scholarly journals Singular LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qingxiang Fang ◽  
Baolin Zhang ◽  
Jun-e Feng
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Free State ◽  
Algebraic Riccati Equation ◽  
Equivalence Transformation ◽  
State Pair ◽  
Lq Problem ◽  
Control State

This paper is concerned with the singular LQ problem for irregular singular systems with persistent disturbances. The full information feedback control method is employed to achieve the optimal control. By restricted system equivalence transformation, the system state is decomposed into free state and restricted state and the input is decomposed into free input and forced input. Some sufficient conditions for the unique existence of optimal control-state pair are derived and these conditions are all described unitedly with matrix rank equalities. The optimal control-state pair can be explicitly formulated via solving an algebraic Riccati equation and a Sylvester equation. Moreover, under the optimal control-state pair, the resulting system has no free state.

scholarly journals Indefinite LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qingxiang Fang ◽  
Jigen Peng ◽  
Feilong Cao
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Algebraic Riccati Equation ◽  
Closed Loop System ◽  
State Pair ◽  
Lq Problem ◽  
Control State

The indefinite LQ problem for irregular singular systems is investigated. Under some general conditions, the optimal control-state pair is obtained by solving an algebraic Riccati equation. The optimal control is synthesized as state feedback. All the finite poles of the closed-loop system are located on the left-half complex plane. An example is given to show the validity of the proposed conclusion.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

Robotica ◽  
2019 ◽  
Vol 38 (1) ◽  
pp. 29-47 ◽  
Author(s):  
G. Rigatos ◽  
K. Busawon ◽  
J. Pomares ◽  
M. Abbaszadeh
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Control Method ◽  
Taylor Series Expansion ◽  
Nonlinear Optimal Control ◽  
Algebraic Riccati Equation ◽  
Time Step ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Wheeled Inverted Pendulum

SummaryThe article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal (H-infinity) feedback controller is developed. The controller’s gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the H-infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.

scholarly journals A nonlinear optimal control approach for the UAV and suspended payload system

2021 ◽  
pp. 27-39
Author(s):  
Gerasimos G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
State Space Model ◽  
Taylor Series Expansion ◽  
Nonlinear Optimal Control ◽  
Algebraic Riccati Equation ◽  
State Variables ◽  
Time Step ◽  
Control Approach ◽  
Optimal Control Approach

The article proposes a nonlinear optimal control approach for the UAV and suspended load system. The dynamic model of the UAV and payload system undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which recomputed at each iteration of the control method. For the approximately linearized model an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the system. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the UAV and payload system, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the UAV and payload system, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Sevorel Conclusions of Guaranteed Cost for Uncertain Discrete Singular System

2013 ◽  
Vol 655-657 ◽  
pp. 1541-1544
Author(s):  
Jun Na Jiang ◽  
Xue Yu Mi
Keyword(s):  
State Feedback ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Algebraic Riccati Equation ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Closed Loop Systems ◽  
Guaranteed Cost ◽  
Discrete Singular Systems

In this papar we research the guaranteed cost control for a class of norm bounded uncertain discrete singular systems was considered in this paper. The objective is to design state-feedback controllers such that the closed-loop systems is regular, causal, stable and the corresponding cost function have a certain upper bound minimized for all admissible uncertainties. Two sufficient conditions for the existence of state-feedback guaranteed cost controllers are obtained in terms of algebraic Riccati equation and linear matrix inequalities, respectively. And the numerical examples show the validity of our inclusion.

Nonlinear optimal control for synchronization of distributed hydropower generators

2020 ◽  
pp. 014233122095003
Author(s):  
Gerasimos Rigatos ◽  
Pierluigi Siano ◽  
Masoud Abbaszadeh
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Taylor Series Expansion ◽  
Nonlinear Optimal Control ◽  
Algebraic Riccati Equation ◽  
Time Step ◽  
H Infinity ◽  
Control Approach ◽  
Linearized Model

Synchronization of distributed hydropower units is necessary for ensuring the quality of the electric power produced by renewable sources. In this article, a nonlinear optimal control approach is proposed for stabilization and synchronization of distributed hydropower generators. The dynamic model of the interacting hydropower generation units undergoes approximate linearization with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. The linearization point is updated at each time-step of the control method. For the approximately linearized model of the distributed hydropower system an H-infinity feedback controller is designed. This controller achieves solution of the related optimal control problem under model uncertainty and external perturbations. For the computation of the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to achieve state estimation-based control for the system of the distributed hydropower generators the H-infinity Kalman Filter is used as a robust state estimator.

The human-like trajectory planning for autonomous vehicles based on optimal control in a test track environment

2021 ◽  
pp. 095440702110090
Author(s):  
Xing Xu ◽  
Minglei Li ◽  
Feng Wang ◽  
Ju Xie ◽  
Xiaohan Wu ◽  
...  
Keyword(s):  
Optimal Control ◽  
Autonomous Vehicles ◽  
Optimal Trajectory ◽  
Control Method ◽  
Autonomous Vehicle ◽  
Trajectory Data ◽  
Test Track ◽  
Optimal Control Method ◽  
The Future ◽  
On The Road

A human-like trajectory could give a safe and comfortable feeling for the occupants in an autonomous vehicle especially in corners. The research of this paper focuses on planning a human-like trajectory along a section road on a test track using optimal control method that could reflect natural driving behaviour considering the sense of natural and comfortable for the passengers, which could improve the acceptability of driverless vehicles in the future. A mass point vehicle dynamic model is modelled in the curvilinear coordinate system, then an optimal trajectory is generated by using an optimal control method. The optimal control problem is formulated and then solved by using the Matlab tool GPOPS-II. Trials are carried out on a test track, and the tested data are collected and processed, then the trajectory data in different corners are obtained. Different TLCs calculations are derived and applied to different track sections. After that, the human driver’s trajectories and the optimal line are compared to see the correlation using TLC methods. The results show that the optimal trajectory shows a similar trend with human’s trajectories to some extent when driving through a corner although it is not so perfectly aligned with the tested trajectories, which could conform with people’s driving intuition and improve the occupants’ comfort when driving in a corner. This could improve the acceptability of AVs in the automotive market in the future. The driver tends to move to the outside of the lane gradually after passing the apex when driving in corners on the road with hard-lines on both sides.

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