Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.     

Distributed stochastic mirror descent algorithm for resource allocation problem

In this paper, we consider a distributed resource allocation problem of minimizing a global convex function formed by a sum of local convex functions with coupling constraints. Based on neighbor communication and stochastic gradient, a distributed stochastic mirror descent algorithm is designed for the distributed resource allocation problem. Sublinear convergence to an optimal solution of the proposed algorithm is given when the second moments of the gradient noises are summable. A numerical example is also given to illustrate the eff ectiveness of the proposed algorithm.     

Consistent Kalman filters for nonlinear uncertain systems over sensor networks

In this paper, we study how to design filters for nonlinear uncertain systems over sensor networks. We introduce two Kalman-type nonlinear filters in centralized and distributed frameworks. Moreover, the tuning method for the parameters of the filters is established to ensure the consistency, i.e., the mean square error is upper bounded by a known parameter matrix at each time. We apply the consistent filters to the track-to-track association analysis of multi-targets with uncertain dynamics. A novel track-to-track association algorithm is proposed to identify whether two tracks are from the same target. It is proven that the resulting probability of mis-association is lower than the desired threshold. Numerical simulations on track-to-track association are given to show the effectiveness of the methods.     

Discrete-time inverse linear quadratic optimal control over finite time-horizon under noisy output measurements

In this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal is to recover the corresponding quadratic objective function using noisy observations. First, the identifiability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifiable. Next, we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown, yet the exact observations on the initial states are available. We formulate the problem as a risk minimization problem and approximate the problem using empirical average. It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees. We then study the case where the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian (with unknown mean and covariance). EM-algorithm is used to estimate the parameters in the objective function. The effectiveness of our results are demonstrated by numerical examples.     

Fast adaptive regression-basedmodel predictive control

Model predictive control (MPC) is an optimal control method that predicts the future states of the system being controlled and estimates the optimal control inputs that drive the predicted states to the required reference. The computations of the MPC are performed at pre-determined sample instances over a finite time horizon. The number of sample instances and the horizon length determine the performance of the MPC and its computational cost. A long horizon with a large sample count allows the MPC to better estimate the inputs when the states have rapid changes over time, which results in better performance but at the expense of high computational cost. However, this long horizon is not always necessary, especially for slowly-varying states. In this case, a short horizon with less sample count is preferable as the same MPC performance can be obtained but at a fraction of the computational cost. In this paper,we propose an adaptive regression-based MPC that predicts the bestminimum horizon length and the sample count from several features extracted from the time-varying changes of the states. The proposed technique builds a synthetic dataset using the system model and utilizes the dataset to train a support vector regressor that performs the prediction. The proposed technique is experimentally compared with several state-of-the-art techniques on both linear and non-linear models. The proposed technique shows a superior reduction in computational time with a reduction of about 35–65% compared with the other techniques without introducing a noticeable loss in performance.     

Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method

The bipartite consensus problem is addressed for a class of nonlinear time-delay multiagent systems in this paper. Therein, the uncertain nonlinear dynamics of all agents satisfy a Lipschitz growth condition with unknown constants, and part of the state information cannot be measured. In this case, a time-varying gain compensator is constructed, which only utilizes the output information of the follower and its neighbors. Subsequently, a distributed output feedback control protocol is proposed on the basis of the compensator. According to Lyapunov stability theory, it is proved that the bipartite consensus can be guaranteed by means of the designed control protocol. Different from the existing literature, this paper studies the leader–follower consensus problem under a weaker connectivity condition, i.e., the signed directed graph is structurally balanced and contains a directed spanning tree. Two simulation examples are carried out to show the feasibility of the proposed control strategy     

Periodic event-triggered secure consensus for networked mechanical systems under Denial-of-Service attacks

This paper concentrates on the secure consensus problem of networked mechanical/Euler–Lagrange systems. First, a new periodic event-triggered (PET) secure distributed observer is proposed to estimate the leader information. The proposed distributed observer only relies on the PET data from its neighbors, which can significantly reduce the communication and computational burden. More importantly, it is secure in the sense that it can work normally regardless of the Denial-of-Service (DoS) attacks. Second, based on the proposed distributed observer, an adaptive fuzzy control law is proposed for each Euler– Lagrange system. A PET mechanism is integrated into the controller, which can reduce the control update. This is helpful for both energy saving and fault tolerance of actuators. Moreover, the PET mechanism naturally makes the controller easy to be implemented in digital platform. The property of fuzzy logic systems and Gronwall inequality are skillfully utilized to show the stability of the closed-loop system. Finally, the proposed control scheme is verified on real Euler–Lagrange systems, which contain a robot manipulator and several servo motors.     

Distributed solver for linear matrix inequalities: an optimization perspective

In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.     

Distributed multi-agent temporal-difference learning with full neighbor information

This paper presents a novel distributed multi-agent temporal-difference learning framework for value function approximation, which allows agents using all the neighbor information instead of the information from only one neighbor. With full neighbor information, the proposed framework (1) has a faster convergence rate, and (2) is more robust compared to the state-of-the-art approaches. Then we propose a distributed multi-agent discounted temporal difference algorithm and a distributed multi-agent average cost temporal difference learning algorithm based on the framework. Moreover, the two proposed algorithms’ theoretical convergence proofs are provided. Numerical simulation results show that our proposed algorithms are superior to the gossip-based algorithm in convergence speed, robustness to noise and time-varying network topology.     

