Guess-Free Pseudospectral Solution for Time Optimal Swing-Up of a Rotary Inverted Pendulum

2017 ◽  
Author(s):  
Paul J. Frontera ◽  
Matthew Feemster ◽  
Michael Hurni ◽  
Mark Karpenko
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Minimum Principle ◽  
Problem Formulation ◽  
Fixed Time ◽  
Time Problem ◽  
Time Optimal ◽  
Switching Structure ◽  
Original Time ◽  
Rotary Inverted Pendulum

Control of the inverted pendulum is a canonical problem in nonlinear and optimal control. Over the years, many workers have developed solutions for inverting the pendulum link (swing-up phase) and for maintaining the pendulum link upright (stabilization/disturbance rejection). In this paper, the time-optimal swing-up of a rotary inverted pendulum is studied. Previous solutions to this problem have required that the original time-optimal problem formulation be transformed to a more computationally tractable form. For example, one transformation is to a fixed-time problem with bounds on the control. Other approaches involve guessing the switching structure in order to construct a candidate solution. Advances in computational optimal control theory, particularly pseudospectral optimal control, allow the original time-optimal problem to be solved directly, and without the need for a guess. One such solution is presented in this paper. It is shown that the result adheres to the conditions of Pontryagin’s minimum principle. An experimental implementation of the solution illustrates its feasibility in practice.

scholarly journals Boundary conditions optimal control

1989 ◽  
Vol 30 (3) ◽  
pp. 343-349 ◽  
Author(s):  
B. D. Craven
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Fixed Time ◽  
Rigorous Approach ◽  
Time Problem ◽  
Time Optimal

AbstractA simple rigorous approach is given to finding boundary conditions for the adjoint differential equation in an optimal control problem. The boundary conditions for a time-optimal problem are calculated from the simpler conditions for a fixed-time problem.

Solution of Finite-Time LQP Optimal Control Problems for Discrete-Time Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 151-157 ◽  
Author(s):  
M. J. Grimble ◽  
J. Fotakis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Time Optimal Control ◽  
Infinite Time ◽  
Time Problem ◽  
Z Domain ◽  
Time Optimal ◽  
Time Optimal Control Problem

The deterministic discrete-time optimal control problem for a finite optimization interval is considered. A solution is obtained in the z-domain by embedding the problem within a equivalent infinite time problem. The optimal controller is time-invariant and may be easily implemented. The controller is related to the solution of the usual infinite time optimal control problem due to Wiener. This new controller should be of value in self-tuning control laws where a finite interval controller is particularly important.

Time-optimal control of multiple unmanned aerial vehicles with human control input

2019 ◽  
Vol 12 (1) ◽  
pp. 138-152 ◽  
Author(s):  
Tao Han ◽  
Bo Xiao ◽  
Xi-Sheng Zhan ◽  
Jie Wu ◽  
Hongling Gao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Minimum Principle ◽  
Time Optimal Control ◽  
Control Problems ◽  
Control Input ◽  
Content Type ◽  
Human Control ◽  
Time Optimal ◽  
The Cost

Purpose The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle (UAV) systems to achieve predefined flying shape. Design/methodology/approach Two time-optimal protocols are proposed for the situations with or without human control input, respectively. Then, Pontryagin’s minimum principle approach is applied to deal with the time-optimal control problems for UAV systems, where the cost function, the initial and terminal conditions are given in advance. Moreover, necessary conditions are derived to ensure that the given performance index is optimal. Findings The effectiveness of the obtained time-optimal control protocols is verified by two contrastive numerical simulation examples. Consequently, the proposed protocols can successfully achieve the prescribed flying shape. Originality/value This paper proposes a solution to solve the time-optimal control problems for multiple UAV systems to achieve predefined flying shape.

scholarly journals Minimum time optimal control simulation of a GP2 race car

2017 ◽  
Vol 232 (9) ◽  
pp. 1180-1195 ◽  
Author(s):  
Nicola Dal Bianco ◽  
Roberto Lot ◽  
Marco Gadola
Keyword(s):  
Optimal Control ◽  
Degrees Of Freedom ◽  
Load Transfer ◽  
Control Method ◽  
Multibody Model ◽  
Race Car ◽  
Optimal Control Method ◽  
Time Problem ◽  
Time Optimal ◽  
The Impact

In this work, optimal control theory is applied to minimum lap time simulation of a GP2 car, using a multibody car model with enhanced load transfer dynamics. The mathematical multibody model is formulated with use of the symbolic algebra software MBSymba and it comprises 14 degrees of freedom, including full chassis motion, suspension travels and wheel spins. The kinematics of the suspension is exhaustively analysed and the impact of tyre longitudinal and lateral forces in determining vehicle trim is demonstrated. An indirect optimal control method is then used to solve the minimum lap time problem. Simulation outcomes are compared with experimental data acquired during a qualifying lap at Montmeló circuit (Barcelona) in the 2012 GP2 season. Results demonstrate the reliability of the model, suggesting it can be used to optimise car settings (such as gearing and aerodynamic setup) before executing track tests.

