Optimal birth control of free horizon problems for predator-prey system with age-structure

We study optimal birth policies for three age-dependent populations in a predator-prey system, which is controlled by fertility. New results on problems with free final time and integral phase constraints are presented, the approximate controllability of system is discussed.     

Optimal ℋ∞-state feedback control for continuous-time linear systemsfeedback control for continuous-time linear systems

This paper proposes a convex programming method to achieve optimal -state feedback control for continuous-time linear systems. State space conditions, formulated in an appropriate parameter space, define a convex set containing all the stabilizing control gains that guarantee an upper bound on the -norm of the closed-loop transfer function. An optimization problem is then proposed, in order to minimize this upper bound over the previous convex set, furnishing the optimal -control gain as its optimal solution. A limiting bound for the optimum -norm can easily be calculated, and the proposed method will achieve minimum attenuation whenever a feasible state feedback controller exists. Generalizations to decentralized and output feedback control are also investigated. Numerical examples illustrate the theory.This research has been supported in part by grants from Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP and Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq—Brazil. The authors are grateful to the anonymous referees for their useful comments on this paper.     

Optimal boundary control of the wave equation with pointwise control constraints

In optimal control problems frequently pointwise control constraints appear. We consider a finite string that is fixed at one end and controlled via Dirichlet conditions at the other end with a given upper bound M for the L ^∞-norm of the control. The problem is to control the string to the zero state in a given finite time. If M is too small, no feasible control exists. If M is large enough, the optimal control problem to find an admissible control with minimal L ²-norm has a solution that we present in this paper.     

Optimal variational principle for backward stochastic control systems associated with Lévy processes

The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel’s martingales and an independent multi-dimensional Brownian motion,where Teugel’s martin- gales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see e.g.,Nualart and Schoutens’ paper in 2000).We derive the necessary and sufficient conditions for the existence of the op- timal control by means of convex variation methods and duality techniques.As an application,the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (or backward linear-quadratic problem,or BLQ problem for short) is discussed and characterized by a stochastic Hamilton system.     

Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems

In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.     

Optimal distributed control of nonlinear Cahn–Hilliard systems with computational realization

The goal of this work is to present some optimal control aspects of distributed systems described by nonlinear Cahn–Hilliard equations (CH). Theoretical conclusions on distributed control of CH system associated with quadratic criteria are obtained by the variational theory (see [17]). A computational result is stated by a new semi-discrete algorithm, constructed on the basis of the finite-element method with the updated (nonlinear) conjugate gradient method for minimizing the performance index efficiently. Finally, the implementation of a laboratory demonstration is included to show the efficiency of the proposed nonlinear scheme.     

A control point based curve with two exponential shape parameters

A generalization of a recently developed trigonometric Bézier curve is presented in this paper. The set of original basis functions are generalized also for non-trigonometric functions, and essential properties, such as linear independence, nonnegativity and partition of unity are proved. The new curve—contrary to the original one—can be defined by arbitrary number of control points meanwhile it preserves the properties of the original curve.     

Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE’s with a small parameter

In this paper, we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.     

Admission control for a multi-server queue with abandonment

In a M/M/N+M queue, when there are many customers waiting, it may be preferable to reject a new arrival rather than risk that arrival later abandoning without receiving service. On the other hand, rejecting new arrivals increases the percentage of time servers are idle, which also may not be desirable. We address these trade-offs by considering an admission control problem for a M/M/N+M queue when there are costs associated with customer abandonment, server idleness, and turning away customers. First, we formulate the relevant Markov decision process (MDP), show that the optimal policy is of threshold form, and provide a simple and efficient iterative algorithm that does not presuppose a bounded state space to compute the minimum infinite horizon expected average cost and associated threshold level. Under certain conditions we can guarantee that the algorithm provides an exact optimal solution when it stops; otherwise, the algorithm stops when a provided bound on the optimality gap is reached. Next, we solve the approximating diffusion control problem (DCP) that arises in the Halfin–Whitt many-server limit regime. This allows us to establish that the parameter space has a sharp division. Specifically, there is an optimal solution with a finite threshold level when the cost of an abandonment exceeds the cost of rejecting a customer; otherwise, there is an optimal solution that exercises no control. This analysis also yields a convenient analytic expression for the infinite horizon expected average cost as a function of the threshold level. Finally, we propose a policy for the original system that is based on the DCP solution, and show that this policy is asymptotically optimal. Our extensive numerical study shows that the control that arises from solving the DCP achieves a very similar cost to the control that arises from solving the MDP, even when the number of servers is small.     

Some aspects of reachability for parabolic boundary control problems with control constraints

A class of one-dimensional parabolic optimal boundary control problems is considered. The discussion includes Neumann, Robin, and Dirichlet boundary conditions. The reachability of a given target state in final time is discussed under box constraints on the control. As a mathematical tool, related exponential moment problems are investigated. Moreover, based on a detailed study of the adjoint state, a technique is presented to find the location and the number of the switching points of optimal bang-bang controls. Numerical examples illustrate this procedure.     

Special features of strongly coupled systems of convection–diffusion equations with two small parameters

Strong coupling of convection–diffusion equations with two small parameters generates a solution decomposition which differs significantly from that for the one-parameter case. We explain the basic features and prove pointwise estimates for the first-order derivatives which allow us to analyze the upwind finite difference scheme on layer-adapted meshes.     

Delay-range-dependent synchronization criterion for Lur’e systems with delay feedback control

In this paper, a master–slave synchronization scheme is investigated by using feedback control mechanism with time-varying delay. The time-delay is assumed to be a time-varying continuous function belonging to a given range. By constructing a novel Lyapunov–Krasovskii functional, which includes the information of the range, new delay-range-dependent synchronization criterion is established in term of LMI. It is shown that the new criterion improve some of the previous results in the earlier references. Simulation example is given to show the effectiveness and less conservatism of the proposed criterion.     

Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities

This paper presents a synthesis of an optimal control solution for cooperative collision avoidance strategies for aircraft (ships) with unequal turn capabilities in a close proximity coplanar encounter. The analytic expressions for the extremals are presented and their properties are analyzed. Simple algorithms for the synthesis of optimal control are developed. The structure of the synthesis is analyzed and its behavior with a change in the nondimensional turn rate ratio is studied. It is shown that Merz’s solution for identical aircraft (see Merz in Proc. Joint Automatic Control Conf., Paper 15-3, pp. 449–454, 1973; Navigation 20(2):144–152, 1973; Tarnopolskaya and Fulton in J. Optim. Theory Appl. 140(2):355–375, 2009) is a degenerate case of this more general solution. The results of this paper are useful for benchmarking and validating automated proximity management and collision avoidance systems.     

Fault tolerant saturated control for T–S fuzzy discrete-time systems with delays

In this paper, fault tolerant saturated control (FTSC) problem for discrete-time T–S fuzzy systems with delay is studied. Sufficient conditions for observer based control design with saturation constraints are developed. Based on a multiple Lyapunov functions and the slack variables, design conditions are formulated in LMI terms using the cone complementarity technique. The obtained results are illustrated on a numerical example showing fault detection, its localization and reconfiguration of the control law to maintain asymptotic stability even in the presence of both permanent sensor faults and saturation on the control.