Polynomial-Chaos-Based Numerical Method for the LQR Problem With Uncertain Parameters in the Formulation

2010 ◽  
Author(s):  
Emmanuel Blanchard ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Numerical Method ◽  
Polynomial Chaos ◽  
Linear Quadratic Regulator ◽  
Mean Value ◽  
Optimal Controller ◽  
Linear Quadratic ◽  
Case Scenario ◽  
Worst Case ◽  
Lqr Problem ◽  
And Performance

This paper proposes a polynomial chaos based numerical method providing an optimal controller for the linear-quadratic regulator (LQR) problem when the parameters in the formulation are uncertain, i.e., a controller minimizing the mean value of the LQR cost function obtained for a certain distribution of the uncertainties which is assumed to be known. The LQR problem is written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework, and an iterative algorithm converges to the optimal answer. The algorithm is applied to a simple example for which the answer is already known. Polynomial chaos based methods have the advantage of being computationally much more efficient than Monte Carlo simulations. The Linear-Quadratic Regulator controller is not very well adapted to robust design, and the optimal controller does not guarantee a minimum performance or even stability for the worst case scenario. Stability robustness and performance robustness in the presence of uncertainties are therefore not guaranteed. However, this is a first step aimed at designing more judicious controllers if combined with other techniques in the future. The next logical step would be to extend this numerical method to H2 and then H-infinity problems.

Initial Price Strategies of Polish Micro and Small Enterprises

2017 ◽  
pp. 126-143
Author(s):  
Mariusz Maciejczak ◽  
Adrian Słodki
Keyword(s):  
Game Theory ◽  
Point Of View ◽  
Medium Size ◽  
Small Enterprises ◽  
Small Companies ◽  
Case Scenario ◽  
Worst Case ◽  
The Game Theory ◽  
Real Market ◽  
And Performance

The sector of micro, small and medium size enterprises is important for any economy. It is important also for Poland. Analyzing the industrial organization of this sector it was confirmed that the owners and managers of such companies are applying strategies, which are rational from their point of view, but not from the perspective of real market conditions. It is argued therefore that the game theory is for them a solution in enhancing competences and performance of their organizations. Based on randomized sample of Polish micro and small companies the paper aimed to find out if the managers apply the game theory rationales when choosing price strategy when enter the market. It was confirmed that they do not and that they don't play Nash equilibrium in the strategic interaction when it comes to the price level. There was applied maxmin strategy, which maximises the worst - case scenario from the game. Thus there is a real chance that if entrepreneurs would analyze the situation with respect of game theory, their strategies would be more accurate and provide better outcomes.

scholarly journals System design for inverted pendulum using LQR control via IoT

2020 ◽  
Vol 11 ◽  
pp. 12
Author(s):  
Dechrit Maneetham ◽  
Petrus Sutyasadi
Keyword(s):  
Inverted Pendulum ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Lqr Controller ◽  
Model Tuning ◽  
And Performance ◽  
Performance Results ◽  
And Control

This research proposes control method to balance and stabilize an inverted pendulum. A robust control was analyzed and adjusted to the model output with real time feedback. The feedback was obtained using state space equation of the feedback controller. A linear quadratic regulator (LQR) model tuning and control was applied to the inverted pendulum using internet of things (IoT). The system's conditions and performance could be monitored and controlled via personal computer (PC) and mobile phone. Finally, the inverted pendulum was able to be controlled using the LQR controller and the IoT communication developed will monitor to check the all conditions and performance results as well as help the inverted pendulum improved various operations of IoT control is discussed.

scholarly journals Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

2010 ◽  
Vol 20 (4) ◽  
pp. 655-664 ◽  
Author(s):  
Keyword(s):  
Semidefinite Programming ◽  
Linear Quadratic Regulator ◽  
Descriptor Systems ◽  
Programming Approach ◽  
State Control ◽  
Linear Quadratic ◽  
Control Pair ◽  
Elegant Method ◽  
Lqr Problem ◽  
Primal Dual

Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systemsThis paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.

scholarly journals Improve Linear Quadratic Regulator by Particle Swarm Optimization Algorithms for Two Wheeled Self Balancing Mobile robot

2017 ◽  
Vol 13 (2) ◽  
pp. 173-179
Author(s):  
Ekhlas Karam ◽  
Noor Mjeed
Keyword(s):  
Particle Swarm Optimization ◽  
Numerical Method ◽  
Control Method ◽  
Particle Swarm ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Balancing Robot ◽  
The Stability ◽  
Multivariable Feedback

The aim of this paper is to suggest a methodical smooth control method for improving the stability of two wheeled self-balancing robot under effect disturbance. To promote the stability of the robot, the design of linear quadratic regulator using particle swarm optimization (PSO) method and adaptive particle swarm optimization (APSO). The computation of optimal multivariable feedback control is traditionally by LQR approach by Riccati equation. Regrettably, the method as yet has a trial and error approach when selecting parameters, particularly tuning the Q and R elements of the weight matrices. Therefore, an intelligent numerical method to solve this problem is suggested by depending PSO and APSO algorithm. To appraise the effectiveness of the suggested method, The Simulation result displays that the numerical method makes the system stable and minimizes processing time.

