The Experts below are selected from a list of 6498 Experts worldwide ranked by ideXlab platform
Renjin Jiang - One of the best experts on this subject based on the ideXlab platform.
-
Lipschitz Continuity of solutions of poisson equations in metric measure spaces
Potential Analysis, 2012Co-Authors: Renjin JiangAbstract:Let (X, d) be a pathwise connected metric space equipped with an Ahlfors Q-regular measure μ, Q ∈ [1, ∞ ). Suppose that (X, d, μ) supports a 2-Poincare inequality and a Sobolev–Poincare type inequality for the corresponding “Gaussian measure”. The author uses the heat equation to study the Lipschitz regularity of solutions of the Poisson equation Δu = f, where \(f\in L^{p}_{\rm{loc}}\). When p > Q, the local Lipschitz Continuity of u is established.
-
Lipschitz Continuity of solutions of poisson equations in metric measure spaces
arXiv: Analysis of PDEs, 2010Co-Authors: Renjin JiangAbstract:Let $(X,d)$ be a pathwise connected metric space equipped with an Ahlfors $Q$-regular measure $\mu$, $Q\in[1,\infty)$. Suppose that $(X,d,\mu)$ supports a 2-Poincar\'e inequality and a Sobolev-Poincar\'e type inequality for the corresponding "Gaussian measure". The author uses the heat equation to study the Lipschitz regularity of solutions of the Poisson equation $\Delta u=f$, where $f\in L^p_\loc$. When $p>Q$, the local Lipschitz Continuity of $u$ is established.
Aaron D. Ames - One of the best experts on this subject based on the ideXlab platform.
-
CDC - Sufficient conditions for the Lipschitz Continuity of QP-based multi-objective control of humanoid robots
52nd IEEE Conference on Decision and Control, 2013Co-Authors: Benjamin J. Morris, Matthew J. Powell, Aaron D. AmesAbstract:In this paper we analyze the Continuity properties of feedback controllers that are formulated as state-dependent quadratic programs (QP), with specific application to motion control for humanoid robots. With a desire to achieve multiple simultaneous goals in locomotion and manipulation, we develop a generalized QP-based control law through the use of multiple control Lyapunov functions (CLFs). Motivated by simulation studies showing cases where QP-based control loses Lipschitz Continuity, the main result of this paper is a set of sufficient conditions under which such Continuity properties will hold. This result provides conditions under which any number of tasks encoded as CLFs can be simultaneously exponentially stabilized. Finally, these results are demonstrated in a simulation of a simple humanoid robot climbing a vertical ladder.
-
Sufficient conditions for the Lipschitz Continuity of QP-based multi-objective control of humanoid robots
52nd IEEE Conference on Decision and Control, 2013Co-Authors: Benjamin Morris, Matthew J. Powell, Aaron D. AmesAbstract:In this paper we analyze the Continuity properties of feedback controllers that are formulated as state-dependent quadratic programs (QP), with specific application to motion control for humanoid robots. With a desire to achieve multiple simultaneous goals in locomotion and manipulation, we develop a generalized QP-based control law through the use of multiple control Lyapunov functions (CLFs). Motivated by simulation studies showing cases where QP-based control loses Lipschitz Continuity, the main result of this paper is a set of sufficient conditions under which such Continuity properties will hold. This result provides conditions under which any number of tasks encoded as CLFs can be simultaneously exponentially stabilized. Finally, these results are demonstrated in a simulation of a simple humanoid robot climbing a vertical ladder.
Peijin Li - One of the best experts on this subject based on the ideXlab platform.
-
Lipschitz Continuity of quasiconformal mappings and of the solutions to second order elliptic pde with respect to the distance ratio metric
Complex Analysis and Operator Theory, 2018Co-Authors: Peijin Li, Saminthan PonnusamyAbstract:The main aim of this paper is to study the Lipschitz Continuity of certain $$(K, K^{\prime })$$ -quasiconformal mappings with respect to the distance ratio metric, and the Lipschitz Continuity of the solution of a quasilinear differential equation with respect to the distance ratio metric.
