Optimal Control of Linear Distributed Parameter Systems With Constrained Inputs

1969 ◽  
Vol 91 (2) ◽  
pp. 161-167 ◽  
Author(s):  
W. A. Weigand ◽  
A. F. D’Souza
Keyword(s):  
Optimal Control ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Inequality Constraints ◽  
Open Loop ◽  
Fredholm Integral Equations ◽  
Loop Control ◽  
Linear Partial Differential Equations ◽  
Control Functions ◽  
Unconstrained Problem

The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special case. Energy type inequality constraints are imposed on the control inputs. The problem is formulated as a minimization problem in Hilbert space. The necessary and sufficient conditions for a minimum are obtained and it is proved that these conditions yield the global minimum. It is shown how the solution to the constrained problem can be obtained from the solution of the unconstrained problem. The optimal control functions satisfy Fredholm integral equations with symmetric kernels. The paper presents an example where the solution is obtained by eigenfunction expansion.

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

SYNCHRONIZATION CRITERIA FOR TWO BOOLEAN NETWORKS BASED ON LOGICAL CONTROL

2013 ◽  
Vol 23 (11) ◽  
pp. 1350178 ◽  
Author(s):  
HONGWEI CHEN ◽  
YANG LIU ◽  
JIANQUAN LU
Keyword(s):  
Sufficient Conditions ◽  
Open Loop ◽  
Boolean Networks ◽  
Space Representation ◽  
Complete Synchronization ◽  
Loop Control ◽  
State Space Representation ◽  
Logic Control ◽  
Logical Control ◽  
Necessary And Sufficient

This paper investigates the complete synchronization of two Boolean networks via logic control. Both feedback control and open-loop control are proposed to make the slave network completely synchronized with the master Boolean network. Using the algebraic state-space representation of Boolean networks, we derive several necessary and sufficient conditions for complete synchronization between two Boolean networks. Two examples are given to illustrate the obtained results.

A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

2020 ◽  
pp. 014233122097743
Author(s):  
Mohamed Sadok Attia ◽  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Open Loop ◽  
System Stability ◽  
Gronwall Lemma ◽  
Interconnected System ◽  
Control Approach ◽  
State Dependent ◽  
And Control

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.

scholarly journals On the optimal control of affine nonlinear systems

2005 ◽  
Vol 2005 (4) ◽  
pp. 465-475 ◽  
Author(s):  
M. Popescu ◽  
A. Dumitrache
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Lie Algebra ◽  
Closed Form Solution ◽  
Bilinear System ◽  
Open Loop ◽  
Form Solution ◽  
Loop Control ◽  
Nilpotent Operators ◽  
Affine Nonlinear Systems

The minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control corresponding to the first-, second-, and third-order nilpotent operators is determined. In this paper, we have considered the minimum fuel problem for the multi-input nilpotent control and for a scalar input bilinear system for such systems. For the multi-input system, usually an analytic closed-form solution for the optimal controlui∗(t)is not possible and it is necessary to use numerical integration for the set ofmnonlinear coupled second-order differential equations. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices. It should be noted that we have obtained an open-loop control depending on the initial value of the statex0.

Optimal Control of Flywheel Hybrid Transmissions

1978 ◽  
Vol 100 (1) ◽  
pp. 24-33 ◽  
Author(s):  
L. M. Sweet ◽  
D. A. Anhalt
Keyword(s):  
Optimal Control ◽  
Energy Recovery ◽  
Power Flow ◽  
Open Loop ◽  
Flow Path ◽  
Design Parameters ◽  
Storage Element ◽  
Loop Control ◽  
Variable Transmission ◽  
Path System

Selection of variable transmission ratio in a vehicle with a flywheel energy storage element to maximize the kinetic energy transfer for specified vehicle accelerations is formulated as an optimal control problem. Models for single and parallel power-flow path configurations are presented as generic hybrid propulsion system types. For both systems variation of the ratio of the continuously variable transmission results in inherently nonlinear control, with velocity trajectories found by the solution of two-point boundary value problems. For the single power-flow path system a closed loop controller is synthesized which tracks acceleration command. For the parallel path system, which is representative of conventional power split transmissions, the open loop control yields useful information, indicating tradeoffs between system energy recovery efficiency and component design parameters. Maximum energy recovery during regenerative braking is achieved by minimizing power losses to vehicle drag and transmission elements. Planetary gear geometry is shown to have the strongest influence on efficiency, maximum transmission component loading, and CVT ratio range.

