scholarly journals Strong local optimality for bang-bang-singular extremals in single input control problems

2017 ◽  
Vol 50 (1) ◽  
pp. 6128-6133 ◽  
Author(s):  
Laura Poggiolini ◽  
Gianna Stefani
Keyword(s):  
Control Problems ◽  
Local Optimality ◽  
Singular Extremals ◽  
Input Control ◽  
Single Input

scholarly journals Singular extremals in L1-optimal control problems: sufficient optimality conditions

2020 ◽  
Vol 26 ◽  
pp. 99
Author(s):  
Francesca C. Chittaro ◽  
Laura Poggiolini
Keyword(s):  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Sufficient Optimality Conditions ◽  
Local Optimality ◽  
Second Variation ◽  
Absolute Value ◽  
Singular Extremals ◽  
Hamiltonian Methods ◽  
The Second Variation

In this paper we are concerned with generalised L1-minimisation problems, i.e. Bolza problems involving the absolute value of the control with a control-affine dynamics. We establish sufficient conditions for the strong local optimality of extremals given by the concatenation of bang, singular and inactive (zero) arcs. The sufficiency of such conditions is proved by means of Hamiltonian methods. As a by-product of the result, we provide an explicit invariant formula for the second variation along the singular arc.

scholarly journals Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Rehan ◽  
Keum-Shik Hong
Keyword(s):  
Electrical Stimulation ◽  
Nonlinear Control ◽  
Control Law ◽  
Input Control ◽  
Control Schemes ◽  
Multiple Input ◽  
Cognitive Diseases ◽  
Single Input ◽  
Error Dynamics ◽  
Nonlinear Control Law

Synchronization of chaotic neurons under external electrical stimulation (EES) is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN) neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and theL2gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides theL2bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.

Modeling of a Dynamic Mirror With Antagonistic Piezoelectric Stack Actuation

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
James A. Mynderse ◽  
George T. C. Chiu
Keyword(s):  
Constitutive Models ◽  
Open Loop ◽  
Step Response ◽  
Experimental Frequency ◽  
Loop Control ◽  
Response Data ◽  
Input Control ◽  
Proposed Model ◽  
Single Input ◽  
Charging Dynamics

A dynamic mirror actuator utilizing antagonistic piezoelectric stack actuators is presented for use in laser printers. Exhibiting hysteresis and other nonlinearities in open-loop operation, the dynamic mirror actuator (DMA) requires a control structure to achieve accurate mirror positioning. A linear DMA model is developed for extending operational bandwidth under closed-loop control, employing explicit piezoelectric stack actuator (PESA) charging dynamics and incorporating two modes for single input control of opposing PESA drives. Compared to constitutive models from literature, the proposed model displays a comparable fit with experimental frequency response data while retaining a lower model order. As further validation, simulated step response data are shown to agree with experimental data.

Fractional High-Order Differential Estimator and Feedback Controller Design for a Single-Input–Single-Output Affine Chaotic System

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Erdinc Sahin ◽  
Mustafa Sinasi Ayas
Keyword(s):  
Chaotic System ◽  
High Order ◽  
Feedback Controller ◽  
Control Problems ◽  
Single Input Single Output ◽  
Single Output ◽  
System Output ◽  
Single Input ◽  
Estimation And Control ◽  
And Control

Abstract Control of chaos generally refers to realize a desired behavior of chaotic system output and its states. In this manner, we design a fractional high-order differential feedback controller (FHODFC) to increase tracking performance of a nonlinear system output and its differentials for a desired trajectory signal. The proposed controller is based on fractional calculus and high-order extracted differentials of error signal. The suggested fractional approach is applied to a single-input–single-output affine Duffing-Holmes dynamical system in matlab/simulink environment. Duffing-Holmes system is analyzed for two different problems: estimation and control problems. The simulation results clearly demonstrate superior dynamic behavior of the FHODFC compared to the classical high-order differential feedback controller (HODFC) version for both estimation and control problems.

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