Trade-Offs Between Identification and Control in Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 939-945 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Henryk Flashner
Keyword(s):  
Dynamic Systems ◽  
Trial And Error ◽  
Plant Identification ◽  
Single Degree Of Freedom ◽  
Energy Constraint ◽  
Linear Dynamic Systems ◽  
Trade Offs ◽  
Optimal Inputs ◽  
Augmented State ◽  
And Control

A quantitative study of the trade-offs between the tasks of control law design and plant identification for linear dynamic systems is presented. The problem is formulated in the context of optimal control and optimal identification through the intermediary concept of an optimal input. The duality between identification and control is quantified by optimal inputs, which have a specified amount of energy, and which minimizes the objective function. The optimization problem together with the energy constraint is formulated by using an augmented state vector. This results in a nonlinear two-point boundary value problem and eliminates the need for using a trial and error approach to satisfy the energy constraint. An example of a single-degree-of-freedom oscillator is used to illustrate the basic concepts underlying the proposed approach. Significant trade-offs between identification and control tasks are observed, the trade-offs becoming increasingly important for increasing levels of input energy.

Path Planning and Control of Redundant Manipulators Using Bilevel Optimization

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Uriel Nusbaum ◽  
Miri Weiss Cohen ◽  
Yoram Halevi
Keyword(s):  
Optimal Control ◽  
Dynamic Systems ◽  
Bilevel Optimization ◽  
Complex Tasks ◽  
Planning And Control ◽  
Optimal Inputs ◽  
Saturation Constraints ◽  
Level Problem ◽  
Upper Level ◽  
And Control

Abstract Redundancy is a useful feature in dynamic systems which can be exploited to enhance performance in various tasks. In this work, redundancy will be utilized to minimize the energy consumption of a linear manipulator, while in some cases an additional task of end-effector tracking will also be required and achieved. Optimal control theory has been extensively used for the optimization of dynamic systems; however, complex tasks and redundancy make these problems computationally expensive, numerically difficult to solve, and in many cases, ill-defined. In this paper, evolutionary bilevel optimization for the problem is presented. This is done by setting up an upper level optimization problem for a set of decision variables and a lower level one that actually calculates the optimal inputs and trajectories. The upper level problem is solved by a genetic algorithm (GA), whereas the lower level problem uses classical optimal control. As a result, the proposed algorithm allows the optimization of complex tasks that usually cannot be solved in practice using standard optimal control tools. In addition, despite the use of penalty functions to enforce saturation constraints, the algorithm leads to global energy minimization. Illustrative examples of a redundant x-y robotic manipulator with complex overall tasks will be presented, solved, and discussed.

Estimation and Control Theory: Application to Modeling Human Behavior

1977 ◽  
Vol 19 (4) ◽  
pp. 315-329 ◽  
Author(s):  
William B. Rouse ◽  
Daniel Gopher
Keyword(s):  
Control Theory ◽  
Human Behavior ◽  
Dynamic Systems ◽  
Optimal Estimation ◽  
Linear Dynamic Systems ◽  
Discrete Time Systems ◽  
Theory Application ◽  
Estimation And Control ◽  
And Control ◽  
Time Systems

The methodology of estimation and control theory is considered in terms of response, stability, estimation, and control of linear dynamic systems. Within the context of discrete-time systems, multi-input, multi-output, nth-order linear systems are discussed, and general results for optimal estimation, optimal control, and other topics are presented. The application of these results to modeling human behavior is considered with special emphasis on man-machine system models.

Exact Decoupling of Non-Classically Damped Matrix Second-Order Linear Mechanical Systems

2009 ◽  
Author(s):  
Verica Radisavljevic ◽  
Dobrila Skataric
Keyword(s):  
Dynamic Systems ◽  
Second Order ◽  
Distributed Parameter ◽  
Order Linear ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Subsystem Level ◽  
Damped Systems ◽  
And Control ◽  
Analytical Tools

Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, civil, aerospace engineering, and related fields. This class of systems is also obtained by approximating dynamics of systems described by partial differential equations (distributed parameter systems). There are many papers in the engineering literature on analysis and control of matrix second-order linear damped systems. They provide either approximate (simplified) analytical results or accurate numerical results (usually computationally involved). In this paper, we show how to decouple exactly a matrix second-order linear system into scalar second-order subsystems and study exactly the corresponding system dynamics at the subsystem level using simple analytical tools. Conditions are established under which the presented procedure is applicable. An example is included to demonstrate the efficiency of the proposed technique.

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