scholarly journals Adaptive Critic Learning-Based Robust Control of Systems with Uncertain Dynamics

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jun Zhao ◽  
Qingliang Zeng ◽  
Bin Guo
Keyword(s):  
Optimal Control ◽  
Robust Control ◽  
Control Problem ◽  
Control Method ◽  
System Modeling ◽  
Uncertain System ◽  
Nonsmooth Dynamics ◽  
Adaptive Critic ◽  
Uncertain Dynamics ◽  
Critic Neural Network

Model uncertainties are usually unavoidable in the control systems, which are caused by imperfect system modeling, disturbances, and nonsmooth dynamics. This paper presents a novel method to address the robust control problem for uncertain systems. The original robust control problem of the uncertain system is first transformed into an optimal control of nominal system via selecting the appropriate cost function. Then, we develop an adaptive critic leaning algorithm to learn online the optimal control solution, where only the critic neural network (NN) is used, and the actor NN widely used in the existing methods is removed. Finally, the feasibility analysis of the control algorithm is given in the paper. Simulation results are given to show the availability of the presented control method.

scholarly journals Intrinsic Optimal Control for Mechanical Systems on Lie Group

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Shengjing Tang ◽  
Jie Guo
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Control Method ◽  
Geodesic Distance ◽  
Infinite Horizon ◽  
Mechanical Systems ◽  
Programming Approach

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

2020 ◽  
Vol 42 (16) ◽  
pp. 3135-3155
Author(s):  
Neda Nasiri ◽  
Ahmad Fakharian ◽  
Mohammad Bagher Menhaj
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Riccati Equation ◽  
Power Transmission ◽  
Control Method ◽  
Main Idea ◽  
Robotic Systems ◽  
Flexible Joint ◽  
State Dependent ◽  
Highly Nonlinear

In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying disturbances. The proposed observer-based robust (OBR) controller is applied to two highly nonlinear, coupled and large robotic systems: namely a manipulator presenting joint flexibility due to deformation of the power transmission elements between the actuator and the robot known as flexible-joint robot (FJR) and also an FJR incorporating geared permanent magnet DC motor dynamics in its dynamic model called electrical flexible-joint robot (EFJR). A novel state-dependent coefficient (SDC) form is introduced for uncertain EFJRs. Rather than coping with the OBR control problem for such complex uncertain robotic systems, the main idea is to solve an equivalent nonlinear optimal control problem where the uncertainty and disturbance bounds are incorporated in the performance index. The stability proof is presented. Solving the complicated robust control problem for FJRs and EFJRs subject to uncertainty and disturbances via a simple and flexible nonlinear optimal approach and no need of state measurement are the main advantages of the proposed control method. Finally, simulation results are included to verify the efficiency and superiority of the control scheme.

Comparative studies for the fractional optimal control in transmission dynamics of West Nile virus

2017 ◽  
Vol 10 (07) ◽  
pp. 1750095 ◽  
Author(s):  
N. H. Sweilam ◽  
O. M. Saad ◽  
D. G. Mohamed
Keyword(s):  
Optimal Control ◽  
West Nile Virus ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Comparative Studies ◽  
Control Method ◽  
Euler Method ◽  
West Nile ◽  
Iterative Optimal Control

In this paper, optimal control for a novel West Nile virus (WNV) model of fractional order derivative is presented. The proposed model is governed by a system of fractional differential equations (FDEs), where the fractional derivative is defined in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Two numerical methods are used to study the fractional-order optimal control problem. The methods are, the iterative optimal control method (OCM) and the generalized Euler method (GEM). Positivity, boundedness and convergence of the IOCM are studied. Comparative studies between the proposed methods are implemented, it is found that the IOCM is better than the GEM.

scholarly journals A bilevel optimal motion planning (BOMP) model with application to autonomous parking

2019 ◽  
Vol 3 (4) ◽  
pp. 370-382 ◽  
Author(s):  
Shenglei Shi ◽  
Youlun Xiong ◽  
Jiankui Chen ◽  
Caihua Xiong
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Motion Planning ◽  
Control Problem ◽  
Control Method ◽  
Significant Feature ◽  
Optimal Motion ◽  
Optimal Control Method ◽  
Optimal Motion Planning ◽  
Upper Level

Abstract In this paper, we present a bilevel optimal motion planning (BOMP) model for autonomous parking. The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and the lower level is for geometry collision-free constraints. The significant feature of the BOMP model is that the lower level is a linear programming problem that serves as a constraint for the upper-level problem. That is, an optimal control problem contains an embedded optimization problem as constraints. Traditional optimal control methods cannot solve the BOMP problem directly. Therefore, the modified approximate Karush–Kuhn–Tucker theory is applied to generate a general nonlinear optimal control problem. Then the pseudospectral optimal control method solves the converted problem. Particularly, the lower level is the $$J_2$$J2-function that acts as a distance function between convex polyhedron objects. Polyhedrons can approximate objects in higher precision than spheres or ellipsoids. As a result, a fast high-precision BOMP algorithm for autonomous parking concerning dynamical feasibility and collision-free property is proposed. Simulation results and experiment on Turtlebot3 validate the BOMP model, and demonstrate that the computation speed increases almost two orders of magnitude compared with the area criterion based collision avoidance method.

