Minimum Energy Control of Redundant Systems Using Evolutionary Bi-Level Optimization

2018 ◽  
Author(s):  
Uriel Nusbaum ◽  
Miri Weiss Cohen ◽  
Yoram Halevi
Keyword(s):  
Optimal Control ◽  
Degrees Of Freedom ◽  
Energy Savings ◽  
Level Structure ◽  
Minimum Energy ◽  
Inequality Constraints ◽  
Constrained Optimal Control ◽  
Reduced Order ◽  
Control Comparison ◽  
Level Problem

Redundant manipulators are mechanical systems with more degrees of freedom than required for their task. The paper considers the problem of energy minimization, given a required task, for such systems. The problem is formulated as a constrained optimal control with additional inequality constraints. A dynamic projection enables transforming the problem into an equivalent unconstrained, reduced order one. The solution scheme presented here combines the problems of path planning and tracking control. It includes decomposition of the problem into a bi-level structure. The parametric, higher-level problem is solved using a genetic algorithm and the lower level one is solved using optimal control. Comparison with full optimal control solutions shows the superiority of the combined evolutionary algorithm in terms of computational feasibility and overall energy savings.

A Constraining Hyperplane Technique for State Variable Constrained Optimal Control Problems

1973 ◽  
Vol 95 (4) ◽  
pp. 380-389 ◽  
Author(s):  
K. Martensson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Control Problems ◽  
State Control ◽  
Constrained Optimal Control ◽  
State Variable

A new approach to the numerical solution of optimal control problems with state-variable inequality constraints is presented. It is shown that the concept of constraining hyperplanes may be used to approximate the original problem with a problem where the constraints are of a mixed state-control variable type. The efficiency and the accuracy of the combination of constraining hyperplanes and a second-order differential dynamic programming algorithm are investigated on problems of different complexity, and comparisons are made with the slack-variable and the penalty-function techniques.

On Optimal Control Laws for a Class of Constrained Dynamical Systems (With Application to Control of Bipedal Locomotion)

1977 ◽  
Vol 99 (2) ◽  
pp. 98-102 ◽  
Author(s):  
M. A. Townsend ◽  
T. C. Tsai
Keyword(s):  
Optimal Control ◽  
Degrees Of Freedom ◽  
Inequality Constraints ◽  
Control Law ◽  
Bipedal Locomotion ◽  
Control Laws ◽  
Smooth Control ◽  
Proper Formulation ◽  
Constrained Dynamical Systems ◽  
Dynamical Constraints

The physical and dynamical constraints of a constrained dynamical system are related to system controllability and stability. Proper formulation of these inequality constraints and treatment of the active ones leads to stabilizing controls with relatively smooth control efforts—in all cases, control laws. These approaches were useful in a study of the biomechanics of climbing and descending gaits by mathematical synthesis techniques, necessitated by the increased importance of terrain and lower extremity kinematics and incomplete specification of the tasks. The general criteria entail no uniqueness requirements on system motions and controls, although for the most common (and probably most desirable) condition of the constraints (fewer active constraints than system degrees of freedom) an “optimal” control law can be derived. Two examples are presented, and some general discussion is given relating mainly to the control of biped locomotion.

scholarly journals Efficient Therapy Planning via Model Reduction for Laser-Induced Interstitial Thermotherapy

2018 ◽  
Author(s):  
Kevin Tolle ◽  
Nicole Marheineke
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Reduced Order Models ◽  
Therapy Planning ◽  
Constrained Optimal Control ◽  
Reduced Order ◽  
Computationally Expensive ◽  
Simplified Modeling ◽  
Interstitial Thermotherapy ◽  
Constrained Optimal Control Problem

We investigate the planning of minimally invasive tumor treatments via laser-induced thermotherapy. The goal is to control the laser in order to obtain an optimal treatment, e.g. eradicating the tumor, while leaving as much healthy tissue unharmed as possible. To this end, we define a PDE-constrained optimal control problem. As these problems are usually computationally expensive, we propose a simplified modeling approach using reduced-order models. Numerical results illustrate the viability of our approach.

