Globally Feedback Linearizable Time-Invariant Systems: Optimal Solution for Mayer’s Problem

1998 ◽  
Vol 122 (2) ◽  
pp. 343-347 ◽  
Author(s):  
M. Schlemmer ◽  
S. K. Agrawal
Keyword(s):  
Optimal Solution ◽  
Point Boundary ◽  
Direct Solution ◽  
Alternate Form ◽  
Input System ◽  
Time Problem ◽  
Single Input ◽  
Actuator Constraints ◽  
Time Invariant ◽  
Minimum Time Problem

This paper discusses the optimal solution of Mayer’s problem for globally feedback linearizable time-invariant systems subject to general nonlinear path and actuator constraints. This class of problems includes the minimum time problem, important for engineering applications. Globally feedback linearizable nonlinear systems are diffeomorphic to linear systems that consist of blocks of integrators. Using this alternate form, it is proved that the optimal solution always lies on a constraint arc. As a result of this optimal structure of the solution, efficient numerical procedures can be developed. For a single input system, this result allows to characterize and build the optimal solution. The associated multi-point boundary value problem is then solved using direct solution techniques. [S0022-0434(00)02002-5]

Determining Human Control Intent Using Inverse LQR Solutions

2013 ◽  
Author(s):  
M. Cody Priess ◽  
Jongeun Choi ◽  
Clark Radcliffe
Keyword(s):  
Human Subjects ◽  
Optimal Solution ◽  
Linear Matrix ◽  
Minimization Method ◽  
Human Control ◽  
Balance Task ◽  
Lqr Problem ◽  
Seated Balance ◽  
Gradient Based ◽  
Time Invariant

In this paper, we have developed a method for determining the control intention in human subjects during a prescribed motion task. Our method is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? We describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. We develop a model for an upright seated-balance task which will be suitable for identification of human control intent once experimental data is available.

Optimal Trajectories of Open-Chain Robot Systems: A New Solution Procedure Without Lagrange Multipliers

1998 ◽  
Vol 120 (1) ◽  
pp. 134-136 ◽  
Author(s):  
Sunil K. Agrawal ◽  
Pana Claewplodtook ◽  
Brian C. Fabien
Keyword(s):  
Differential Equations ◽  
Lagrange Multipliers ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Optimal Trajectories ◽  
Point Boundary ◽  
Open Chain ◽  
Robot Systems

For an n d.o.f. robot system, optimal trajectories using Lagrange multipliers are characterized by 4n first-order nonlinear differential equations with 4n boundary conditions at the two end time. Numerical solution of such two-point boundary value problems with shooting techniques is hard since Lagrange multipliers can not be guessed. In this paper, a new procedure is proposed where the dynamic equations are embedded into the cost functional. It is shown that the optimal solution satisfies n fourth-order differential equations. Due to absence of Lagrange multipliers, the two-point boundary-value problem can be solved efficiently and accurately using classical weighted residual methods.

A Trigonometric Solution to a Minimum Time Problem

1984 ◽  
Vol 77 (3) ◽  
pp. 220-221
Author(s):  
Ray C. Shiflett ◽  
Harris S. Shultz
Keyword(s):  
Minimum Time ◽  
Time Problem ◽  
Trigonometric Solution ◽  
Minimum Time Problem

A Simple Algorithm for Pole Assignment in a Multiple Input Linear Time Invariant Dynamic System

1974 ◽  
Vol 96 (1) ◽  
pp. 13-18 ◽  
Author(s):  
M. R. Chidambara ◽  
R. B. Broen ◽  
J. Zaborszky
Keyword(s):  
Dynamic System ◽  
Linear Time ◽  
Simple Algorithm ◽  
Pole Assignment ◽  
Asymptotic State ◽  
Linear Time Invariant ◽  
Input System ◽  
Multiple Input ◽  
System Equations ◽  
Time Invariant

This paper is concerned with the development of a simple algorithm for solving the problem of pole assignment in a multiple input linear time-invariant dynamic system, by means of state variable feedback. Unlike other existing methods which solve the same problem, the proposed algorithm does not require the transformation of the system equations to a special canonical form or the reduction of the multiple input system to an equivalent single input system. Analogously, the dual problem of constructing an asymptotic state estimator for a multiple output system is solved, with the solution enjoying analogous advantages.

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