Design of Control Lyapunov Functions for Homogeneous Jurdjevic-Quinn Systems

This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called «Jurdjevic-Quinn conditions». For these systems a positive definite function V_0 is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this «weak» Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration

Conjugate Times for Smooth Singular Trajectories and Bang-Bang Extremals

Colloque international et interdisciplinaire, Institut supérieur de philosophie, Université Catholique de Louvain, 28-30 avril 2010. Activité organisée par le séminaire de doctorat en philosophie (ISP 3200) consacré cette année à l’esthétique philosophique, en association avec le groupe de contact F.R.S./FNRS Esthétique et philosophie de l’art, l’école doctorale de philosophie (ED1) et l’école doctorale en arts et sciences de l’art (ED20). En tant qu’activité de formation doctorale, le collo..

Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov's Theorem. We use our methods to build strict Lyapunov functions for time-varying hybrid systems that contain mixtures of continuous and discrete time evolutions.Comment: 14 pages. Accepted for publication in Nonlinear Analysis: Hybrid Systems and Applications on September 6, 200

Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems

This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this “weak” Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration

Classification of local optimal syntheses for time minimal control problems with state constraints

This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state constraints}. We use geometric methods to evaluate \textit{the small time reachable set} and necessary optimality conditions. Our work is motivated by the \textit{optimal control of the atmospheric arc for the re-entry of a space shuttle}, where the vehicle is subject to constraints on the thermal flux and on the normal acceleration

CONTROL LYAPUNOV FUNCTIONS FOR HOMOGENEOUS “JURDJEVIC-QUINN” SYSTEMS

This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this “weak” Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration