Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality

2016 ◽  
Vol 171 (3) ◽  
pp. 980-997 ◽  
Author(s):  
Geovani Nunes Grapiglia ◽  
Jinyun Yuan ◽  
Ya-xiang Yuan
Keyword(s):  
Second Order ◽  
Control Algorithms ◽  
Complexity Bounds ◽  
Stepsize Control ◽  
Nonlinear Stepsize Control

scholarly journals Formation-Containment Control of Second-Order Multiagent Systems via Intermittent Communication

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Mao-Dong Xia ◽  
Cheng-Lin Liu ◽  
Fei Liu
Keyword(s):  
Multiagent Systems ◽  
Lyapunov Functions ◽  
Second Order ◽  
Control Algorithms ◽  
Distributed Coordination ◽  
Time Intervals ◽  
Containment Control ◽  
Convergence Conditions ◽  
Intermittent Communication ◽  
Theoretical Results

This paper investigates the formation-containment control of second-order multiagent systems with intermittent communication. Distributed coordination control algorithms are proposed under aperiodic intermittent communication, where each agent only communicates with its neighboring agents on some disconnected time intervals. By means of constructing Lyapunov functions, sufficient convergence conditions are obtained for the leaders reaching a prescribed formation asymptotically and the followers converging into the convex hull formed by leaders asymptotically, respectively. Besides, sufficient convergence conditions are also provided for second-order multiagent systems converging to the desired formation-containment under time-varying communication delay and intermittent communication. Finally, the validity of theoretical results is illustrated by numerical simulations.

scholarly journals Complexity bounds for second-order optimality in unconstrained optimization

2012 ◽  
Vol 28 (1) ◽  
pp. 93-108 ◽  
Author(s):  
C. Cartis ◽  
N.I.M. Gould ◽  
Ph.L. Toint
Keyword(s):  
Unconstrained Optimization ◽  
Second Order ◽  
Complexity Bounds

scholarly journals Stabilization of Unstable Second-Order Delay Plants under PID Control: A Nyquist Curve Analysis

Actuators ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 227
Author(s):  
Li Sun ◽  
Dan Ma
Keyword(s):  
Control Systems ◽  
Pid Control ◽  
Time Delays ◽  
Closed Loop ◽  
Second Order ◽  
Control Algorithms ◽  
Special Cases ◽  
Communication Links ◽  
Nyquist Stability ◽  
Real Poles

Time delays arise in various components of control systems, including actuators, sensors, control algorithms, and communication links. If not properly taken into consideration, time delays will degrade the closed-loop performance and may even result in instability. This paper studies the stabilization problem of the second-order delay plants with two unstable real poles. Stabilization conditions under PD and PID control are derived using the Nyquist stability criterion. Algorithms for computing feasible PD and PID parameter regions are proposed. In some special cases, the maximal range of delay for stabilization under PD control is also given.

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