Dynamic Systems and Control with Applications

Ahmed, Nasir

doi:10.1142/6262

Cited by 95 publications

(74 citation statements)

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“…where ψ(t) ∈ R 4 , t ∈ I, is a vector of Lagrange multipliers whose elements are the costates of the system [2]. We now derive the necessary conditions of optimality feedback model (5).…”

Section: Linear Time-varying State-feedback Lawmentioning

confidence: 99%

“…Here, we propose a promising alternative solution to the Brockett's problem for a nonholonomic car-like vehicle (Ackermann steering vehicle) with a linear time-varying state-feedback law. The proposed optimal feedback law is determined by modifying the classical Pontryagin's minimum principle [2]. By doing so, both point stabilization and trajectory tracking problems of a nonholonomic vehicle are addressed as a unified manner.…”

Section: Introductionmentioning

confidence: 99%

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Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

Miah¹,

Farkas²,

Gueaieb³

et al. 2017

International Journal of Robotics and Automation

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In this paper, we propose an optimal state feedback control law for addressing point stabilization and tracking problems of nonholonomic vehicles with Ackermann steering in a unified manner. Unlike other feedback controllers that perform dynamic linearization of vehicle models, the proposed optimal feedback controller provides the state feedback control to the original nonlinear vehicle model for achieving excellent state-tracking performance.In addition, nonlinear control techniques suggested in the literature to date require that the desired trajectory of the robot is generated using persistently excited inputs. This may be too restrictive and non-realistic hypothesis to mimic a real scenario. Here, we address this issue by developing a smooth state-feedback control law that is formulated by modifying the classical Pontryagin's minimum principle. The proposed control law can be applied for solving control problems of a general class of nonlinear affine systems. The proposed control scheme offers a modular solution to other control techniques for a large number of mobile robot applications. The theoretical results are validated through computer simulations.

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Section: Linear Time-varying State-feedback Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

Miah¹,

Farkas²,

Gueaieb³

et al. 2017

International Journal of Robotics and Automation

View full text Add to dashboard Cite

show abstract

“…The feedback model (33) with the quadratic cost functional (28) is similar to the optimal linear quadratic regulator problem, which is stable in the Lyapunov sense [2]. In other words, the optimality leads to stability.…”

Section: T)p(t) − Q(t) − P(t)f(t)+ P(t)g(t)r −1 (T)g T (T)p(t) P(tmentioning

confidence: 99%

RFID-Based Mobile Robot Trajectory Tracking and Point Stabilization Through On-line Neighboring Optimal Control

Miah

Gueaieb

2014

J Intell Robot Syst

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In this manuscript, we propose an on-line trajectorytracking algorithm for nonholonomic Differential-Drive Mobile Robots (DDMRs) in the presence of possibly large parametric and measurement uncertainties. Most mobile robot tracking techniques that depend on reference RF beacons rely on approximating line-of-sight (LOS) distances between these beacons and the robot. The approximation of LOS is mostly performed using Received Signal Strength (RSS) measurements of signals propagating between the robot and RF beacons. However, accurate mapping between RSS measurements and LOS distance remains a significant challenge and is almost impossible to achieve in an indoor reverberant environment. This paper contributes to the development of a neighboring optimal control strategy where the two major control tasks, trajectory tracking and point stabilization, are solved and treated as a unified manner using RSS measurements emitted from Radio Frequency IDentification (RFID) tags. The proposed control scheme is divided into two cascaded phases. The first phase provides the robot's nominal control inputs (speeds) and its trajectory using full-state feedback. In the second phase, we design the neighboring optimal controller, where RSS measurements are used to better estimate the robot's pose by employing an optimal filter. Simulation and experimental results are presented to demonstrate the performance of the proposed optimal feedback controller for solving the stabilization and trajectory tracking problems using a DDMR. Keywords Mobile robot navigation · RFID systems · optimal control · trajectory tracking · robot stabilization · nonholonomic systems. Frequently Used Symbols K(t)Feedback control gain at time t H K Hamiltonian's gradient with respect to K s Number of RFID tags in the environment ψ Costate variable (Lagrange multiplier)Robot's actual and desired pose at time t q j t ∈ R 3 jth tag position in 3D space t 0 ,t f Initial and final time instantsRobot's control input vector at time t ξ (t) Robot's actuator noise at time t ζ (t)Measurement noise vector at time t (·) o , (·) ε , (·) ad Optimal, perturb, admissible value of (·) L Lebesgue measurable function space ν T dJ(·) Gateaux (directional) derivative of J in direction ν 1 Introduction

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“…Assumption 1 ensures that the dynamic system (1)- (2) admits a unique solution corresponding to each candidate solution pair (τ, ζ) ∈ T × Z [18]. We denote this solution by x(·|τ, ζ).…”

Section: Problem Formulationmentioning

confidence: 99%

A gradient-based parameter identification method for time-delay chaotic systems

Chai

Loxton

2014

Proceedings of the 33rd Chinese Control Conference

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In this paper, the parameter identification problem for a general class of time-delay chaotic systems is considered. The objective of the problem is to determine optimal values for an unknown time-delay and unknown system parameters such that the dynamic model of the system best fits given experimental data. We propose a gradient-based optimization algorithm to solve this problem, where accurate values for the partial derivatives of the error function are obtained by solving a set of auxiliary time-delay systems. Simulation results for two example problems show that the proposed algorithm is robust and efficient.

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Dynamic Systems and Control with Applications

Cited by 95 publications

References 0 publications

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

RFID-Based Mobile Robot Trajectory Tracking and Point Stabilization Through On-line Neighboring Optimal Control

A gradient-based parameter identification method for time-delay chaotic systems

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