Fast Algorithm for Estimating Control Horizon of Input Constrained Linear Quadratic Regulation

2012 ◽  
Vol 546-547 ◽  
pp. 1056-1062
Author(s):  
Wei Wei Zhang ◽  
Yong Sun
Keyword(s):  
Linear Programming ◽  
Upper Bound ◽  
Fast Algorithm ◽  
Linear Programming Problem ◽  
Infinite Horizon ◽  
Finite Horizon ◽  
Linear Quadratic ◽  
Lqr Problem ◽  
Linear Quadratic Regulation ◽  
On Line

A fast algorithm for estimating the control horizon of the input constrained linear quadratic regulation (LQR) problem is presented. It is known that there exists a finite horizon such that the infinite horizon constrained LQR problem can be solved as a finite horizon constrained LQR problem. An efficient algorithm to estimate the upper bound of the horizon is presented based on the linear programming. It only needs to solve a linear programming problem for on line application. Finally, the comparison among some methods is shown by an example. The proposed algorithm has less conservative than those of other algorithms.

AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

2013 ◽  
Vol 30 (03) ◽  
pp. 1340012 ◽  
Author(s):  
TOMONARI KITAHARA ◽  
SHINJI MIZUNO
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Upper Bound ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Selection Rule ◽  
Dual Simplex Method ◽  
Unimodular Matrix ◽  
Dual Simplex ◽  
Pivoting Rule

Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.

scholarly journals Linear-quadratic programming and its application to data correction of improper linear programming problems

2020 ◽  
Vol 10 (1) ◽  
pp. 48-55
Author(s):  
Victor Gorelik ◽  
Tatiana Zolotova
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Linear Programming Problem ◽  
Optimization Problems ◽  
Lagrange Function ◽  
Frobenius Norm ◽  
Linear Quadratic ◽  
Quadratic Constraints ◽  
Linear Programming Problems ◽  
The Right

AbstractThe problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints.

scholarly journals Real-Time Energy Management of Parallel Hybrid Electric Vehicles Using Linear Quadratic Regulation

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5538
Author(s):  
Bảo-Huy Nguyễn ◽  
João Pedro F. Trovão ◽  
Ronan German ◽  
Alain Bouscayrol
Keyword(s):  
Real Time ◽  
Energy Management ◽  
Electric Vehicles ◽  
Hybrid Electric Vehicles ◽  
Engine Fuel ◽  
Linear Quadratic ◽  
Loop Control ◽  
Parallel Hybrid ◽  
Linear Quadratic Regulation ◽  
Hybrid Electric

Optimization-based methods are of interest for developing energy management strategies due to their high performance for hybrid electric vehicles. However, these methods are often complicated and may require strong computational efforts, which can prevent them from real-world applications. This paper proposes a novel real-time optimization-based torque distribution strategy for a parallel hybrid truck. The strategy aims to minimize the engine fuel consumption while ensuring battery charge-sustaining by using linear quadratic regulation in a closed-loop control scheme. Furthermore, by reformulating the problem, the obtained strategy does not require the information of the engine efficiency map like the previous works in literature. The obtained strategy is simple, straightforward, and therefore easy to be implemented in real-time platforms. The proposed method is evaluated via simulation by comparison to dynamic programming as a benchmark. Furthermore, the real-time ability of the proposed strategy is experimentally validated by using power hardware-in-the-loop simulation.

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