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The problem of transforming a single-input single-output nonlinear discrete-time state equations into the extended observer form is studied in this paper. Unlike previous solutions which compute the injection terms from the input–output equations, in this paper the computations utilize directly the given state equations. An algorithm is given to find step-by-step the necessary transformation by computing backward-shifts of functions computed in previous step. It is shown that the integrability conditions presented in the algorithm are necessary and sufficient for solvability of the problem. Various examples have been studied to demonstrate the usefulness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The sequential stabilizing spline (SSS) algorithm is a remarkable algorithm for identifying linear dynamical systems. It can guarantee the stability of an estimated model by polishing the maximum modulus roots of an equation. Therefore, the root structure of an equation plays an important role in the SSS algorithm. Although the traditional power iterative method can be applied to approximate the extremal eigenvalues which have the largest modulus, it has two limitations: (1) the extremal eigenvalues must be real numbers, and (2) the structures of the extremal eigenvalues should be known a priori. In this paper, a novel power iterative method is proposed to approximate the extremal eigenvalues. Compared with the traditional power iterative method, the method in this paper can (1) determine the types of the extremal eigenvalues without prior knowledge of the matrix; (2) approximate the true values of the extremal eigenvalues regardless of their type; (3) become a worthy addition to SSS algorithm and gradient descent algorithm. Simulation examples demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose novel data-driven optimal dynamic controller design frameworks, via both state-feedback and output-feedback, for solving optimal output regulation problems of linear discrete-time systems subject to unknown dynamics and unmeasurable disturbances using reinforcement learning (RL). Fundamentally different from existing research on optimal output regulation problems and RL, the proposed procedures can determine both the optimal control gain and the optimal dynamic compensator simultaneously instead of presetting a non-optimal dynamic compensator. Moreover, we present incremental dataset-based RL algorithms to learn the optimal dynamic controllers that do not require the measurements of the external disturbance and the exostate during learning, which is of great practical importance. Besides, we show that the proposed incremental dataset-based learning methods are more robust to a class of measurement noises with arbitrary magnitudes than routine RL algorithms. Comprehensive simulation results validate the efficacy of our methodologies. [ABSTRACT FROM AUTHOR]

This paper studies the problem of resilient cluster consensus for discrete-time high-order multi-agent systems in the presence of malicious adversaries. Based on a decomposition form of the system matrices, a high-order resilient cluster consensus algorithm is proposed. Necessary and sufficient conditions for the normal agents to reach resilient cluster consensus despite the influence of the malicious adversaries are provided. In contrast to the existing results, the proposed algorithm is suitable for general high-order multi-agent systems and can reduce the network redundancy needed to tolerate the same number of malicious adversaries. Two examples are simulated to validate the effectiveness of the theoretical results. [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]

This paper studies the distributed resource allocation problem with nonsmooth local cost functions subject to the coupled equality and inequality constraints. In particular, each local cost function is expressed as the sum of a differentiable function and two nonsmooth functions. By using the operator splitting and primal–dual method, a continuous-time distributed proximal algorithm is developed, which can be applied to more general local cost functions that are convex but not necessarily smooth. In addition, the proposed algorithm is fully distributed in the sense that the gain parameter can be determined locally and does not require any global information of the network. By applying Lyapunov stability analysis and convex optimization theory, it is shown that the decision variables of all the agents converge to an optimal solution. Finally, a simulation example is carried out to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]