Time-optimal control strategy for saturating linear discrete systems

An easily implemented strategy for obtaining the required minimal-time and time-optimal control sequence for a given initial state of an nth-order linear discrete system with constraints on the input is described. This strategy uses the boundary faces of the reachable set for the determination of the minimal time. The time-optimal control sequence is achieved by dividing the reachable set into linear and saturated parts.     

基于改进遗传算法的时间最优控制问题求解

对原有遗传算法的不足进行分析 ,提出改进的遗传算法。对于高维、高精度问题 ,改进算法相对原算法可节省大量存储空间和解码时间。提出的选择算子仅与父代的大小顺序有关 ,既可避免原算法对适应值必须为正的限制 ,又可避免算法过早收敛到局部解。证明了新算法的全局收敛性 ,并对新的选择算子进行了性能分析。将改进的遗传算法引入受约束时间最优控制问题的求解 ,获得了令人满意的结果     

Stabilization bound of discrete two-time-scale systems

In this paper, the exact ε-bound problem in various types of discrete two-time-scale (TTS) system is considered. A set of stability criteria based on the frequency domain representation is derived. Two interesting examples are used to demonstrate the proposed scheme.     

Time-optimal production control in a manufacturing system

This study demonstrates the use of control engineering techniques to regulate the product inventory levels of a workshop in a manufacturing system by manipulating the number of machines and the labour time employed during production. The production policy that minimizes the production time is obtained by time-optimal control techniques.     

Order-reducing approximation of two-time-scale discrete linear time-varying systems

In this paper we study a two-time-scale discrete-time linear time-varying system. We heuristically find a reduced-order approximation to its asymptotic behaviour as the time-scale separation tends to infinity. This approximation results in a white noise representation of the fast state vector, and a corresponding approximation error in the slow state vector. After introducing the approximate system we define concepts of continuity and rate of variation which are needed in the discrete-time analysis. We then prove that as the time-scale separation increases, the state of the reduced-order system asymptotically coincides with the slow state of the original system in the mean-square sense on compact time intervals. We also find the order of the slow state approximation error covariance.     

Time-optimal control of a single-DOF mechanical system withfriction

Presents the exact solution to the minimum-time optimal control problem of a single-degree-of-freedom (DOF) mechanical systems with friction. In particular, the optimal control input can be synthesized in feedback form. The effect of Coulomb friction, which has been ignored or precompensated in prior works, is taken into full account. As a result, the admissible range of control input can be maximized so as to achieve faster responses. A practical example using a direct-driven single-DOF robotic manipulator is discussed to demonstrate the practical use of the optimal solution     

Time-optimal control for discrete-time hybrid automata

In this paper, the problem of time-optimal control for hybrid systems with discrete-time dynamics is considered. The hybrid controller steers all trajectories starting from a maximal set to a given target set in minimum time. We derive an algorithm that computes this maximal winning set. Also, algorithms for the computation of level sets associated with the value function rather than the value function itself are presented. We show that by solving the reachability problem for the discrete time hybrid automata we obtain the time optimal solution as well. The control synthesis is subject to hard constraints on both control inputs and states. For linear discrete-time dynamics, linear programming and quantifier elimination techniques are employed for the backward reachability analysis. Emphasis is given on the computation of operators for non-convex sets using an extended convex hull approach. A two-tank example is considered in order to demonstrate the techniques of the paper.     

Time-optimal feedback control for small disturbances

This paper introduces a new technique for the analysis of time-optimal systems having multidimensional inputs. The method provides a cellular decomposition of the controllable set for small response times for a new generic class of systems called "minimally controllable systems." The decomposition permits a complete study of the time-optimal flow near the origin and forms the basis for the synthesis of closed-loop optimal control. The method, while generally applicable, is restricted here to the simplest, nontrivial case of third-order systems with two-dimensional controls.     

Time-optimal control of a particle in a dielectrophoretic system

We study the time-optimal control of a particle in a dielectrophoretic system. This system consists of a time-varying nonuniform electric field which acts upon the particle by creating a dipole within it. The interaction between the induced dipole and the electric field generates the motion of the particle. The control is the voltage on the electrodes which induces the electric field. Since we are considering the motion of a particle on an invariant line in a chamber filled with fluid flowing at low Reynolds number, the dynamics have a two dimensional state; one for the particle position and the other for the induced dipole moment. In regard to time-optimal control, we address the issue of existence and uniqueness of optimal trajectories, and explicitly compute the optimal control and the corresponding minimum time. Finally, we cast our analysis in the framework of symplectic reduction theory in order to provide geometric insight into the problem.     

