Optimal control computation for linear time-lag systems with linear terminal constraints

1984 ◽  
Vol 44 (3) ◽  
pp. 509-526 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong ◽  
D. J. Clements
Keyword(s):  
Optimal Control ◽  
Linear Time ◽  
Time Lag ◽  
Terminal Constraints

scholarly journals An optimal control problem involving a class of linear time-lag systems

1986 ◽  
Vol 28 (1) ◽  
pp. 93-113 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong ◽  
Z. S. Wu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Linear Time ◽  
Convergence Property ◽  
Time Lag ◽  
Necessary Condition ◽  
Terminal Constraints ◽  
Linear Control Constraints

A class of convex optimal control problems involving linear hereditary systems with linear control constraints and nonlinear terminal constraints is considered. A result on the existence of an optimal control is proved and a necessary condition for optimality is given. An iterative algorithm is presented for solving the optimal control problem under consideration. The convergence property of the algorithm is also investigated. To test the algorithm, an example is solved.

scholarly journals Data-Driven Optimal Control of Linear Time-Invariant Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 7191-7196
Author(s):  
Dzmitry Kastsiukevich ◽  
Natalia Dmitruk
Keyword(s):  
Optimal Control ◽  
Linear Time ◽  
Data Driven ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals On the existence of a solution for some distributed optimal control hyperbolic system

2000 ◽  
Vol 23 (5) ◽  
pp. 297-311 ◽  
Author(s):  
Dariusz Idczak ◽  
Stanislaw Walczak
Keyword(s):  
Optimal Control ◽  
Hyperbolic System ◽  
Convex Set ◽  
Linear Time ◽  
Time Varying ◽  
Optimal Process ◽  
Existence Of A Solution ◽  
Distributed Optimal Control ◽  
Absolutely Continuous ◽  
State Variable

We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.

Minimum Energy Control of a Unicycle Model Robot

2021 ◽  
Author(s):  
Youngjin Kim ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Minimum Energy ◽  
Kinematic Model ◽  
Elliptic Functions ◽  
Terminal Point ◽  
Jacobi Elliptic Functions ◽  
Differential Drive ◽  
Terminal Constraints ◽  
Differential Drive Robot ◽  
Point To Point

Abstract Point-to-point path planning for a kinematic model of a differential-drive wheeled mobile robot (WMR) with the goal of minimizing input energy is the focus of this work. An optimal control problem is formulated to determine the necessary conditions for optimality and the resulting two point boundary value problem is solved in closed form using Jacobi elliptic functions. The resulting nonlinear programming problem is solved for two variables and the results are compared to the traditional shooting method to illustrate that the Jacobi elliptic functions parameterize the exact profile of the optimal trajectory. A set of terminal constraints which lie on a circle in the first quadrant are used to generate a set of optimal solutions. It is noted that for maneuvers where the angle of the vector connecting the initial and terminal point is greater than a threshold, which is a function of the radius of the terminal constraint circle, the robot initially moves into the third quadrant before terminating in the first quadrant. The minimum energy solution is compared to two other optimal control formulations: (1) an extension of the Dubins vehicle model where the constant linear velocity of the robot is optimized for and (2) a simple turn and move solution, both of whose optimal paths lie entirely in the first quadrant. Experimental results are used to validate the optimal trajectories of the differential-drive robot.

Time-Lag Optimal Control Problems

2021 ◽  
pp. 371-439
Author(s):  
Kok Lay Teo ◽  
Bin Li ◽  
Changjun Yu ◽  
Volker Rehbock
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Time Lag ◽  
Control Problems
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