Preview control for a class of linear stochastic systems with multiplicative noise

ABSTRACT

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective.     

增广控制的延时补偿法

本文提出适合于综合多延时系统的增广控制的方法,给出其能稳、能检测及最优控制存在的条件,与增广状态方法相比,增广控制方法的优点在于延时补偿的通道少、能用于连续系统的延时补偿、不提高状态及相应的Riccati方程的维数,即计算工作量少。     

Design of an augmented automatic choosing control with constrained input by Hamiltonian and absolute antiwindup measures

In this paper, we present a novel approach for a nonlinear feedback control which is called an augmented automatic choosing control (AACC) of the antiwindup type for nonlinear systems with constrained inputs. Constant terms which arise from section-wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by the genetic algorithm so as to minimize a performance made of the Hamiltonian and the absolute antiwindup measure. This approach is applied to a field excitation control problem of a power system to demonstrate the superiority of the AACC. Simulation results show that the new controller can improve performance remarkably well. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Least-restrictive robust periodic model predictive control applied to room temperature regulation

State-feedback model predictive control (MPC) of constrained discrete-time periodic affine systems is considered. The periodic systems’ states and inputs are subject to periodically time-dependent, hard, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The objective is to design MPC laws that robustly enforce constraint satisfaction in a manner that is least-restrictive, i.e., have the largest possible domain. The proposed design method is demonstrated on a building climate control example. The proposed method is directly applicable to time-invariant MPC.     

Two-stage estimation of time-invariant and time-varying parameters in linear systems†

A two-stage method for estimating time-invariant and time-varying parameters in linear systems is developed. The linear system is decomposed into two subsystems which have time-invariant and time-varying parameters, respectively. The unknown time-varying parameters are considered as control inputs and a linear state regulator quadratic cost function dynamic optimization problem is formulated. The solution of the associated two-point boundary-value problem for the optimum control results in an estimate for the time-varying parameters. The time-invariant parameters are estimated by a minimum mean-square error solution of a set of linear equations obtained by discretization of augmented state equations. The method is computationally simple and its effectiveness is illustrated by numerous examples.     

Robust practical output regulation for a class of uncertain linear minimum‐phase systems by output‐based event‐triggered control

In this paper, we consider the robust practical output regulation problem for a class of SISO uncertain linear minimum‐phase systems subject to external disturbances by an output‐based event‐triggered control law, where the reference inputs and the external disturbances are both generated by a so‐called exosystem with known dynamics. Our approach consists of two steps. First, on the basis of the internal model principle, we convert the problem into the robust practical stabilization problem of a well‐defined augmented system. Second, we design an output‐based event‐triggered mechanism and an output‐based event‐triggered control law to solve the stabilization problem, which in turn leads to the solvability of the original problem. What is more, we show that the event‐triggered mechanism prevents the Zeno behavior from happening. A numerical example is given to illustrate the design. Copyright © 2017 John Wiley & Sons, Ltd.     

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.     

一类线性离散广义系统最优预见控制器设计

提出一类广义线性离散系统的预见控制问题.首先,利用差分算子构造扩大误差系统,然后通过引入一些恒等式,把可预见的目标信号的差分也包含在扩大误差系统的状态向量中,把所考虑的广义系统的预见控制问题转化为一个形式上的普通广义系统的控制问题.由熟知的广义系统最优控制理论的结论,得到广义系统的带有预见作用的控制器.对扩大误差系统的R-能稳性和能检测性进行了详细讨论.     

The preview control of a class of linear systems and its application in the fault-tolerant control theory

In the fault-tolerant control theory based on model following control, the desired signal of the control system is the output of a reference system. This paper is concerned with the design of the preview controller for a class of fault systems. A composite vector is introduced by including error vector, fault system state vector and reference system state vector. Then, we derived an augmented system from the known system equation, in which the reference input has equal status with the desired signal in the traditional preview control theory. Therefore, we can use the known theory to design the preview controller for the augmented system, then the preview controller of the original fault system can be obtained by the integration method. This paper strictly discusses the connection between stabilisation and detectability of the augmented system and the corresponding characteristics of the original system. Finally, by applying this theory to a real steam generator water level control system, it is found that the actions of the reference input preview and the fault signal preview can effectively eliminate the effect of the fault signal on the water level of the steam generator. The simulation shows the effectiveness of the controller designed.     

