Robust optimal control: low-error operation for the longest time

The problem of maximising the time during which an open-loop system can operate without exceeding a specified error bound is considered for linear systems that are subject to uncertainties about their parameters and their initial conditions, and whose operation is hampered by disturbance signals. The objective is to characterise an optimal input signal that keeps performance errors within specified bounds for the longest time. It is shown that such an input signal exists, and that it can be approximated by a bang-bang input signal without significantly affecting performance.     

Robust optimal control during feedback disruption for nonlinear systems controlled by an observer-based output feedback controller

In this paper, a robust optimal control problem during feedback disruption is considered for a class of nonlinear systems which have been controlled by an observer-based output feedback controller. It is shown that during feedback disruption, there exists an optimal control input which keeps both system states and observer errors within a specified bound for the longest time. Then, it is shown that such an optimal control input can be practically implemented by using a bang-bang control input in terms of control performance. One numerical and one practical examples are given for clear illustration.     

Optimal periodic output feedback control: a continuous-time approach and a case study

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of high-precision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.     

Adaptive output feedback control using fault compensation and fault estimation for linear system with actuator failure

The problem of linear systems subject to actuator faults（outage,loss of efectiveness and stuck）,parameter uncertainties and external disturbances is considered.An active fault compensation control law is designed which utilizes compensation in such a way that uncertainties,disturbances and the occurrence of actuator faults are account for.The main idea is designing a robust adaptive output feedback controller by automatically compensating the fault dynamics to render the close-loop stability.According to the information from the adaptive mechanism,the updating control law is derived such that all the parameters of the unknown input signal are bounded.Furthermore,a disturbance decoupled fault reconstruction scheme is presented to evaluate the severity of the fault and to indicate how fault accommodation should be implemented.The advantage of fault compensation is that the dynamics caused by faults can be accommodated online.The proposed design method is illustrated on a rocket fairing structural-acoustic model.     

An optimal control for a flotation circuit

The optimal operation of a flotation circuit, which is used to separate two minerals is discussed. The optimal control of the flotation circuit at Lake Dufault is found to be a bang-bang control, to contain a singular sub-arc, or to be totally singular depending on the various practical constraints. The influence of the time-delay on the optimal control of the flotation circuit is then investigated. Although the influence of the delay is quite significant, the basic structure of the optimal policy remains roughly the same. Thus it is not unreasonable to ignore the delay, although the optimality suffers from this.     

人工神经网络在伺服最优鲁棒控制中的应用

提出了一种基于神经网络的伺服最优鲁棒控制，介绍了利用神经网络的学习特性对被控对象的模型不确定性进行补偿和控制。仿真结果表明，所控制器优于一般伺服控制的性能，并有较强的鲁棒性。     

Direct discrete time design of robust state derivative feedback control laws

This paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.     

Simultaneous H2/H∞ optimal control The state feedback case

A simultaneous H₂/H_∞ control problem is considered. This problem seeks to minimize the H₂ norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H_∞ norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (Automatica, 27, 307–316, 1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H₂/H_∞ problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H₂ norm performance measure. This class of problems subsumes the class of regular problems.     

一类不确定系统的最优鲁棒控制

运用最优方法探讨了一类模型不确定系统的鲁棒控制问题。定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,并通过调整标称控制器最小化加权敏感度误差在整个频段上的方差,从而为一类不确定系统提供了一种最优的鲁棒控制器设计方法,可使系统性能对模型误差具有良好的鲁棒性。针对控制工程领域典型的一阶时滞系统进行仿真研究,其结果说明了该方法的有效性。     

Optimal robust control of nonlinear time-delay systems: Maintaining low operating errors during feedback outages

The problem of maintaining low operating errors during feedback outages is considered for a class of nonlinear systems with time-delays in the input channel. It is shown that there are optimal controllers that keep operating errors below a specified bound for the longest time possible. Furthermore, it is shown that optimal performance can be approximated as closely as desired by using bang-bang controllers – controllers that are relatively easy to calculate and implement.     

Depth control of autonomous underwater vehicles using indirect robust control method

In this article, we propose a robust depth control design scheme for autonomous underwater vehicles (AUVs) in the presence of hydrodynamic parameter uncertainties and disturbances. The controller is designed via a new indirect robust control method that handles the uncertainties by formulating the uncertainty bounds into the cost functional and then transforming the robust control problem into an equivalent optimal control problem. Both robust asymptotic stability and optimality can be achieved and proved with this new formulation. The θ-D method is utilised to solve the resultant nonlinear optimal control problem such that an approximate closed-form feedback controller can be obtained and thus is easy to implement onboard without intensive computation load. Simulation results demonstrate that robust depth control is accomplished under the system parameter uncertainties and disturbances with small control fin deflection requirement.     

