Chaos attractor behaviour is usually preserved if the four basic arithmetic operations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dim...
详细信息
Chaos attractor behaviour is usually preserved if the four basic arithmetic operations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dimensional real discrete dynamical systems and nonautonomous real continuous-time dynamical systems are also dynamical systems and their Lyapunov exponents are kept, if they are twice differentiable. These two conclusions are shown here by the definitions of dynamical system and Lyapunov exponent. Numerical simulations support our analytical results. The conclusions can apply to higher order differential systems if their corresponding order differentials exist.
作者：
Zeng, XianlinLei, JinlongChen, JieBeijing Inst Technol
Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Tongji Univ
Shanghai Res Inst Intelligent Autonomous Syst Dept Control Sci & Engn Shanghai 200070 Peoples R China
This article develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This article analyzes critica...
详细信息
This article develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This article analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is O((1)/(t)2 ) by choosing suitable parameters. As far as we know, this is the first continuous-time primal dual accelerated method that can obtain the optimal rate. Then, this article applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.
This article considers the distributed time-varying optimal resource allocation problem with time-varying quadratic cost functions and a time-varying coupled equality constraint for multiagent systems. The objective i...
详细信息
This article considers the distributed time-varying optimal resource allocation problem with time-varying quadratic cost functions and a time-varying coupled equality constraint for multiagent systems. The objective is to design a distributed algorithm for agents with single-integrator dynamics to cooperatively satisfy the coupled equality constraint and minimize the sum of all local cost functions. Here, both the coupled equality constraint and cost functions depend explicitly on time. The cost functions are in quadratic form and may have nonidentical time-varying Hessians. To solve the problem in a distributed manner, an estimator based on the distributed average tracking method is first developed for each agent to estimate certain global information. By leveraging the estimated global information and an adaptive gain scheme, a distributed continuous-time algorithm is proposed, which ensures the agents to find and track the time-varying optimal trajectories with vanishing errors. We illustrate the applicability of the proposed method in the optimal hose transportation problem using multiple quadrotors.
The Lagrange multiplier method is widely used for solving constrained optimization problems. In this brief, the classic Lagrangians are generalized to a wider class of functions that satisfies the strong duality betwe...
详细信息
The Lagrange multiplier method is widely used for solving constrained optimization problems. In this brief, the classic Lagrangians are generalized to a wider class of functions that satisfies the strong duality between primal and dual problems. Then the generalized Karush-Kuhn-Tucker conditions for this generalized Lagrange multiplier method are derived. This useful method has applications in optimization problems and designs of consensus protocols, which is demonstrated by proposing a new continuous-time algorithm and its distributed version for optimization. The convergence advantages of the distributed algorithm are shown in a simulation example.
Recently, a continuous-time, deterministic analog solver based on ordinary differential equations (CTDS) was introduced, to solve Boolean satisfiability (SAT), a family of discrete constraint satisfaction problems. Si...
详细信息
Recently, a continuous-time, deterministic analog solver based on ordinary differential equations (CTDS) was introduced, to solve Boolean satisfiability (SAT), a family of discrete constraint satisfaction problems. Since SAT is NP-complete, efficient algorithms would benefit solving a large number of decision type problems, both within industry and the sciences. Here we present a graphics processing units (GPU) based implementation of the CTDS and its variants and show that one can achieve significantly improved performance within a wide range of SAT problems. We present and discuss three versions of our GPU implementation and compare their performance to CPU implementations, showing an improvement factor of up to two orders of magnitude. We illustrate the performance of our GPU-based solver on random SAT problems and a notoriously difficult graph coloring problem, the Ramsey number problem R(3, 3, 3, 3), and compare it with the state-of-the-art SAT solver MiniSAT's performances on CPUs. (c) 2020 Elsevier B.V. All rights reserved.
Considering a game with quadratic cost functions, this paper presents a distributed algorithm with security, whereby each player updates its strategy variable without. using its private data and still achieves the Nas...
详细信息
Considering a game with quadratic cost functions, this paper presents a distributed algorithm with security, whereby each player updates its strategy variable without. using its private data and still achieves the Nash equilibrium. By using the theory of differential inclusions, Lyapunov function and invariance principle, the algorithm is proved to be convergent. Our algorithm can be used when it is required to seek the Nash equilibrium without disclosure of private data.
暂无评论