The Optimal Adaptive Sampled-Data Regulator

1974 ◽  
Vol 96 (3) ◽  
pp. 334-340
Author(s):  
R. A. Schlueter ◽  
A. H. Levis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Open Loop ◽  
Sampled Data ◽  
Threshold Values ◽  
Regulator Problem

The optimal control problem for sampled-data processes in which sampling is not triggered by a timer, but occurs when one or more outputs attain preset threshold values is formulated as an adaptive optimal sampled-data regulator problem. Both open loop and closed loop solutions are determined and a comparison of a system’s performance with adaptive and with periodic sampling is presented.

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

scholarly journals Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system

2021 ◽  
Author(s):  
Xin Zhang ◽  
Xun Li ◽  
Jie Xiong
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Regime Switching ◽  
Closed Loop ◽  
Open Loop ◽  
Switching System ◽  
Linear Quadratic ◽  
Markovian Regime Switching ◽  
Markovian Regime

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markovian regime switching system is derived by the technique of It{\^o}'s formula with jumps. For the stochastic LQ optimal control problem of Markovian regime switching system, we establish the equivalence between the open-loop (closed-loop, resp.) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint (the existence of a regular solution to Riccati equations). Also, we analyze the interrelationship between the strongly regular solvability of Riccati equations and the uniform convexity of the cost functional. Finally, we present an example which is open-loop solvable but not closed-loop solvable.

scholarly journals Prediction error's minimization through a controller based on a Metaheuristic Algorithm

2020 ◽  
Vol 43 (3) ◽  
pp. 5-11
Author(s):  
Viorel Mînzu
Keyword(s):  
Optimal Control ◽  
Theoretical Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Predictive Control ◽  
Closed Loop ◽  
Open Loop ◽  
The Other ◽  
Metaheuristic Algorithm ◽  
Prediction Technique

A Metaheuristic Algorithm (MA) can be a realistic method to solve a given Optimal Control Problem (OCP), but the result is an open-loop solution. If the Metaheuristic Algorithm is integrated within the Model Predictive Control (MPC) structure, a closed-loop solution can be achieved. The controller works using a prediction technique and prediction error's minimization. On the other side, the MA optimizes (minimizes or maximizes) the OCP's objective function. The controller is faced with two optimization tasks. This paper proves through theoretical analysis and simulations that the prediction error's minimization is implicitly accomplished.

scholarly journals Existence and uniqueness of constrained globally optimal feedback controls in a linear-quadratic framework

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Yashan Xu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Closed Loop ◽  
Synthesis Method ◽  
Open Loop ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Loop Control

A constrained closed-loop optimal control problem is considered in a linear-quadratic framework. To solve the problem, a special type open-loop optimal control problem and a standard open-loop optimal control problem are introduced and carefully studied, via which the existence and uniqueness of the globally optimal closed-loop control is established by a synthesis method.

scholarly journals An optimal control problem in closed-loop neuroprostheses

2011 ◽  
Author(s):  
Gautam Kumar ◽  
Vikram Aggarwal ◽  
Nitish V. Thakor ◽  
Marc H. Schieber ◽  
Mayuresh V. Kothare
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop
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