Hybrid Feedback Control Methods for Robust and Global Power Conversion

In this paper, the applicability and importance of hybrid system tools for the design of control algorithms for energy conversion in power systems is illustrated in two hybrid control designs, one pertaining to DC/DC conversion and the other to DC/AC inversion. In particular, the mathematical models considered consist of constrained switched differential equations/inclusions that include all possible modes of operation of the systems. Furthermore, the obtained models can be analyzed and their algorithms designed using hybrid system tools so as to attain key desired properties, such as stability, forward invariance, global convergence, and robustness. We argue that hybrid system tools provide a systematic approach for analysis and controller design of power systems. In particular, hybrid system tools usually leads to power quantities that have better performance and robustness to state perturbations. Furthermore, they provide guidelines on how to tune the controller parameters based on design requirements. These factors motivate the implementation of the proposed hybrid controllers in modern power conversion systems that use renewable energy sources. Simulations illustrating the main results and benchmark tests are included

Pointwise minimum norm control laws for hybrid systems

Minimum-norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or jumps. The proposed control laws are defined as the pointwise minimum norm selection from the set of inputs guaranteeing a decrease of a control Lyapunov function. The cases of individual and common inputs during flows and jumps, as well as when inputs enter through one of the system dynamics, are considered. Examples illustrate the results. ©2013 IEEE

Robust hybrid global asymptotic stabilization of rigid body dynamics using dual quaternions

A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme

On Robust Stability of Limit Cycles for Hybrid Systems with Multiple Jumps

In this paper, we address stability and robustness properties of hybrid limit cycles for a class of hybrid systems with multiple jumps in one period. The main results entail equivalent characterizations of stability of hybrid limit cycles for hybrid systems. The hybrid limit cycles may have multiple jumps in one period and the jumps are allowed to occur on sets. Conditions guaranteeing robustness of hybrid limit cycles are also presented

Observer-based Synchronization of Multi-agent Systems Using Intermittent Output Measurements

The problem of synchronizing multiple continuous-time linear time-invariant systems connected over a complex network, with intermittently available measurements of their outputs, is considered. To solve this problem, we propose a distributed observer-based feedback controller that utilizes a local hybrid observer to estimate neighboring states only from output measurements at such potentially nonperiodic isolated event times. Due to the inherent continuous and discrete dynamics emerging from coupling the impulsive measurement updates and the interconnected networked systems, we use hybrid systems to model and analyze the resulting closed-loop system. The problem of synchronization and state estimation is then recast as a set stabilization problem, and, utilizing a Lyapunov-based analysis for hybrid systems, we provide sufficient conditions for global exponential stability of the synchronization and zero estimation error set. A numerical example is provided to illustrate the results

A framework for modeling and analysis of dynamical properties of spiking neurons

A hybrid systems framework for modeling and analysis of robust stability of spiking neurons is proposed. The framework is developed for a population of n interconnected neurons. Several well-known neuron models are studied within the framework, including both excitatory and inhibitory simplified Hodgkin-Huxley, Hopf, and SNIPER models. For each model, we characterize the sets that the solutions to each system converge to. Using Lyapunov stability tools for hybrid systems, the stability properties for each case are established. An external stimuli is introduced to the simplified Hodgkin-Huxley model to achieve a global asymptotic stability property. Due to the regularity properties of the data of the hybrid models considered, the asserted stability properties are robust to small perturbations. Simulations provide insight on the results and the capabilities of the proposed framework. © 2014 American Automatic Control Council