Multirate sampled-data control of two-time-scale systems

Two-time-scale decoupling is adopted to obtain slow and fast subsystems. Based on these subsystems, a multirate composite control strategy is derived. It is shown how a recently presented multirate scheme can be modified to handle slow, nonzero mean disturbances, by introducing time incremental models. The improvements with the given multirate control law are illustrated by an example     

Time-optimal feedback control laws for certain third-order relay control systems

Time-optimal feedback control laws for six third-order plants having real, non-positive eigenvalues and a single saturable control input are calculated explicitly by direct application of Gulko's predictive control strategy. Errors in a previous treatment of three of the plants are discussed.     

基于AGA的时间最优机械臂轨迹规划算法*

根据机械臂运动学约束,提出了关节空间基于自适应遗传算法(AGA)的3-5-3多项式插值轨迹规划算法。利用运动学约束,以最优时间为目标,针对关节型机器人在静态环境下点到点的轨迹规划问题,利用AGA算法解算多项式插值的时间。通过与基于GA的3-5-3多项式机械臂轨迹规划进化曲线和运动位置、速度、加速度曲线对比,证明该方法在算法收敛、运行平稳度上都有突出优点。     

基于信赖域算法的机械臂时间最优轨迹规划

为了提高机械臂的工作效率,提出了一种新的时间最优轨迹规划方法.通过逆运动学运算得到与任务空间轨迹对应的关节空间位置序列,采用7次B样条曲线构造关节空间插值轨迹,将运动学约束转换为对B样条轨迹曲线控制顶点的约束,并适当放大约束条件,然后采用信赖域方法求解时间优化问题,从而规划出速度、加速度和脉动均连续且满足运动学约束的时间最优轨迹.仿真结果验证了所提出时间最优轨迹规划方法的有效性.     

Time-optimal control with finite bandwidth

Time-optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving regime in many physical systems, these capabilities have yet to be fully exploited for the precise control of quantum systems, as other limitations, such as the generation of higher harmonics or the finite response time of the control apparatus, prevent the implementation of theoretical time-optimal control. Here we present a method to achieve time-optimal control of qubit systems that can take advantage of fast driving beyond the rotating wave approximation. We exploit results from time-optimal control theory to design driving protocols that can be implemented with realistic, finite-bandwidth control fields, and we find a relationship between bandwidth limitations and achievable control fidelity.     

Output feedback control of linear two-time-scale systems

Output feedback control of linear time-invariant singularly perturbed systems is studied. The set of all compensators that stabilize a singularly perturbed system while preserving its two-time-scale structure is parameterized. The parameterization is used to show that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The parallel connection of the two compensators forms a two-frequency-scale stabilizing compensator for the singularly perturbed system.     

Event-triggered output feedback control for two-time-scale systems with structured uncertainty

This paper investigates the event-triggered output feedback control problem for the two-time-scale systems with structured uncertainty. Due to the non-ignorable problem in applications such as equipment aging or parameter drifting, the robustness of the designed controller is worth discussing. A dynamic event-triggered scheme is proposed to reduce the computational cost of the control signal. The results indicate that with the proposed event-triggered controller, the system can achieve asymptotic stability without some common restrictions on the fast system rather than practical stability. Moreover, the Zeno behavior is excluded. Simulation examples with comparison studies illustrate the effectiveness of the proposed method.     

Fuzzy logic-based design of the generalized adaptation algorithm for the discrete control system of flexible spacecraft

Consideration was given to a generalization of an earlier adaptation algorithm developed for the case where two elastic modes make significant contribution to the elastic oscillations arising in the spacecraft structure under the action of discrete control. Sensitivity of the individual modes of elastic oscillations to the adaptation parameter, the discreteness period T ₀ of the control system, was analyzed. In addition to the previous algorithm, designed were relations in other linguistic variables and the control structure carrying out the choice of the working areas of the adapted parameter and its transition from one domain to another with the aim of providing successive damping of both significant modes of elastic oscillations. Results of modeling a flexible spacecraft with adaptive control system were presented.     

Time-optimal plug&control for integrating and FOPDT processes

The plug&control feature (i.e. to automatically make the controller work properly after simply connecting it in the control architecture, without further intervention from the operator) is desired in industrial regulators in order to minimize the tuning effort from the user and in order to speed up the startup of the controller. In this context, a new strategy for plug&control is proposed for integrating and first order plus dead time (FOPDT) processes. It is based on the use of three-state and PID control, and on the use of a simple least-squares based identification technique. The main advantage of the methodology is that it is time-optimal, i.e. the process output attains the desired set-point value in minimum time, subject to the saturation limits of the actuator. Simulation results are given to show the effectiveness of the method.     

State feedback controller design of two-time-scale discrete systems via singular perturbation approach

The design of a state feedback controller for a two-time-scale discrete-time system is considered via a two-stage design approach. After discrete-time modelling via slow and fast sampling rates has been discussed, state feedback design approaches for the fast sampling model (i.e. the two-stage design approach and the direct approach) are studied, and the relation between them is clarified. Following these results, the eigenvalue assignment and the stabilizing problems are investigated.