scholarly journals Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Weihai Zhang ◽  
Guiling Li
Keyword(s):  
Discrete Time ◽  
Terminal State ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Second Moment ◽  
New Class ◽  
The Matrix ◽  
Moment Constraint ◽  
Lq Problem ◽  
The Cost

This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other.

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.

scholarly journals Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Xikui Liu ◽  
Guiling Li ◽  
Yan Li
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Discrete Time ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Discrete Time Systems ◽  
Quadratic Optimal Control ◽  
The Cost ◽  
Time Systems ◽  
Difference Riccati Equation

The Karush-Kuhn-Tucker (KKT) theorem is used to study stochastic linear quadratic optimal control with terminal constraint for discrete-time systems, allowing the control weighting matrices in the cost to be indefinite. A generalized difference Riccati equation is derived, which is different from those without constraint case. It is proved that the well-posedness and the attainability of stochastic linear quadratic optimal control problem are equivalent. Moreover, an optimal control can be denoted by the solution of the generalized difference Riccati equation.

scholarly journals State estimation in a decentralized discrete time LQG control for a multisensor system

2017 ◽  
Vol 27 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Zdzislaw Duda
Keyword(s):  
Discrete Time ◽  
Global State ◽  
Linear Quadratic ◽  
Control Laws ◽  
Decentralized System ◽  
Multisensor System ◽  
State Estimators ◽  
Local Measurements ◽  
Information Pattern ◽  
The Cost

Abstract In the paper a state filtration in a decentralized discrete time Linear Quadratic Gaussian problem formulated for a multisensor system is considered. Local optimal control laws depend on global state estimates and are calculated by each node. In a classical centralized information pattern the global state estimators use measurements data from all nodes. In a decentralized system the global state estimates are computed at each node using local state estimates based on local measurements and values of previous controls, from other nodes. In the paper, contrary to this, the controls are not transmitted between nodes. It leads to nonconventional filtration because the controls from other nodes are treated as random variables for each node. The cost for the additional reduced transmission is an increased filter computation at each node.

Solving the LQ and Non-Conventional Performance Index Optimal Problem With the Use of the Simulated Annealing Algorithm

2007 ◽  
Author(s):  
Horacio Marti´nez-Alfaro ◽  
Manuel Valenzuela-Rendo´n
Keyword(s):  
Simulated Annealing ◽  
Performance Index ◽  
Simulated Annealing Algorithm ◽  
Mimo Systems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control ◽  
Annealing Algorithm ◽  
Lq Problem ◽  
Time Invariant

An approach to solve the discrete-time, time-invariant linear quadratic optimal control problem is presented. The design approach presented in here transforms the LQ problem into a combinatorial optimization problem and uses the Simulated Annealing algorithm to optimize the performance index. In addition, a non-conventional performance index is proposed. Some SISO and MIMO systems are tested. Results proved the approach to be an excellent option to find a solution to the problem.

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