Suboptimality of a Decentralized Feedback Control Law

1999 ◽  
Vol 121 (2) ◽  
pp. 305-308
Author(s):  
El Kebi´r Boukas ◽  
A. Swierniak ◽  
H. Yang
Keyword(s):  
Feedback Control ◽  
Linear System ◽  
Upper Bound ◽  
Optimization Problem ◽  
Control Law ◽  
Relative Cost ◽  
Numerical Example ◽  
Uncertain Linear System ◽  
The Absolute ◽  
The Cost

In this note, a new estimating method for the upper bound of the cost of the uncertain linear system used by Trinh and Aldeen (1993) is proposed. We have also estimated the absolute cost loss and relative cost loss of this kind of optimization problem. To show the usefulness of our results a numerical example has been developed.

Risk-Aware Control

2014 ◽  
Vol 26 (12) ◽  
pp. 2669-2691 ◽  
Author(s):  
Terence D. Sanger
Keyword(s):  
Feedback Control ◽  
Robot Control ◽  
Human Movement ◽  
Spiking Neurons ◽  
Cost Functions ◽  
Control Law ◽  
Time Varying ◽  
Unknown Parameters ◽  
Current State ◽  
The Cost

Human movement differs from robot control because of its flexibility in unknown environments, robustness to perturbation, and tolerance of unknown parameters and unpredictable variability. We propose a new theory, risk-aware control, in which movement is governed by estimates of risk based on uncertainty about the current state and knowledge of the cost of errors. We demonstrate the existence of a feedback control law that implements risk-aware control and show that this control law can be directly implemented by populations of spiking neurons. Simulated examples of risk-aware control for time-varying cost functions as well as learning of unknown dynamics in a stochastic risky environment are provided.

Dynamic logarithmic state and control quantization for continuous-time linear systems

Robotica ◽  
2022 ◽  
pp. 1-16
Author(s):  
Jiashuo Wang ◽  
Shuo Pan ◽  
Zhiyu Xi
Keyword(s):  
Feedback Control ◽  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Control Law ◽  
Quantized Feedback ◽  
Single Input ◽  
Simulation Results ◽  
And Control ◽  
Time Linear

Abstract This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

scholarly journals Tight Bounds for Delay-Sensitive Aggregation

2010 ◽  
Vol Vol. 12 no. 1 (Distributed Computing and...) ◽  
Author(s):  
Yvonne Anne Pignolet ◽  
Stefan Schmid ◽  
Roger Wattenhofer
Keyword(s):  
Distributed Computing ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Optimization Problem ◽  
Tree Topology ◽  
Trade Off ◽  
Transmission Cost ◽  
Delay Sensitive ◽  
International Audience ◽  
The Cost

Distributed Computing and Networking International audience This article studies the fundamental trade-off between delay and communication cost in networks. We consider an online optimization problem where nodes are organized in a tree topology. The nodes seek to minimize the time until the root is informed about the changes of their states and to use as few transmissions as possible. We derive an upper bound on the competitive ratio of O(min (h, c)) where h is the tree's height, and c is the transmission cost per edge. Moreover, we prove that this upper bound is tight in the sense that any oblivious algorithm has a ratio of at least Omega(min (h, c)). For chain networks, we prove a tight competitive ratio of Theta(min (root h, c)). Furthermore, we introduce a model for value-sensitive aggregation, where the cost depends on the number of transmissions and the error at the root.

scholarly journals A computational method for a class of jump linear quadratic systems

1995 ◽  
Vol 36 (4) ◽  
pp. 414-423
Author(s):  
K. H. Wong ◽  
N. Lock ◽  
K. Kaji
Keyword(s):  
Nonlinear Programming ◽  
Feedback Control ◽  
Stochastic Control ◽  
Optimization Problem ◽  
Original Problem ◽  
Computational Method ◽  
Control Law ◽  
Linear Quadratic ◽  
Programming Technique ◽  
Parameter Values

AbstractA class of linear systems subject to sudden jumps in parameter values is considered. To solve this class of stochastic control problem, we try to seek the best feedback control law depending only on the measurable output. Based on this idea, we convert the original problem into an approximate constrained deterministic optimization problem, which can be easily solved by any existing nonlinear programming technique. An example is solved to illustrate the efficiency of the method.