Stochastic sub-gradient algorithm for distributedoptimization with random sleep scheme

In this paper, we consider a distributed convex optimization problem of a multi-agent system with the global objective function as the sum of agents’ individual objective functions. To solve such an optimization problem, we propose a distributed stochastic sub-gradient algorithm with random sleep scheme. In the random sleep scheme, each agent independently and randomly decides whether to inquire the sub-gradient information of its local objective function at each iteration. The algorithm not only generalizes distributed algorithms with variable working nodes and multi-step consensus-based algorithms, but also extends some existing randomized convex set intersection results. We investigate the algorithm convergence properties under two types of stepsizes: the randomized diminishing stepsize that is heterogeneous and calculated by individual agent, and the fixed stepsize that is homogeneous. Then we prove that the estimates of the agents reach consensus almost surely and in mean, and the consensus point is the optimal solution with probability 1, both under randomized stepsize. Moreover, we analyze the algorithm error bound under fixed homogeneous stepsize, and also show how the errors depend on the fixed stepsize and update rates.     

Adaptive output consensus for heterogeneous nonlinear multi‑agent systems with multi‑type input constraints under switching‑directed topologies

This study concentrates on solving the output consensus problem for a class of heterogeneous uncertain nonstrict-feedback nonlinear multi-agent systems under switching-directed communication topologies, in which all followers are subjected to multi-type input constraints such as unknown asymmetric saturation, unknown dead-zone and their integration. A unified representation is presented to overcome the difficulties originating from multi-agent input constraints. Moreover, the uncertain system functions in a non-lower triangular form and the interaction terms among agents are dealt with by exploiting the fuzzy logic systems and their special property. Furthermore, by introducing a nonlinear filter to alleviate the problem of “explosion of complexity” during the backstepping design, a distributed common adaptive control protocol is proposed to ensure that the synchronization errors converge to a small neighborhood of the origin despite the existence of multiple input constraints and arbitrary switching communication topologies. Both stability analysis and simulation results are conducted to show the effectiveness and performance of the proposed control methodology.     

Mu-based trajectory tracking control for a quad-rotor UAV

In this paper, the design and application of a robust mu-synthesis-based controller for quad-rotor trajectory tracking are presented. The proposed design approach guarantees robust performance over a weakly nonlinear range of operation of the quad-rotor, which is a practical range that suits various applications. The controller considers different structured and unstructured uncertainties, such as unmodeled dynamics and perturbation in the parameters. The controller also provides robustness against external disturbances such as wind gusts and wind turbulence. The proposed controller is fixed and linear; therefore, it has a very low computational cost. Moreover, the controller meets all design specifications without tuning. To validate this control strategy, the proposed approach is compared to a linear quadratic regulator (LQR) controller using a high- fidelity quad-rotor simulation environment. In addition, the experimental results presented show the validity of the proposed control strategy.     

Optimal energy consuming planning for a home‑based microgrid with mobility constraint of electric vehicles and tractors

This research deals with the energy management problem to minimize the cost of non-renewable energy for a small-scale microgrid with electric vehicles (EV) and electric tractors (ET). The EVs and ETs function as batteries in the power system, while they often have to leave it for their mobility and agricultural work. Each State of Charge (SoC), which is the charge rate of the battery from 0 to 1, and the operating time of ETs are optimized under the assumption that the required electrical energy, the arrival and departure time of EVs, and the working time of ETs are given by users, but they include uncertainties. In this paper, we deal with these uncertainties by constraints for robust energy planning and expected optimization based on scenarios, and show that the scheduling of the SoC assuming the worst case and the optimal home-based power consumption planning that considers the cost of each scenario corresponding to each variation can be obtained. Our proposed method is formulated as a mixed integer linear programming (MILP), and numerical simulations show that the optimal cooperative operation among multiple houses can be obtained and its global optimal or sub-optimal solution can be quickly obtained by using CPLEX.     

Adaptive output regulation for cyber-physical systems under time-delay attacks

In this paper, we present an output regulation method for unknown cyber-physical systems (CPSs) under time-delay attacks in both the sensor-to-controller (S-C) channel and the controller-to-actuator (C-A) channel. The proposed approach is designed using control inputs and tracking errors which are accessible data. Reinforcement learning is leveraged to update the control gains in real time using policy or value iterations. A thorough stability analysis is conducted and it is found that the proposed controller can sustain the convergence and asymptotic stability even when two channels are attacked. Finally, comparison results with a simulated CPS verify the effectiveness of the proposed output regulation method.     

