposed. Then, the necessary and sufficient condition for the existence of optimal control is obtained. Finally, an enterprize's inventory problem is given to illustrate usefulness of the proposed model.

scholarly journals A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Shaolin Ji ◽  
Qingmeng Wei ◽  
Xiumin Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Differential Equation ◽  
State Constraints ◽  
Terminal State ◽  
Necessary Condition ◽  
Variation Principle ◽  
Linear Quadratic ◽  
Doubly Stochastic

We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.

scholarly journals Optimal control for controllable stochastic linear systems

2020 ◽  
Vol 26 ◽  
pp. 98
Author(s):  
Xiuchun Bi ◽  
Jingrui Sun ◽  
Jie Xiong
Keyword(s):  
Optimal Control ◽  
Linear Systems ◽  
Optimal Parameter ◽  
Linear Manifold ◽  
Terminal State ◽  
Linear Quadratic ◽  
Initial State ◽  
Linear Quadratic Optimal Control ◽  
Lq Problem ◽  
Stochastic Linear Systems

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of stochastic linear systems is studied. Then the optimal control is explicitly obtained by considering a parameterized unconstrained backward LQ problem and an optimal parameter selection problem. A notable feature of our results is that, instead of solving an equation involving derivatives with respect to the parameter, the optimal parameter is characterized by a matrix equation.

A Chebyshev-Based State Representation for Linear Quadratic Optimal Control

1993 ◽  
Vol 115 (1) ◽  
pp. 1-6 ◽  
Author(s):  
M. L. Nagurka ◽  
S.-K. Wang
Keyword(s):  
Optimal Control ◽  
Necessary Condition ◽  
Algebraic Equations ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Finite Term ◽  
Linear Algebraic Equations ◽  
Quadratic Performance ◽  
The Difference ◽  
Necessary Condition Of Optimality

A computationally attractive method for determining the optimal control of unconstrained linear dynamic systems with quadratic performance indices is presented. In the proposed method, the difference between each state variable and its initial condition is represented by a finite-term shifted Chebyshev series. The representation leads to a system of linear algebraic equations as the necessary condition of optimality. Simulation studies demonstrate computational advantages relative to a standard Riccati-based method, a transition matrix method, and a previous Fourier-based method.

scholarly journals Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Yuefen Chen ◽  
Minghai Yang
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
State Constraint ◽  
Terminal State ◽  
Necessary Condition ◽  
Lagrangian Multiplier ◽  
Lq Optimal Control ◽  
System States ◽  
Lq Problem ◽  
Terminal State Constraint

Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper.

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