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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]

In this paper we deal with decision-coupled problems involving multiple agents over a network. Each agent has its own local objective function and local constraints, and all agents aim at finding the value of a common decision vector that minimizes the sum of all agents' cost functions and satisfies all local constraints. To this purpose, we introduce a Proximal-Tracking distributed optimization algorithm that integrates dynamic average consensus within the proximal minimization method. Convergence to an optimal consensus solution is guaranteed for any value of a constant penalty parameter, under a convexity assumption only, without requiring differentiability, Lipschitz continuity, or smoothness of the local objective functions. Numerical simulations show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a class of optimization problems is investigated, where the objective function is the sum of N convex functions viewed as local functions and the constraints are N nonidentical closed convex sets. Additionally, it is aimed to solve the considered optimization problem in a distributed manner and thus a sequence of time-varying unbalanced directed graphs is introduced first to depict the information connection topologies. Then, the novel push-sum based constrained optimization algorithm (PSCOA) is developed, where the new gradient descent-like method is applied to settle the involved closed convex set constraints. Furthermore, the rigorous convergence analysis is shown under some standard and common assumptions and it is proved that the developed distributed discrete-time algorithm owns a convergence rate of O ( ln t t ) in general case. Specially, the convergence rate of O ( 1 t ) can be further obtained under the assumption that at least one objective function is strongly convex. Finally, simulation results are given to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces the concept and characterization of Disturbance-Dwell-Time invariance (DDT-invariance) and Constraint Admissible DDT-invariance (CADDT-invariance) for constrained systems with additive disturbance under dwell-time switching. Using the characterization, necessary and sufficient conditions for DDT-invariance and algorithms for the computation of the minimal and maximal constraint admissible convex DDT-invariant sets are provided. Numerical examples of such sets for several systems are also provided. [Copyright &y& Elsevier]

Abstract: Nonlinear constrained optimal trajectory planning is a challenging and fundamental area of research. This paper proposes bio-inspired fast-time approaches for this type of problems based on the inspiration drawn from the natural phenomenon known as the motion camouflage. Two algorithms are proposed: the virtual motion camouflage (VMC) subspace method and the sequential VMC method. As a hybrid approach, the sequential VMC method works through a two-step structure in each iteration. First, the VMC subspace method will solve for an optimal solution over a selected subspace. Second, an algorithm consisting of a linear programming and a line search will vary the subspace so that the next VMC subspace result will be guaranteed not to be worse than that of the current step. The dimension and time complexities of the algorithms will be analyzed, and the optimality of the solution via the sequential VMC approach will be studied. Through the VMC approaches, the state and control variables in the kinematics or dynamics models of vehicles in the selected subspace can be represented by a single degree-of-freedom vector, called the path control parameter vector. The reduction in dimension and no involvement of equality constraints will in practice make the convergence faster and easier, and a much smaller computational cost is expected. Two simulation examples, the Breakwell problem and a minimum time robot obstacle avoidance problem with different numbers of obstacles, are used to demonstrate the capabilities of the algorithms. [Copyright &y& Elsevier]

Abstract: This paper considers output feedback robust model predictive control for the quasi-linear parameter varying (quasi-LPV) system with bounded disturbance. The so-called quasi-LPV means that the varying parameters of the linear system are known at the current time, but unknown in the future. The control law is parameterized as a parameter-dependent dynamic output feedback, and the closed-loop stability is specified by the notion of quadratic boundedness. An iterative algorithm is proposed for the on-line synthesis of the control law via convex optimization. A numerical example is given to illustrate the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper presents a novel transformation-proximal bundle algorithm for multistage adaptive robust optimization problems. By partitioning recourse decisions into state and control decisions, the proposed algorithm applies affine control policy only to state decisions and allows control decisions to be fully adaptive, thus transforming the original problem into an equivalent two-stage Adaptive Robust Optimization (ARO) problem. Importantly, this multi-to-two transformation is general enough to be employed with any two-stage ARO solution algorithms, thus opening a new avenue for a variety of multistage ARO algorithms. The proximal bundle method is developed for the resulting two-stage problem along with convergence analysis. In an inventory control application, the affine disturbance-feedback control policy suffers from a severe suboptimality with an average gap of 34.88%, while the proposed algorithm generates an average gap of merely 1.68%. [ABSTRACT FROM AUTHOR]

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel distributedapprox − Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete distributed approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous distributed approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the distributedapprox − Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods. [ABSTRACT FROM AUTHOR]