H∞-Based Pinning Synchronization of General Complex Dynamical Networks with Coupling Delays

This paper investigates the synchronization of complex dynamical networks with coupling delays and external disturbances by applying local feedback injections to a small fraction of nodes in the whole network. Based on H∞ control theory, some delay-independent and -dependent synchronization criteria with a prescribed H∞ disturbances attenuation index are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to reach network synchronization. A simulation example is included to validate the theoretical results

On The Dynamics and Control Strategy of Time-Delayed Vibro-Impact Oscillators

Being able to control nonlinear oscillators, which are ubiquitous, has significant engineering implications in process development and product sustainability design. The fundamental characteristics of a vibro-impact oscillator, a non-autonomous time-delayed feedback oscillator, and a time-delayed vibro-impact oscillator are studied. Their being stochastic, nonstationary, non-smooth, and dynamically complex render the mitigation of their behaviors in response to linear and stationary inputs very difficult if not entirely impossible. A novel nonlinear control concept featuring simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is developed and subsequently incorporated to maintain dynamic stability in these nonlinear oscillators by denying bifurcation and route-to-chaos from coming to pass. Convergence of the controller is formulated to be inherently unconditional with the optimization step size being self-adaptive to system identification and control force input. Optimal initial filter weights are also derived to warrant fast convergence rate and short response time. These novel features impart adaptivity, intelligence, and universal applicability to the wavelet based nonlinear time-frequency control methodology. The validity of the controller design is demonstrated by evaluating its performance against PID and fuzzy logic controllers in controlling the aperiodic, broad bandwidth, discontinuous responses characteristic of the time-delayed, vibro-impact oscillator