ACTIVE VIBRATION CONTROL OF SEISMICALLY EXCITED STRUCTURES BY ATMDS: STABILITY AND PERFORMANCE ROBUSTNESS PERSPECTIVE

2010 ◽  
Vol 10 (03) ◽  
pp. 501-527 ◽  
Author(s):  
ARASH MOHTAT ◽  
AGHIL YOUSEFI-KOMA ◽  
EHSAN DEHGHAN-NIRI
Keyword(s):  
Vibration Control ◽  
Structural Damage ◽  
Fuzzy Logic Controller ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Structural Vibration ◽  
Linear Quadratic ◽  
And Performance ◽  
Performance Robustness

This paper demonstrates the trade-off between nominal performance and robustness in intelligent and conventional structural vibration control schemes; and, proposes a systematic treatment of stability robustness and performance robustness against uncertainty due to structural damage. The adopted control strategies include an intelligent genetic fuzzy logic controller (GFLC) and reduced-order observer-based (ROOB) controllers based on pole-placement and linear quadratic regulator (LQR) conventional schemes. These control strategies are applied to a seismically excited truss bridge structure through an active tuned mass damper (ATMD). Response of the bridge-ATMD control system to earthquake excitation records under nominal and uncertain conditions is analyzed via simulation tests. Based on these results, advantages of exploiting heuristic intelligence in seismic vibration control, as well as some complexities arising in realistic conventional control are highlighted. It has been shown that the coupled effect of spill-over (due to reduction and observation) and mismatch between the mathematical model and the actual plant (due to uncertainty and modeling errors) can destabilize the conventional closed-loop system even if each is alone tolerated. Accordingly, the GFLC proves itself to be the dominant design in terms of the compromise between performance and robustness.

Optimal Roll Control of a Single-Unit Lorry

1996 ◽  
Vol 210 (1) ◽  
pp. 45-55 ◽  
Author(s):  
R C Lin ◽  
D Cebon ◽  
D J Cole
Keyword(s):  
Single Unit ◽  
Load Transfer ◽  
Linear Quadratic Regulator ◽  
Lateral Acceleration ◽  
Hydraulic Actuator ◽  
Linear Quadratic ◽  
Mean Power ◽  
Worst Case ◽  
Limited Bandwidth ◽  
Roll Control

Lateral acceleration control and linear quadratic regulator (LQR) theory are used to design active roll control systems for heavy goods vehicles. The suspension consists of a limited bandwidth hydraulic actuator in series with an anti-roll bar. The procedure used to determine suitable controller gains is described. The simulation results show that roll control of a single-unit lorry requires an actuator bandwidth of 6 Hz and mean power of approximately 17 kW for a ‘worst case’ random steering input. The static roll-over threshold of this vehicle is increased by 66 per cent when compared with the same vehicle with passive suspensions and the r.m.s. lateral load transfer is reduced by 34 per cent for a typical random steering input.

Optimal Control of Complex Air-Path Systems for Advanced Diesel Engines

2009 ◽  
Author(s):  
Fengjun Yan ◽  
Benjamin Haber ◽  
Junmin Wang
Keyword(s):  
Optimal Control ◽  
Diesel Engines ◽  
Linear Quadratic Regulator ◽  
Mean Value ◽  
Diffusion Combustion ◽  
Linear Quadratic ◽  
Control Approach ◽  
Engine Model ◽  
Path System ◽  
Linearized Model

This paper describes a linear optimal control approach for advanced diesel engines equipped with complex air-path systems including a dual-loop exhaust gas recirculation (EGR) and a two-stage turbocharger. Such complex air-path systems are instrumental to achieve smooth and stable transient operation of diesel engines running advanced multiple combustion modes such as low temperature diffusion combustion (LTDC) and homogeneous charge compression ignition (HCCI). A mean-value engine model was developed to capture the main dynamics of the advanced air-path system. A linear quadratic regulator (LQR) optimal controller was designed based on a linearized model at a fixed operating point. Simulation results using a high-fidelity detailed GT-Power engine model show the effectiveness of the controller.

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