Hybrid Dynamical Systems

Abstract

Hybrid systems are natural models of complex interactive networks such as manufacturing, communication, power, and transportation systems. Hybrid systems can be viewed as systems that allow interactions between discrete events and continuous dynamics. For example, in the context of power systems, the large disturbance behavior of such systems is characterized by complex interactions between continuous dynamics and discrete events. Components such as generators and loads drive the continuous behavior, while other components such as tap-changing transformers, switched shunts, and protective devices exhibit event-driven behavior. A satisfactory theory for such systems, which draws from several fields including control theory, computer science, and applied mathematics, will have an enormous potential for impact on a variety of application domains. The hybrid nature of the problem may also show up in the design and implementation of controls for such systems. As such, computational and algorithmic approaches to such problems encounter considerable difficulties. In addition to modeling and analysis of such systems, this session will explore novel computational implementations that can accommodate uncertainties in the system at various levels.We have accepted three papers for this minitrack. The first paper deals with the stability of limit cycles in hybrid systems. Limit cycles are common in such systems. However, the nonsmooth dynamics of such systems makes stability analysis difficult. Its characteristic multipliers determine the stability of a limit cycle. This paper uses some recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of nonsmooth limit cycles. In the next paper, a new state-space self-tuning control scheme is presented for adaptive digital control of continuous multivariable nonlinear stochastic hybrid systems with input saturation. Here, the continuous nonlinear stochastic system is assumed to have unknown system parameters, system and measurement noises, and inaccessible system states.The final paper analyzes the structure of stability boundary of a stable equilibrium point for nonlinear dynamics subject to state limits. The presence of state limits implies that the underlying dynamics does not satisfy the Lipschitz condition ensuring existence of a unique classical solution, complicating traditional analysis of stability boundaries. By analyzing the geometric properties of the solutions of the constrained dynamics, the paper establishes a characterization of the stability boundary.