On receding horizon feedback control

Receding horizon feedback control (RHFC) was originally introduced as an easy method for designing stable state-feedback controllers for linear systems. Here those results are generalized to the control of nonlinear autonomous systems, and we develop a performance index which is minimized by the RHFC (inverse optimal control problem). Previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the RHFC horizon distance a function of the state. That functional dependence was implicit and difficult to implement on-line. Here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state.     

Optimal control of a solar collector loop using a distributed-lumped model

This paper considers the optimal control of a solar collector loop described by a bilinear distributed parameter model for the collector fluid temperature and a bilinear lumped parameter model for the storage fluid temperature. The objective is to control the collector fluid velocity so as to maximize the net energy collected over a fixed time period. Necessary conditions for optimality, given by a set of equations whose solution yields the optimal control, are derived. It is shown that the optimal control is an open-loop, bang-bang control which depends on two terms: a measurable quantity which depends on the state of the collector fluid, and a quantity which depends on a future knowledge of the weather data. It is also shown that for the case in which only two switches occur during the period of operation, the optimal control depends only on the temperature difference across the collector. Thus, one can construct a feedback on/off controller for the system provided that it is known a priori that only two switches will occur during the time interval under consideration.     

Realization of a bounded feedback in a nonlinear control problem

We substantiate a method for design of a limited feedback to control a system whose mathematical model includes a nonlinear state function. Designing such a feedback is based on a positional solution of auxiliary optimal control problems which provides the transition from the vicinity of one equilibrium state to the vicinity of a new equilibrium state and stabilization of the system in the new state. Preassigned additional constrains on the trajectory of the control system are satisfied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 108–116, January–February 2009.     

Optimal control of a single-link flexible manipulator

This paper deals with an exact state space dynamic model for manipulators with flexible links. We use the Bernoulli-Euler beam equations to derive a frequency domain matrix transfer function. This transfer function is then used to compute the Laplace transform of the state vector as a function of the lateral position along a single link manipulator. The problem of optimal end point control of the beam is then addressed. A sixth-order state space model is derived for the manipulator and the controller is based on this model. Several control laws are studied for this model. Next, the manipulator is modeled as eighth order but the control law based on the sixth-order model is retained. We then estimate the six states from the output of the eighth-order model and feed these states back to the controller to derive the control torque used to drive the manipulator. A filter is introduced to compensate for spillover. The results are very satisfactory, and are illustrated by simulated case studies.     

Optimal decentralized control of dynamic systems

In this paper, several aspects of decentralized control theory applied to dynamic systems are studied. First of all, some classical definitions about matricial functions and new results on gradient calculations are presented. In the following we generalize to matricial problems the method of gradient projection of Rosen. Finally, some aspects of stability, initialization and initial condition independence are studied in detail, and two numerical examples are considered in order to emphasize the advantages of the given procedure: the decentralized Kalman filter and the optimal power-frequency control.     

基于最佳滑移率的ABS复合控制器设计

针对目前的防抱制动系统(ABS)控制算法只局限于理论研究,不能在实际的ABS系统中得到应用的现状,提出了一种实用的ABS复合控制方案.研究了基于最佳滑移率的ABS控制器设计目标,提出了一种实用的鲁棒、逻辑门限复合控制方案,给出了控制器的设计方法.在单轮ABS系统上进行了试验,试验结果表明,在两种不同路面条件下,实际滑移率都能保持在最佳滑移率附近.因此,所提复合控制方案是可行和有效的.     

Optimal control for a polynomial system with a quadratic criterion over infinite horizon

This paper proposes an optimal control algorithm for a polynomial system with a quadratic criterion over infinite horizon. The designed regulator gives a closed-form solution to the infinite horizon optimal control problem for a polynomial system with a quadratic criterion. The obtained solution consists of a feedback control law obtained by solving a Riccati algebraic equation dependent on the state. Numerical simulations in the example show advantages of the developed algorithm.     

Optimal controllers and output feedback stabilization

In this paper the output feedback stabilizability problem is explored in terms of control Lyapunov functions. Sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem. Our main results extends those developed in [31] and generalize a theorem due to Sontag [23].