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With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the robust stabilization issues on uncertain system with ${H_\infty }$ performance are investigated by applying impulsive time related control algorithm. A hybrid control scheme is novelly proposed using proportional impulsive plus integral mechanism. This impulse-time-dependent (ITD) feedback controller employs the proportional control action ${K_{p}}$ at impulse instants for stabilizing. Then, intermittently the integral control strategy ${K_{I}(t)}$ is implemented between impulsive time intervals for improving the state convergence. Sufficient conditions are derived to ensure the closed-loop performance. In addition, a memory controller ${K_{D}}$ is introduced to tackle the stabilization problem of system with signal transmission delay. Furthermore, a distributed time-varying delay ${\delta _{k}(t)}$ is defined in the impulsive control-based system. Considering discrete and distributed time-varying delays concurrently, the ITD stability criteria are deduced to guarantee the ${H_\infty }$ performance on uncertain system with exogenous disturbance. Numerical examples are conducted to show the expected stabilization and state convergence response with disturbance attenuation of this development. [ABSTRACT FROM AUTHOR]

This paper considers the problem of data driven iterative learning control (DDILC) for a class of nonaffine nonlinear systems subject to data quantization and sensor saturation. Two novel quantized DDILC (QDDILC) algorithms are proposed based on saturated and quantized information of system outputs. The convergence of the proposed QDDILC algorithms is strictly proved and the effects of output saturation and data quantification are also analyzed. It is shown that sensor saturation does not change the convergence property, thus it causes the convergence rate to slow down. For the QDDILC algorithm, data quantization will cause the tracking error to converge to a bound depending on the quantization level. However, the modified QDDILC algorithm, which using the different quantization scheme from QDDILC algorithm, can ensure that the tracking error converges to zero. Illustrative simulations are exploited to verify the theoretical results. [ABSTRACT FROM AUTHOR]

For systems that can only be locally stabilized, control laws and their effective regions are both important. In this paper, invariant policy iteration is proposed to solve the optimal control of discrete-time systems. At each iteration, a given policy is evaluated in its invariantly admissible region, and a new policy and a new region are updated for the next iteration. Theoretical analysis shows the method is regionally convergent to the optimal value and the optimal policy. Combined with sum-of-squares polynomials, the method is able to achieve the near-optimal control of a class of discrete-time systems. An invariant adaptive dynamic programming algorithm is developed to extend the method to scenarios where system dynamics is not available. Online data are utilized to learn the near-optimal policy and the invariantly admissible region. Simulated experiments verify the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Periodic vehicle routing problem with time windows (PVRPTWs) is an important combinatorial optimization problem that can be applied in different fields. It is essentially a multiobjective optimization problem due to the problem nature. In this paper, a typical multiobjective PVRPTW with five objectives is first defined and new nonsymmetric real-world multiobjective PVRPTW instances are generated. Then, a hybrid multiobjective memetic algorithm is proposed for solving multiobjective PVRPTW. In the proposed algorithm, a two-phase strategy is devised to improve the comprehensive performance in terms of the convergence and diversity. In this strategy, several extreme solutions near an approximate Pareto front (PF) are identified at Phase I, and then the approximate PF is extended at Phase II. The proposed algorithm is extensively tested on both real-world instances and traditional instances. Experiment results show that the proposed algorithm outperforms two representative competitor algorithms on most of the instances. The effectiveness of the two-phase strategy is also confirmed. [ABSTRACT FROM AUTHOR]

Under consensus-based economic dispatch (ED) algorithm, multiple agents, which control local generation units, cooperatively minimize the total generation cost subject to the balance of the generation and expected demand in smart grids. As ubiquitous time delays on communication links exist in communication networks, studying the effect of delays on the dispatch performance is of both theoretical merit and practical value for the efficient and stable operation of smart grids. In this paper, we consider a well-developed consensus-based ED protocol under constant time delays. We find that there always exists a sufficiently small learning gain parameter under finite constant delays such that the convergence of the consensus-based algorithm is guaranteed. Further, an analytical expression of the upper bound is established for the learning gain parameter, which is determined by the largest delay, the weight matrix and the parameters of generation cost functions. In order to guarantee the optimality of the final solution, we propose the updating rule for iterations when initial states are not received by their neighbors due to time delays. The optimality of the final solution under the proposed updating rule is analyzed. We validate our theoretical results through extensive simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, we present a direct multirate adaptive control algorithm that ensures global stabilization of a class of (potentially unstable and invertible) linear time-invariant discrete-time plants of known order and relative degree one. An essential feature of our scheme is that no projections are needed, no appeal is made to the persistence of excitation arguments for the stability proof and it has a better transient performance than existing schemes. The implementation of the controller requires some prior information about its Markov parameters, namely, upper and lower bounds on the systems impulse response. It is directly applicable to plants with interlacing real poles and zeros, i.e., with Cauchy index equal to the plant order, provided the adaptation gain is restricted to be smaller than some value determined by the measure of relative primeness of the pole and zero polynomial. This class contains some practically interesting systems, for instance, resistor–inductor or resistance–capacitance circuits. [ABSTRACT FROM AUTHOR]

By employing the finite-time control method, the consensus control algorithm for higher-order multiagent systems is designed in this paper. Under a neighbor-based rule, a higher-order finite-time consensus algorithm is explicitly constructed, which only uses local information. The finite-time consensus control algorithm can guarantee that the state consensus is achieved in a finite time. In addition, for multiagent systems having a leader-following structure, the consensus algorithm is also designed. Finally, two examples are presented to show the effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic leader selection process of a multirobot system with leader–follower strategies is studied in terms of formation control. A fuzzy inference system is employed to evaluate the status of robots by means of their states. Based on the status, an affection-based model is proposed to trigger a leader selection module. Followers send out unsatisfied signals when they are disappointed at the current leader. The abashment value of the leader changes with its own status as well as the number of unsatisfied signals received from its followers. When its abashment value goes beyond a given threshold, a leader reselection process is triggered. Moreover, a swap-greedy algorithm is proposed to approximate the optimal solution for confirming the leader–follower relationship, which can be described as a combinatorial optimization problem to minimize the total travel distance of all the robots. Extensive simulation results demonstrate that the proposed model can improve the probability of a robot team escaping from local extreme points significantly, and even in the case of leader failure, the team can reselect a leader autonomously and keep moving toward the target. [ABSTRACT FROM AUTHOR]