On the utopian approach to the multiobjective LQ problem

1993 ◽  
Vol 14 (2) ◽  
pp. 111-124 ◽  
Author(s):  
Giuseppe De Nicolao ◽  
Arturo Locatelli
Keyword(s):  
Lq Problem

scholarly journals Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control

2018 ◽  
Vol 63 (9) ◽  
pp. 2771-2786 ◽  
Author(s):  
Yuan-Hua Ni ◽  
Ji-Feng Zhang ◽  
Miroslav Krstic
Keyword(s):  
Mean Field ◽  
Open Loop ◽  
Time Inconsistent ◽  
Lq Problem

Linear Quadratic Optimal Control Via Fourier-Based State Parameterization

1991 ◽  
Vol 113 (2) ◽  
pp. 206-215 ◽  
Author(s):  
V. Yen ◽  
M. Nagurka
Keyword(s):  
Optimal Control ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Quadratic Programming Problem ◽  
Necessary Condition ◽  
Mathematical Programming Problem ◽  
Linear Quadratic ◽  
Linear Algebraic Equations ◽  
Linearly Constrained ◽  
Lq Problem

A method for determining the optimal control of unconstrained and linearly constrained linear dynamic systems with quadratic performance indices is presented. The method is based on a modified Fourier series approximation of each state variable that converts the linear quadratic (LQ) problem into a mathematical programming problem. In particular, it is shown that an unconstrained LQ problem can be cast as an unconstrained quadratic programming problem where the necessary condition of optimality is derived as a system of linear algebraic equations. Furthermore, it is shown that a linearly constrained LQ problem can be converted into a general quadratic programming problem. Simulation studies for constrained LQ systems, including a bang-bang control problem, demonstrate that the approach is accurate. The results also indicate that in solving high order unconstrained LQ problems the approach is computationally more efficient and robust than standard methods.

Singular LQ problem for nonregular descriptor systems

2002 ◽  
Vol 47 (7) ◽  
pp. 1128-1133 ◽  
Author(s):  
Jiandong Zhu ◽  
Shuping Ma ◽  
Zhaolin Cheng
Keyword(s):  
Descriptor Systems ◽  
Lq Problem

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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