Distributed solving Sylvester equations with fractional order dynamics

This paper addresses distributed computation Sylvester equations of the form AX + XB = C with fractional order dynamics. By partitioning parameter matrices A, B and C, we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms, which have more design freedom and have potential to obtain better convergence performance than that of the existing first order algorithms. Then, rewriting distributed algorithms as corresponding frequency distributed models, we design Lyapunov functions and prove that the proposed algorithms asymptotically converge to an exact or least squares solution. Finally, we validate the effectiveness of the proposed algorithms by providing a numerical example     

Output feedback adaptive super twisting sliding mode control for quadrotor UAVs

In this paper, a sliding mode control with adaptive gain combined with a high-order sliding mode observer to solve the tracking problem for a quadrotor UAV is addressed, in presence of bounded external disturbances and parametric uncertainties. The high order sliding mode observer is designed for estimating the linear and angular speed in order to implement the proposed scheme. Furthermore, a Lyapunov function is introduced to design the controller with the adaptation law, whereas an analysis of finite time convergence towards to zero is provided, where sufficient conditions are obtained. Regarding previous works from literature, one important advantage of proposed strategy is that the gains of control are parameterized in terms of only one adaptive parameter, which reduces the control effort by avoiding gain overestimation. Numerical simulations for tracking control of the quadrotor are given to show the performance of proposed adaptive control–observer scheme.     

Distributed robust MPC for nonholonomic robots with obstacle and collision avoidance

Considering that the inevitable disturbances and coupled constraints pose an ongoing challenge to distributed control algorithms, this paper proposes a distributed robust model predictive control (MPC) algorithm for a multi-agent system with additive external disturbances and obstacle and collision avoidance constraints. In particular, all the agents are allowed to solve optimization problems simultaneously at each time step to obtain their control inputs, and the obstacle and collision avoidance are accomplished in the context of full-dimensional controlled objects and obstacles. To achieve the collision avoidance between agents in the distributed framework, an assumed state trajectory is introduced for each agent which is transmitted to its neighbors to construct the polyhedral over-approximations of it. Then the polyhedral over-approximations of the agent and the obstacles are used to smoothly reformulate the original nonconvex obstacle and collision avoidance constraints. And a compatibility constraint is designed to restrict the deviation between the predicted and assumed trajectories. Moreover, recursive feasibility of each local MPC optimization problem with all these constraints derived and input-to-state stability of the closed-loop system can be ensured through a sufficient condition on controller parameters. Finally, simulations with four agents and two obstacles demonstrate the efficiency of the proposed algorithm.     

A hybrid genetic algorithm for the electric vehicle routing problem with time windows

Driven by the newlegislation on greenhouse gas emissions, carriers began to use electric vehicles (EVs) for logistics transportation. This paper addresses an electric vehicle routing problem with time windows (EVRPTW). The electricity consumption of EVs is expressed by the battery state-of-charge (SoC). To make it more realistic, we take into account the terrain grades of roads, which affect the travel process of EVs. Within our work, the battery SoC dynamics of EVs are used to describe this situation. We aim to minimize the total electricity consumption while serving a set of customers. To tackle this problem, we formulate the problem as a mixed integer programming model. Furthermore, we develop a hybrid genetic algorithm (GA) that combines the 2-opt algorithm with GA. In simulation results, by the comparison of the simulated annealing (SA) algorithm and GA, the proposed approach indicates that it can provide better solutions in a short time.     

A solution strategy for distributed uncertain economic dispatch problems via scenario theory

In this paper, an uncertain economic dispatch problem (EDP) is considered for a group of coopertive agents. First, let each agent extract a set of samples (scenarios) from the uncertain set, and then a scenario EDP is obtained using these scenarios. Based on the scenario theory, a prior certification is provided to evaluate the probabilistic feasibility of the scenario solution for uncertain EDP. To facilitate the computational task, a distributed solution strategy is proposed by the alternating direction method of multipliers (ADMM) and a finite-time consensus strategy. Moreover, the distributed strategy can solve the scenario problem over a weight-balanced directed graph. Finally, the proposed solution strategy is applied to an EDP for a power system involving wind power plants.     

Optimal control for spatial-temporal distributed nonlinear autoregressive with exogenous inputs correlation model of steel rolling reheating furnace: a coordinated time-sharing control approach

Accurate control of slab temperature and heating rate is an important significance to improve product performance and reduce carbon emissions for steel rolling reheating furnace (SRRF). Firstly, a spatial temporal distributed–nonlinear autoregressive with exogenous inputs correlation model (STD-NARXCM) to spatial temporal distributed–autoregressive with exogenous inputs correlation model (STD-ARXCM) in working point is established. Secondly, a new coordinated time-sharing control architecture in different time periods is proposed, which is along the length of the SRRF to improve the control performance. Thirdly, a hybrid control algorithm of expert-fuzzy is proposed to improve the dynamic of the temperature and the heating rate during time period 0 to t1. A hybrid control algorithm of expert-fuzzy-PID is proposed to enhance the control accuracy and the heating rate during time period t1 to t2. A hybrid control algorithm of expert-active disturbance rejection control (ADRC) is proposed to boost the anti-interference and the heating rate during time period t2 to t3. Finally, the experimental results show that the coordinated time-sharing algorithm can meet the process requirements, the maximum deviation of temperature value is 8–13.5?C.