Fractional Order LQR for Optimal Robust Control of a Simple Structure

2007 ◽  
Author(s):  
Abdollah Shafieezadeh ◽  
Keri Ryan ◽  
YangQuan Chen
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Fractional Order ◽  
Simple Structure ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Fractional Damping ◽  
Fractional Order Control

This study combines fractional order control with linear quadratic regulator (LQR) for optimal robust control of a simple civil structure. As a first attempt, the purpose of this paper is to demonstrate that, when fractional damping is introduced, additional benefits can be obtained over the best traditional control method. The control problem of this paper can be used as a simple benchmark example to test new control ideas before applying to more complicated models.

scholarly journals Universal Control of Permanent Magnet Synchronous Motors with Uncertain Dynamics

Actuators ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 49
Author(s):  
Rishil Kirankumar Lakhe ◽  
Hicham Chaoui ◽  
Mohamad Alzayed ◽  
Shichao Liu
Keyword(s):  
Vector Control ◽  
Permanent Magnet ◽  
Control Method ◽  
Uncertain System ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Uncertain Dynamics ◽  
Universal Control ◽  
Mathematical Expressions ◽  
Field Oriented Vector Control

This paper focuses on the universal control design of permanent magnet synchronous motors (PMSMs) with uncertain system dynamics. In vector control, classical proportional-integral (PI) controllers are used to control d-q axis currents and speed of the PMSM. This paper uses two control methods: conventional field-oriented vector control and simplified control. First, all the control gains are determined for numerous PMSMs with various power ratings using an empirical study and generalized mathematical expressions are derived for each of the gains. Then, these expressions are used for automatic gain calculation for various PMSMs with a wide power-rating range. In vector control, the control gains are determined using only the motor power ratings. In the simplified control, generalized control gain expressions are obtained using the number of pole pairs and the flux linkage. Compared to the vector control, the simplified control method provides much simpler generalized mathematical expressions. Validation is carried out in MATLAB/Simulink environment using various PMSMs from 0.2 HP to 10 HP, and results show accurate tracking of reference speed and d-q axis reference currents. Thus, the proposed gain scheduling approach is effective and can be used for self-commissioning motor drives.

A TIME-FUEL OPTIMAL CONTROL PROBLEM OF A CRUISE MISSILE BASED ON AN IMPROVED SLIDING MODE VARIABLE STRUCTURE MODEL

2009 ◽  
Vol 51 (2) ◽  
pp. 261-276
Author(s):  
R. LI ◽  
Y. J. SHI
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Method ◽  
Sliding Mode ◽  
Optimal Parameter ◽  
Variable Structure ◽  
Inequality Constraint ◽  
Parameter Selection ◽  
Sliding Mode Variable Structure

AbstractThe inadequacy of the traditional sliding mode variable structure (SMVS) control method for cruise missiles is addressed. An improved SMVS control method is developed, in which the reaching mode segment of the SMVS control is decomposed into an acceleration accessing segment, a speed keeping segment, and a deceleration buffer segment. A time-fuel optimal control problem is formulated as an optimal control problem involving a switched system with unknown switching times and subject to a continuous state inequality constraint. The new design method is developed based on a control parametrization, a time scaling transform and the constraint transcription method. A sequence of approximate optimal parameter selection problems is obtained with fixed switching time points and a canonical state inequality constraint. Each approximate optimal parameter selection problem can be solved effectively by using existing gradient-based optimization techniques. The convergence of these approximate optimal solutions to the true optimal solution is assured. Simulation results show that the proposed method is highly effective. The response speed of the missile under the control law obtained by the proposed method is improved significantly, while the elevator of the missile is constrained to operate within its permitted range.

Optimal Control of a Multifactor Uncertain System

2019 ◽  
Vol 27 (03) ◽  
pp. 397-414
Author(s):  
Yun Sun ◽  
Yuanguo Zhu
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Modern Science ◽  
Uncertain System ◽  
Game Model ◽  
Important Research ◽  
Important Research Topic ◽  
Zero Sum

Along with the development of the modern science and technology, people face a lot of data in different areas of production and life. In dealing with these data which include many indeterminant factors, we can use the multifactor uncertain system to describe a dynamical system with uncertain noises. Optimal control problem is an important research topic which aims at finding the optimal strategy in a dynamical system. In this paper, we consider the optimal control problem for the multifactor uncertain system with two evaluation criterions. Then a two person zero sum differential game model in a multifactor uncertain system is discussed. Finally, as an application, our result is used to solve an uncertain portfolio game model.

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