scholarly journals Robust Parametric Control of Spacecraft Rendezvous

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dake Gu ◽  
Yindong Liu
Keyword(s):  
Cost Function ◽  
Relative Motion ◽  
Model Uncertainty ◽  
Optimization Problem ◽  
Control Law ◽  
Eigenstructure Assignment ◽  
Parametric Control ◽  
Autonomous Rendezvous ◽  
Simulation Results ◽  
The Cost

This paper proposes a method to design the robust parametric control for autonomous rendezvous of spacecrafts with the inertial information with uncertainty. We consider model uncertainty of traditional C-W equation to formulate the dynamic model of the relative motion. Based on eigenstructure assignment and model reference theory, a concise control law for spacecraft rendezvous is proposed which could be fixed through solving an optimization problem. The cost function considers the stabilization of the system and other performances. Simulation results illustrate the robustness and effectiveness of the proposed control.

scholarly journals Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-22
Author(s):  
Jing Tang ◽  
Xueyan Tang ◽  
Andrew Lim ◽  
Kai Han ◽  
Chongshou Li ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Greedy Algorithm ◽  
Branch And Bound ◽  
Upper Bound ◽  
Optimization Problem ◽  
Approximation Factor ◽  
Real World Application ◽  
Efficiency Of Algorithms ◽  
Knapsack Constraint ◽  
Submodular Maximization

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of 0.405, which significantly improves the known factors of 0.357 given by Wolsey and (1-1/e)/2\approx 0.316 given by Khuller et al. More importantly, our analysis closes a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of (1-1/\sqrte )\approx 0.393 in the literature to clarify a long-standing misconception on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than 0.405 between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Dynamic multi-objective matrix control for a class of switched systems

2021 ◽  
pp. 014233122199338
Author(s):  
Ali Thamallah ◽  
Anis Sakly ◽  
Faouzi M’Sahli
Keyword(s):  
Switched Systems ◽  
Optimization Problem ◽  
Control Method ◽  
Optimization Procedure ◽  
Control Law ◽  
Dynamic Matrix Control ◽  
General Reference ◽  
Multi Objective ◽  
Dynamic Matrix ◽  
Matrix Control

This article focuses on the tracking and stabilizing issues of a class of discrete switched systems. These systems are characterized by unknown switching sequences, a non-minimum phase, and time-varying or dead modes. In particular, for those governed by an indeterminate switching signal, it is very complicated to synthesize a control law able to systematically approach general reference-tracking difficulties. Taking into account the difficulty to express the dynamic of this class of systems, the present paper presents a new Dynamic matrix control method based on the multi-objective optimization and the truncated impulse response model. The formulation of the optimization problem aims to approach the general step-tracking issues under persistent and indeterminate mode changes and to overcome the stability problem along with retaining as many desirable features of the standard dynamic matrix control (DMC) method as possible. In addition, the formulated optimization problem integrates estimator variables able to manipulate the optimization procedure in favor of the active mode with an appropriate adjustment. It also provides a progressive and smooth multi-objective control law even in the presence of problems whether in subsystems or switching sequences. Finally, simulation examples and comparison tests are conducted to illustrate the potentiality and effectiveness of the developed method.

Fault accommodation in bilinear systems – a logic-dynamic approach

2014 ◽  
Vol 31 (2) ◽  
pp. 129-143
Author(s):  
Alexey Zhirabok ◽  
Alexey Shumsky ◽  
Yevgeny Bobko
Keyword(s):  
Linear System ◽  
Dynamic Systems ◽  
Design Methodology ◽  
Bilinear System ◽  
Control Law ◽  
Dynamic Approach ◽  
Linear Solution ◽  
Content Type ◽  
Fault Accommodation ◽  
Practical Implications

Purpose – The purpose of this study is to investigate the problem of fault accommodation in bilinear dynamic systems. Design/methodology/approach – Solution to this problem is related to constructing the control law which provides full decoupling with respect to the fault effects. The so-called logic-dynamic approach will be used to solve this problem. The main steps of this approach are: replacing the initial bilinear system by certain linear one, solving the problem under consideration for this linear system by well-known linear methods with some restrictions, taking into account the bilinear term to correct the obtained linear solution. Findings – Existing conditions of the fault accommodation problem in a form of rank equalities and inequalities are formulated. Calculating relations for the control law and the auxiliary systems are given. Practical implications – The suggested method allows determining such a control law that preserves the main performances of the system in the faulty case, while the minor performances may degrade. Originality/value – The main advantage of the logic-dynamic approach is a possibility to solve the problem of fault accommodation for nonlinear systems by linear methods without decreasing the main properties of the obtained solution.

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