Yuchun Li

Results on incremental stability for a class of hybrid systems

Incremental stability is the notion that the distance between every pair of solutions to the system has stable behavior and approaches zero asymptotically. This paper introduces this notion for a class of hybrid systems. In particular, we define incremental stability as well as incremental partial stability, and study their properties. The approach used to derive our results consists of recasting the incremental stability problem as a set stabilization problem, for which the tools for asymptotic stability of hybrid systems are applicable. In particular, we propose an auxiliary hybrid system to study the stability of the diagonal set, which relates to incremental stability of the original system. The proposed notions are illustrated in examples throughout the paper.

A robust finite-time convergent hybrid observer for linear systems

Motivated by the design of observers with good performance and robustness to measurement noise, the problem of estimating the state of a linear time-invariant system in finite time and with robustness to a class of measurement noise is considered. Using a hybrid systems framework, a hybrid observer producing an estimate that converges to the plant state in finite time, even under unknown constant (e.g., bias) and piecewise constant noise is presented. The stability and robustness properties of the observer are shown analytically and validated numerically.

Interconnected Observers for Robust Decentralized Estimation With Performance Guarantees and Optimized Connectivity Graph

Motivated by the need for observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with a noisy output that consists of a combination of N-coupled observers over a connectivity graph. At each node of the graph, the output of these interconnected observers is defined as the average of the estimates obtained using local information. The convergence rate and the robustness to measurement noise of the proposed observers output are characterized in terms of KL bounds. Several optimization problems are formulated to design the proposed observer in order to satisfy a given rate of convergence specification while minimizing the H∞ gain from noise to estimates or the size of the connectivity graph. It is shown that the interconnected observers relax the well-known tradeoff between the rate of convergence and noise amplification, which is a property attributed to the proposed innovation term, that over the graph, couples the estimates between the individual observers. Sufficient conditions involving information of the plant only, ensuring that the estimate obtained at each node of the graph outperforms the one obtained with a single, standard Luenberger observer are given. The results are illustrated in several examples throughout this paper.

A finite-time convergent observer with robustness to piecewise-constant measurement noise

Motivated by the design of observers with good performance and robustness to measurement noise, the problem of estimating the state of a linear time-invariant system in finite time and robustly with respect to measurement noise is considered. Using a hybrid systems framework, a hybrid observer producing an estimate that converges to the plant state in finite time, even under unknown piecewise-constant noise, is presented. The stability and robustness properties of the observer are shown analytically and validated numerically.

Results on stability and robustness of hybrid limit cycles for a class of hybrid systems

This work addresses stability and robustness properties of hybrid limit cycles for a class of hybrid systems, which combine continuous dynamics on a flow set and discrete dynamics on a jump set. Under some mild assumptions, we show that the stability of hybrid limit cycles for a hybrid system is equivalent to the stability of a fixed point of the associated Poincaré map. As a difference to related efforts for systems with impulsive effects, we also explore conditions under which the stability properties of the hybrid limit cycles are robust to small perturbations. The spiking Izhikevich neuron is presented to illustrate the notions and results throughout the paper.

Design of automatic two-axis sun-tracking system

The photovoltaic (PV) panel produces the maximum power as the incident angle of sunlight is 90°. In this paper, two-axis sun-tracking system keeps PV panel perpendicular to sun light by absolute and relative position sensors signal analysis. It is composed of micro-controller, solar illumination sensor, solar position sensors, stepper motors and drivers, two-axis motion mechanism, zero position switches, limit switches and solar system.

On necessary and sufficient conditions for incremental stability of hybrid systems using the graphical distance between solutions

This paper introduces new incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints. Incremental stability is defined as the property that the distance between every pair of solutions to the system has stable behavior (incremental stability) and approaches zero asymptotically (incremental attractivity) in terms of graphical convergence. Basic properties of the class of graphically incrementally stable systems are considered as well as those implied by the new notions are revealed. Moreover, several sufficient and necessary conditions for a hybrid system with such a property are established. Examples are presented throughout the paper to illustrate the notions and results.

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

Abstract 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.

A coupled pair of Luenberger observers for linear systems to improve rate of convergence and robustness to measurement noise

Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems that consists of the combination of two coupled Luenberger observers. The output of the proposed observer is defined as the average between the estimates of the individual ones. The convergence rate and the robustness to measurement noise of the proposed observers output are characterized in terms of ISS estimates. Conditions guaranteeing that these estimates outperform those obtained with a standard Luenberger observer are given. The conditions are exercised in a stable scalar plant, for which a design procedure and numerical analysis are provided, and in a second order plant, numerically.

Robust Distributed Estimation for Linear Systems Under Intermittent Information

We provide a comprehensive solution to the estimation problem of the state for a linear time-invariant system in a distributed fashion over networks that allow only intermittent information transmission. By attaching to each node an observer that employs information received from its neighbors triggered by asynchronous communication events, we propose a distributed state observer that guarantees global exponential stability of the zero estimation error set. The design of parameters is formulated as linear matrix inequalities. A thorough robustness analysis of the proposed observer to unmodeled dynamics, unknown communication times, as well as measurement and communication noise characterized in terms of input-to-state stability is presented. These properties of the proposed observer are shown analytically and validated numerically.