Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness. Finally, the comparative findings are discussed

Time-Delay Systems

Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades

Formation control of nonholonomic mobile robots: the virtual structure approach

PhDIn recent years, there has been a considerable growth in applications of multi-robot systems as opposed to single-robot systems. This thesis presents our proposed solutions to a formation control problem in which mobile robots are required to create a desired formation shape and track a desired trajectory as a whole. In the first instance, we study the formation control problem for unicycle mobile robots. We propose two control algorithms based on a cascaded approach: one based on a kinematic model of a robot and the other based on a dynamic model. We also propose a saturated controller in which actuator limitations are explicitly accounted for. To demonstrate how the control algorithms work, we present an extensive simulation and experimental study. Thereafter we move on to formation control algorithms in which the coordination error is explicitly defined. Thus, we are able to give conditions for robots keeping their desired formation shape without necessarily tracking the desired trajectory. We also introduce a controller in which both trajectory tracking and formation shape maintenance are achieved as well as a saturated algorithm. We validate the applicability of the introduced controllers in simulations and experiments. Lastly, we study the formation control problem for car-like robots. In this case we develop a controller using the backstepping technique. We give conditions for robots keeping their desired formation shape while failing to track their desired trajectories and present simulation results to demonstrate the applicability of the proposed controlle

Optimal Control and Synchronization of Dynamic Ensemble Systems

Ensemble control involves the manipulation of an uncountably infinite collection of structurally identical or similar dynamical systems, which are indexed by a parameter set, by applying a common control without using feedback. This subject is motivated by compelling problems in quantum control, sensorless robotic manipulation, and neural engineering, which involve ensembles of linear, bilinear, or nonlinear oscillating systems, for which analytical control laws are infeasible or absent. The focus of this dissertation is on novel analytical paradigms and constructive control design methods for practical ensemble control problems. The first result is a computational method %based on the singular value decomposition (SVD) for the synthesis of minimum-norm ensemble controls for time-varying linear systems. This method is extended to iterative techniques to accommodate bounds on the control amplitude, and to synthesize ensemble controls for bilinear systems. Example ensemble systems include harmonic oscillators, quantum transport, and quantum spin transfers on the Bloch system. To move towards the control of complex ensembles of nonlinear oscillators, which occur in neuroscience, circadian biology, electrochemistry, and many other fields, ideas from synchronization engineering are incorporated. The focus is placed on the phenomenon of entrainment, which refers to the dynamic synchronization of an oscillating system to a periodic input. Phase coordinate transformation, formal averaging, and the calculus of variations are used to derive minimum energy and minimum mean time controls that entrain ensembles of non-interacting oscillators to a harmonic or subharmonic target frequency. In addition, a novel technique for taking advantage of nonlinearity and heterogeneity to establish desired dynamical structures in collections of inhomogeneous rhythmic systems is derived