Randomized Algorithms for Open-Loop Control of Clutch-to-Clutch Transmissions

1999 ◽  
Vol 121 (3) ◽  
pp. 508-517 ◽  
Author(s):  
Albert Yoon ◽  
Pramod Khargonekar ◽  
Kumar Hebbale
Keyword(s):  
Optimal Control ◽  
Randomized Algorithms ◽  
Automatic Transmission ◽  
Computational Cost ◽  
Control Design ◽  
Open Loop ◽  
Transmission Model ◽  
Open Loop Control ◽  
Loop Control ◽  
Randomized Search

In this paper, randomized algorithms are used to design an open-loop control for a clutch-to-clutch shift automatic transmission and to study the robustness of that control. The open-loop control design problem can be posed as an optimal control problem but because of the computational cost associated with each simulation and the complexity of the transmission model, classical results from optimal control theory are not a practically feasible approach for this problem. We apply randomized search algorithms for optimization to these problems and present some promising results.

DIRECTING ORBITS OF CHAOTIC DYNAMICAL SYSTEMS

1995 ◽  
Vol 05 (02) ◽  
pp. 573-583 ◽  
Author(s):  
M. PASKOTA ◽  
A.I. MEES ◽  
K.L. TEO
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Open Loop ◽  
Open Loop Control ◽  
Target Region ◽  
Loop Control ◽  
Chaotic Dynamical Systems ◽  
Bounded Perturbations

In this paper, we consider the directing of orbits of discrete chaotic dynamical systems towards desired targets. Our aim is to significantly reduce the time needed to reach a target region by applying only small, bounded perturbations. We derive an open-loop control from methods of optimal control theory, and we discuss the effects of random dynamical noise on the open-loop control.

scholarly journals Parametric Approach to Trajectory Tracking Control of Robot Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Shijie Zhang ◽  
Yi Ning
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Optimal Trajectory ◽  
Open Loop ◽  
Parametric Approach ◽  
Trajectory Tracking Control ◽  
Loop Control

The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.

Experiments on Point-to-Point Position Control of a Flexible Beam Using Laplace Transform Technique: Part I—Open-Loop

1991 ◽  
Vol 113 (3) ◽  
pp. 432-437 ◽  
Author(s):  
S. P. Bhat ◽  
M. Tanaka ◽  
D. K. Miu
Keyword(s):  
Position Control ◽  
Flexible Structures ◽  
Open Loop ◽  
Engineering Problem ◽  
Flexible Beam ◽  
Loop Control ◽  
Point Position ◽  
Control Functions ◽  
Laplace Transform Technique ◽  
Point To Point

When lightly damped flexible structures are used in high bandwidth applications, the elimination of residual vibration during point-to-point positioning is an important engineering problem. Using the Laplace domain synthesis technique introduced in earlier publications, experiments on the precise point-to-point position control of a flexible beam have been performed. In Part I of this two-part paper, results related to open-loop control are presented. A variety of candidate control functions are evaluated and performance issues related to robustness and sensitivity are investigated.

Optimal Control Indicators for the Assessment of the Influence of Approximate Optimal Feedback in the Baseline RBC Model

2014 ◽  
Vol 3 (1) ◽  
pp. 1-15
Author(s):  
Iraklis Kollias
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Decision Rule ◽  
Capital Stock ◽  
Open Loop ◽  
Optimal Decision ◽  
Open Loop Control ◽  
Loop Control ◽  
Optimal Decision Rule ◽  
Loop Control System

This paper utilizes the baseline Real Business Cycle (RBC) model in order to construct a time recursive approximate optimal decision rule as a linear function of the model's state variables and an exogenous surprise shock that hits the economy. The constructed rule is subsequently used in order to examine and compare the dynamics of the capital stock and random total factor productivity (TFP). For this purpose, an open-loop control system is analyzed and compared with the closed-loop control system which results from the application of the time recursive approximate optimal decision rule. A set of optimal control indicators is proposed in order to evaluate the effects resulting from the application of this rule on the behavior of the open-loop control system. The results obtained show a significant reduction in the volatility of the capital stock when the constructed approximate optimal decision rule is applied to the open-loop control system.

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