Optimal Control Discipline Research of Hydraulic System of Sugarcane Harvester

2011 ◽  
Vol 199-200 ◽  
pp. 1281-1286
Author(s):  
Yi Zhi Hu ◽  
Ying Chun Hu ◽  
Jun Yan Hou ◽  
Hui Zhu
Keyword(s):  
Optimal Control ◽  
Minimum Principle ◽  
Control Valve ◽  
Flow Control Valve ◽  
State Equations ◽  
Controlling System ◽  
Spring Force ◽  
Time Optimal ◽  
Sugarcane Harvester ◽  
Theory Base

The actiyator of chassis mechanism of sugarcane harvester was a cubage flow regulation circuit consisted of a timing variable pump and a compensated flow control valve. The optimal controlling system described its movement from processing time using differential and state equations. The shortest-time optimal controlling trajectory of spring force of the variable pump was a group of concentric circles based on minimum principle, which controlling signal switched on origin trajectory. Under the condition of optimal control, the stator was pushed by spring to a new balance spot which left off origin 15.5 millimeter in the shortest time of 1.12 seconds, which provided theory base to further controlling system design. Its stability and validity has been proved well in physical product research.

Optimal Transient Control Trajectories in Diesel–Electric Systems—Part I: Modeling, Problem Formulation, and Engine Properties

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Martin Sivertsson ◽  
Lars Eriksson
Keyword(s):  
Optimal Control ◽  
Output Power ◽  
Control Strategies ◽  
Problem Formulation ◽  
Free Variable ◽  
Mean Value ◽  
Engine Model ◽  
Transient Control ◽  
Time Optimal ◽  
Power And Energy

A nonlinear four state-three input mean value engine model (MVEM), incorporating the important turbocharger dynamics, is used to study optimal control of a diesel–electric powertrain during transients. The optimization is conducted for the two criteria, minimum time and fuel, where both engine speed and engine power are considered free variables in the optimization. First, steps from idle to a target power are studied and for steps to higher powers the controls for both criteria follow a similar structure, dictated by the maximum torque line and the smoke-limiter. The end operating point, and how it is approached is, however, different. Then, the power transients are extended to driving missions, defined as, that a certain power has to be met as well as a certain energy has to be produced. This is done both with fixed output profiles and with the output power being a free variable. The time optimal control follows the fixed output profile even when the output power is free. These solutions are found to be almost fuel optimal despite being substantially faster than the minimum fuel solution with variable output power. The discussed control strategies are also seen to hold for sequences of power and energy steps.

Determining Model Accuracy Requirements for Automotive Engine Coldstart Hydrocarbon Emissions Control

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Nasser L. Azad ◽  
Pannag R. Sanketi ◽  
J. Karl Hedrick
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Real Time ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Control Performance ◽  
Automotive Engine ◽  
Engine Model ◽  
Time Optimal ◽  
Hc Emissions

In this work, a systematic method is introduced to determine the required accuracy of an automotive engine model used for real-time optimal control of coldstart hydrocarbon (HC) emissions. The engine model structure and development are briefly explained and the model predictions versus experimental results are presented. The control design problem is represented with a dynamic optimization formulation on the basis of the engine model and solved using the Pontryagin’s minimum principle (PMP). To relate the level of plant/model mismatch and the control performance degradation in practice, a sensitivity analysis using a computationally efficient method is employed. In this way, the sensitivities or the effects of small parameter variations on the optimal solution, which is the minimum of cumulative tailpipe HC emissions over the coldstart period, are calculated. There is a good agreement between the sensitivity analysis results and the experimental data. The sensitivities indicate the directions of the subsequent parameter estimation and model improvement tasks to enhance the control-relevant accuracy, and thus, the control performance. Furthermore, they provide some insights to simplify the engine model, which is critical for real-time implementation of the coldstart optimal control system.

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