Journal ArticleDOI
Design of Switched Linear Systems in the Presence of Actuator Saturation
Liang Lu,Zongli Lin +1 more
TLDR
For a group of linear systems, each under a saturated linear, not necessarily stabilizing, feedback law, the problem of designing such a switching scheme as a constrained optimization problem with the objective of maximizing an estimate of the domain of attraction is solved.Abstract:
For a group of linear systems, each under a saturated linear, not necessarily stabilizing, feedback law, we design a switching scheme such that the resulting switched system is locally asymptotically stable at the origin with a large domain of attraction. By expressing each saturated linear feedback in a convex hull of a group of auxiliary linear feedbacks, we formulate and solve the problem of designing such a switching scheme as a constrained optimization problem with the objective of maximizing an estimate of the domain of attraction. Simulation results indicate that the resulting domain of attraction extends well beyond the linear regions of the actuators.read more
Citations
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Journal ArticleDOI
Neural-Network-Based Constrained Optimal Control Scheme for Discrete-Time Switched Nonlinear System Using Dual Heuristic Programming
TL;DR: A novel iterative two-stage dual heuristic programming (DHP) algorithm is developed to solve the Hamilton-Jacobi-Bellman equation of the switched system with the saturating actuator and the convergence and optimality are strictly proven.
Journal ArticleDOI
A Weighted Least-Squares Approach to Parameter Estimation Problems Based on Binary Measurements
Eric Colinet,Jerome Juillard +1 more
TL;DR: It is proved that the proposed criterion is locally convex and that it is possible to use a simple gradient descent to find a consistent estimate of the unknown system parameters, regardless of the presence of measurement noise at the quantizer's input.
Journal ArticleDOI
A Switching Anti-windup Design Using Multiple Lyapunov Functions
Liang Lu,Zongli Lin +1 more
TL;DR: The resulting domain of attraction is expected to be significantly larger than the one resulting from a single anti-windup gain and a single Lyapunov function, and simulation results demonstrate such a significant improvement.
Journal ArticleDOI
L 2-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation
TL;DR: The problem of L 2-gain analysis and control synthesis is studied for a class of uncertain discrete-time switched linear systems with time delay and saturating actuators by using the multiple Lyapunov functions method.
Journal ArticleDOI
Brief paper: L2 gain analysis for a class of switched systems
Liang Lu,Zongli Lin,Haijun Fang +2 more
TL;DR: It will be shown that a single system under a switching feedback law has stronger disturbance tolerance/rejection capability than a single linear feedback law can achieve.
References
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Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Journal ArticleDOI
Basic problems in stability and design of switched systems
Daniel Liberzon,A.S. Morse +1 more
TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
Journal ArticleDOI
Differential equations with discontinuous right-hand sides☆
TL;DR: In this article, the existence results for differential equations with discontinuous right-hand sides with great generality are established and proved for high-order ordinary and partial differential equations for the following problem.
Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
TL;DR: In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.
Book
Control Systems with Actuator Saturation: Analysis and Design
Tingshu Hu,Zongli Lin +1 more
TL;DR: In this article, a control system with actuator saturation analysis and design is presented, in which a control law is designed a priori to meet either the performance or stability requirement.