Bang-Bang Principle of Time Optimal Controls and Null Controllability of Fractional Order Parabolic Equations

In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty open subset of Ω. The problem is reduced to a new controllability property for this equation, i.e. the null controllability of the system at any given time T 〉 0 when the control is restricted to be active in ω× E, where E is any given subset of [0, T] with positive （Legesgue） measure. The desired controllability result is established by means of a sharp observability estimate on the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano, and a delicate result in the measure theory due to Lions.

Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems

In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and L1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.

Weighted Time-Based Global Hierarchical Path Planning in Dynamic Environment

A weighted time-based global hierarchical path planning method is proposed to obtain the global optimal path from the starting point to the destination with time optimal control. First, the grid-or graph-based modeling is performed and the environment is divided into a set of grids or nodes. Then two time-based features of time interval and time cost are presented. The time intervals for each grid are built, during each interval the condition of the grid remains stable, and a time cost of passing through the grid is defined and assigned to each interval. Furthermore, the weight is introduced for taking both time and distance into consideration, and thus a sequence of multiscale paths with total time cost can be achieved. Experimental results show that the proposed method can handle the complex dynamic environment, obtain the global time optimal path and has the potential to be applied to the autonomous robot navigation and traffic environment.

EQUIVALENCE OF THREE DIFFERENT KINDS OF OPTIMAL CONTROL PROBLEMS FOR STOKES EQUATIONS

This article presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems, and optimal time control problems. Controlled systems in this study are internally controlled Stokes equations.

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.

Time optimal quantum control of two-qubit systems

We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms.We derive an explicit formula to compute the minimum time required to steer the system from an initial state to a specified final state.As applications the minimal time to implement Controlled-NOT gate,SWAP gate and Controlled-U gate is calculated in detail.The experimental realizations of these quantum gates are explicitly presented.

Application of Bat Algorithm Based Time Optimal Control in Multi-robots Formation Reconfiguration

This paper proposes a Bat Algorithm （BA） based Control Parameterization and Time Discretization （BA-CPTD） method to acquire time optimal control law for formation reconfiguration of multi-robots system. In this method, the problem of seeking for time optimal control law is converted into a parameter optimization problem by control parameterization and time discretization, so that the control law can be derived with BA. The actual state of a multi-robots system is then introduced as feedback information to eliminate formation error. This method can cope with the situations where the accurate mathematical model of a system is unavailable or the disturbance from the environment exists. Field experiments have verified the effectiveness of the proposed method and shown that formation converges faster than some existing methods. Further experiment results illustrate that the time optimal control law is able to provide smooth control input for robots to follow, so that the desired formation can be attained rapidly with minor formation error. The formation error will finally be eliminated by using actual state as feedback.

Trajectory optimization and applications using high performance solar sails

The high performance solar sail can enable fast missions to the outer solar system and produce exotic non-Keplerian orbits.As there is no fuel consumption,mission trajectories for solar sail spacecraft are typically optimized with respect to flight time.Several investigations focused on interstellar probe missions have been made,including optimal methods and new objective functions. Two modes of interstellar mission trajectories,namely 'direct flyby' and 'angular momentum reversal trajectory',are compared and discussed.As a foundation,a 3D non-dimensional dynamic model for an ideal plane solar sail is introduced as well as an optimal control framework.A newly found periodic double angular momentum reversal trajectory is presented,and some properties and potential applications of this kind of inverse orbits are illustrated.The method how to achieve the minimum periodic inverse orbit is also briefly elucidated.

MINIMUM PERIOD CONTROL PROBLEM FOR INFINITE DIMENSIONAL SYSTEM

In order to solve the so-called minimum period control problem for a class of abstract evolutionary systems, the authors study an infinite dimensional time optimal control problem with mixed type target set. To the latter problem complete results are established, which then are applied to the former to derive the desirable answer.