-
representation formula and bi Lipschitz Continuity of solutions to inhomogeneous biharmonic dirichlet problems in the unit disk
Journal of Mathematical Analysis and Applications, 2017Co-Authors: Peijin Li, Saminathan PonnusamyAbstract:Abstract The aim of this paper is twofold. First, we establish the representation formula and the uniqueness of the solutions to a class of inhomogeneous biharmonic Dirichlet problems, and then prove the bi-Lipschitz Continuity of the solutions.
-
on the Lipschitz Continuity of certain quasiregular mappings between smooth jordan domains
Israel Journal of Mathematics, 2017Co-Authors: Jiaolong Chen, Peijin Li, Swadesh Kumar Sahoo, Xiantao WangAbstract:We first investigate the Lipschitz Continuity of (K,K’)-quasiregular C 2 mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of the obtained result are given: As a direct consequence, we get the Lipschitz Continuity of ρ-harmonic (K,K’)-quasiregular mappings, and as the other application, we study the Lipschitz Continuity of (K,K’)- quasiconformal self-mappings of the unit disk, which are the solutions of the Poisson equation Δw = g. These results generalize and extend several recently obtained results by Kalaj, Mateljevic and Pavlovic.
-
on the Lipschitz Continuity of certain quasiregular mappings between smooth jordan domains
arXiv: Complex Variables, 2015Co-Authors: Jiaolong Chen, Peijin Li, Swadesh Kumar Sahoo, Xiantao WangAbstract:We first investigate the Lipschitz Continuity of $(K, K')$-quasiregular $C^2$ mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of the obtained result are given: As a direct consequence, we get the Lipschitz Continuity of $\rho$-harmonic $(K, K')$-quasiregular mappings, and as the other application, we study the Lipschitz Continuity of $(K,K')$-quasiconformal self-mappings of the unit disk, which are the solutions of the Poisson equation $\Delta w=g$. These results generalize and extend several recently obtained results by Kalaj, Mateljevi\'{c} and Pavlovi\'{c}.
Le Yi Wang - One of the best experts on this subject based on the ideXlab platform.
-
Lipschitz Continuity of H∞ sensitivity optimization for continuous-time systems
1991 American Control Conference, 1991Co-Authors: Le Yi WangAbstract:Subject to certain high frequency attenuation conditions on weighting functions and plants, a suboptimal sensitivity function can be constructed which satisfies certain Lipschitz Continuity conditions. The Lipschitz conditions accommodate possible perturbations in system delay terms and those causing plant zeros cross the imaginary axis.
-
Lipschitz Continuity of inner outer factorization
Systems & Control Letters, 1991Co-Authors: Le Yi WangAbstract:Abstract Conditions are provided under which inner and outer factor of H ∞ functions (on the unit disk) can be found which depend Lipschitz continuously on data.
-
Lipschitz Continuity of h interpolation
Systems & Control Letters, 1990Co-Authors: Le Yi Wang, G ZamesAbstract:Abstract Optimal H ∞ interpolants may be infinitely sensitive to data. However, δ-suboptimal interpolants of the AAK central (maximal entropy) type are shown to satisfy a Lipschitz condition with respect to data.
Benjamin Morris - One of the best experts on this subject based on the ideXlab platform.
-
Sufficient conditions for the Lipschitz Continuity of QP-based multi-objective control of humanoid robots
52nd IEEE Conference on Decision and Control, 2013Co-Authors: Benjamin Morris, Matthew J. Powell, Aaron D. AmesAbstract:In this paper we analyze the Continuity properties of feedback controllers that are formulated as state-dependent quadratic programs (QP), with specific application to motion control for humanoid robots. With a desire to achieve multiple simultaneous goals in locomotion and manipulation, we develop a generalized QP-based control law through the use of multiple control Lyapunov functions (CLFs). Motivated by simulation studies showing cases where QP-based control loses Lipschitz Continuity, the main result of this paper is a set of sufficient conditions under which such Continuity properties will hold. This result provides conditions under which any number of tasks encoded as CLFs can be simultaneously exponentially stabilized. Finally, these results are demonstrated in a simulation of a simple humanoid robot climbing a vertical ladder.