Search

This paper uses the mirror descent algorithm with periodic dynamic quantization to solve constrained distributed optimization problems with limited communication channels. Due to the imperfect network environment, obtaining accurate information is impractical, and thus a communication scheme under quantization needs to be considered. A periodic dynamic quantizer with finite quantization levels is proposed in this paper to achieve exact optimization. Moreover, a time-varying control parameter in the mirror descent algorithm is designed to control the quantization error. After a comprehensive analysis, the proposed algorithm can obtain an optimal value, and the optimal convergence rate is O (1 / T 0. 25). [ABSTRACT FROM AUTHOR]

As we move to increasingly complex cyber–physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler–Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in 4. 5 ms while respecting workspace constraints and switching between a 'left' and 'right' bend in the elbow joint. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]