A Transformation Method With Two Parameters for Constrained Optimal Control Problems

1978 ◽  
Vol 100 (2) ◽  
pp. 124-131 ◽  
Author(s):  
S. Fujii ◽  
H. Fujimoto
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Inequality Constraint ◽  
Transformation Method ◽  
Control Problems ◽  
Basic Algorithm ◽  
Constrained Optimal Control ◽  
Equality And Inequality Constraints ◽  
Two Parameters

A transformation method with two parameters is described which can be applied to nonconvex optimal control problems with constraints, does not present numerical difficulties, and has a rapid convergence rate. The basic algorithm of the method is summarized for optimal control problems with equality and inequality constraints, the function of the parameters in the method is considered, one modified algorithm is proposed, and its theoretical results are proved. Finally, the method is applied successfully to both convex and nonconvex optimal control problems with a state inequality constraint.

Analysis of Constrained Optimal Control with Related Constraints of Input Variables

2014 ◽  
Vol 39 (5) ◽  
pp. 679-689 ◽  
Author(s):  
Xiong-Lin LUO ◽  
Xiao-Long ZHOU ◽  
Shu-Bin WANG
Keyword(s):  
Optimal Control ◽  
Constrained Optimal Control ◽  
Input Variables

scholarly journals Optimal Control of the Positional Electric Drive and Its Implementation

Machines ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 70
Author(s):  
Vladimir Dotsenko ◽  
Roman Prokudin ◽  
Alexander Litvinenko
Keyword(s):  
Optimal Control ◽  
Wind Turbine ◽  
Electric Drive ◽  
Minimum Energy ◽  
Air Gap ◽  
Synchronous Generators ◽  
Capacitor Discharge ◽  
Wind Speeds ◽  
Minimum Energy Consumption ◽  
Low Wind Speeds

The article deals with the optimal control of the positional electric drive of the stator element of a segment-type wind turbine. The calculation options charts current in the assumption of the minimum energy consumption and the implementation of line chart current using the phenomenon of capacitor discharge. The analysis of the implementation is expressed in a jump-like change in current and a triangular graph of the speed change. This article deals with small capacity synchronous wind turbine generators with a segment type stator. These units have the possibility of intentionally changing the air gap between the rotor and stator. This allows: (1) Reduce the starting torque on the rotor shaft, which will allow the rotor to pick up at low wind speeds. (2) Equivalent to change of air gap in this case is change of excitation of synchronous generators. Thus, the purpose of the article is to consider a method of excitation of generators in a segmented design, by controlling the gap with the electric drive, while providing control should be carried out with minimal losses.

scholarly journals Optimal Control for a Hydraulic Recuperation System Using Endoreversible Thermodynamics

2021 ◽  
Vol 11 (11) ◽  
pp. 5001
Author(s):  
Robin Masser ◽  
Karl Heinz Hoffmann
Keyword(s):  
Optimal Control ◽  
Fuel Consumption ◽  
Energy Savings ◽  
Combustion Engine ◽  
Mechanical Energy ◽  
Hydraulic Systems ◽  
Commercial Vehicles ◽  
Hybrid Drive ◽  
Environmental Considerations ◽  
Onboard System

Energy savings in the traffic sector are of considerable importance for economic and environmental considerations. Recuperation of mechanical energy in commercial vehicles can contribute to this goal. One promising technology rests on hydraulic systems, in particular for trucks which use such system also for other purposes such as lifting cargo or operating a crane. In this work the potential for energy savings is analyzed for commercial vehicles with tipper bodies, as these already have a hydraulic onboard system. The recuperation system is modeled based on endoreversible thermodynamics, thus providing a framework in which realistic driving data can be incorporated. We further used dissipative engine setups for modeling both the hydraulic and combustion engine of the hybrid drive train in order to include realistic efficiency maps. As a result, reduction in fuel consumption of up to 26% as compared to a simple baseline recuperation strategy can be achieved with an optimized recuperation control.

Sign in / Sign up

Export Citation Format

Share Document