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In this paper, the enclosing control problem of second-order multi-agent systems is considered, where the targets can be either stationary or moving. The objective is to achieve an equidistant circular formation for a group of agents to enclose a team of targets. In order to do so, we first introduce a formal definition explaining certain basic properties of the exploring relation between the agents and the targets. We then construct the estimator of the centre of the targets, which is used to build the control protocol to achieve equidistant circular enclosing. Using a Lyapunov function and Lasalle’s Invariance Principle, the convergency of the estimator and control protocol are, respectively, established. We then construct a smooth function to approximate the discontinuous term in the estimator. Finally, the simulations for stationary targets and moving targets are given to verify the validity of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of optimal parameter selection problems with continuous inequality constraints. By introducing a smoothing parameter, we formulate a sequence of KKT (Karush-Kuhn-Tucker) systems of this problem and then transform it into a system of constrained nonlinear equations. Then, the first- and second-order gradients formulae of the cost functional and the constraints are derived. On this basis, a smoothing projected Newton-type algorithm is developed to solving this system of nonlinear equations. To illustrate the effectiveness of the proposed method, some numerical results are solved and presented. [ABSTRACT FROM PUBLISHER]

This article investigates the robust H ∞ control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint, pole constraint and external and controller perturbations. Based on the Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state-feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimisation problem subject to LMI constraints. With the obtained controller, the spacecraft rendezvous mission can be accomplished. An illustrative example is provided to show the effectiveness of the proposed control design method. [ABSTRACT FROM AUTHOR]

In this article, under a concept of supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are proposed for a constrained set-valued vector optimization problem. Weak duality, strong duality, and stability criteria are investigated. The inclusion relations between the image sets of the dual problems are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the optimal design of discrete coefficient FIR filters is considered. A novel hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, is proposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used to locate descent points for previously converged local minima. The gradient-based method is derived from converting the discrete problem to a continuous problem via the Stiefel manifold, where convergence can be guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numerical examples show that better discrete filter designs can be sought via this hybrid descent method. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the numerical performance of a power penalty method for a linear parabolic complementarity problem arising from American option valuation. The penalized problem is a nonlinear parabolic partial differential equation (PDE). A fitted finite volume method and an implicit time-stepping scheme are used for, respectively, the spatial and time discretizations of the PDE. The rate of convergence of the penalty methods with respect to the penalty parameters is investigated both theoretically and numerically. The numerical robustness and computational effectiveness of the penalty method with respect to the market parameters are also studied and compared with those from an existing popular method, project successive over relaxation. [ABSTRACT FROM AUTHOR]

In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the optimal control problem is approximated by a sequence of optimal control problems involving only impulsive ordinary differential equations. Each of them can be viewed as a nonlinear optimization problem. For each of these approximated problems, the gradient formula of the cost functional can be derived and hence can be solved by many efficient optimization techniques. Consequently, the optimal control software, MISER, is applicable for the purpose. Then, we present some convergence results showing the relationship between the sequence of the optimal controls of the approximated problems and that of the original problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]