Overapproximating Reachable Sets by Hamilton-Jacobi Projections

In earlier work, we showed that the set of states which can reach a target set of a continuous dynamic game is the zero sublevel set of the viscosity solution of a time dependent Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE). We have developed a numerical tool—based on the level set methods of Osher and Sethian—for computing these sets, and we can accurately calculate them for a range of continuous and hybrid systems in which control inputs are pitted against disturbance inputs. The cost of our algorithm, like that of all convergent numerical schemes, increases exponentially with the dimension of the state space. In this paper, we devise and implement a method that projects the true reachable set of a high dimensional system into a collection of lower dimensional subspaces where computation is less expensive. We formulate a method to evolve the lower dimensional reachable sets such that they are each an overapproximation of the full reachable set, and thus their intersection will also be an overapproximation of the reachable set. The method uses a lower dimensional HJI PDE for each projection with a set of disturbance inputs augmented with the unmodeled dimensions of that projection's subspace. We illustrate our method on two examples in three dimensions using two dimensional projections, and we discuss issues related to the selection of appropriate projection subspaces.     

Designing fault detection observers for linear systems with mismatched unknown inputs

Algebraic unknown input observers (UIOs) that have been previously reported in the literature can be constructed under the assumption that linear systems with unknown inputs satisfy the so-called observer matching condition. This condition restricts practical applications of UIOs for fault detection and isolation (FDI). We present an algebraic design for fault detection observers (FDOs) for the case in which the observer matching condition is not satisfied. To loosen the restriction imposed by the observer matching condition, the UIO design method combined with the unknown input modeling technique is proposed to design an FDO that decouples the effect of mismatched unknown inputs. To do this, first, unknown inputs that denote the faults of no interest and process disturbances are decomposed into algebraically rejectable unknown inputs and modeled unknown inputs such that the observer matching condition is satisfied. Under the assumption that mismatched unknown inputs are deterministic and can be expressed as the responses of fictitious autonomous dynamical systems, an augmented system is obtained by combining the original system model with the unknown input model. Finally, through the design technique of a UIO for the augmented system, a reduced-order FDO is constructed to estimate an augmented state vector that consists of both the original state variables and the augmentative state variables. The estimated state is then used to generate the residual, which should be designed to be insensitive to unknown inputs while being sensitive to the faults of interest. Two numerical examples are provided to show the usefulness and the feasibility of the presented approach.     

A note on the stability of habituating process control

For a class of single-output processes with at least two control inputs, this note proposes a simple control design and study its stability. To this end, the process is factorized into a stable and non-minimum-phase factor and a possible unstable minimum-phase factor. By the addition of a (low-pass) filter of suitable dimension, one can obtain a process factorization where the minimum-phase factor has a proper and stable inverse. Once the plant has been factorized in this form, the proposed control synthesis method is composed of two main steps; namely, output regulation based on the non-minimum-phase factor and design of an optimization-based divider to compute the value corresponding to the multiple inputs. In this way, one obtains the control transfer function of each control input in a parallel control architecture. An analysis of the control structure is provided, giving sufficient conditions for the stability of the control loop.     

插值算法在模糊控制中的应用与仿真研究

该文针对目前某些模糊控制系统在控制过程中精度比较低的问题,将模糊控制系统离线得到的模糊控制表与双线性插值算法结合起来,提出一种新的基于在线插值的模糊控制系统的设计方法,用此方法使模糊控制器输入、输出值保持连续变化,以此来克服控制器因输入输出量化所造成的调节死区与可能出现的稳态等缺点,从而来达到提高模糊控制系统控制精度的目的。在某舰船控制系统的仿真例子说明了此方法的有效性。     

Cooperative optimal preview tracking control of continuous-time multi-agent systems

This paper presents the cooperative preview control method for continuous-time multi-agent systems with a time-invariant directed communication topology. First, the cooperative tracking preview control problem is transformed into the optimal regulation problem of an augmented system. Next, by applying the results of the standard optimal preview control of continuous-time linear systems, a controller of the augmented system is obtained. Furthermore, the stabilisability and detectability of the augmented system are studied under the fixed digraph and the prescribed leader. Then, we derive the controller of multi-agent systems with error integral and preview action that can guarantee the achievement of cooperative optimal preview tracking. Finally, the effectiveness of the controller is shown by numerical simulations.     

A QFT SUBSONIC ENVELOPE FLIGHT CONTROL SYSTEM DESIGN

An aircraft's response to control inputs varies widely throughout its full flight envelope. Furthermore, the aircraft configuration impacts control response through variations in centre of gravity and moments of inertia. Quantitative feedback theory (QFT) is a robust control system design method which provides a full-envelope flight control system design and gives the engineer direct control over compensator order and gain. A full subsonic flight envelope FCS is designed for using QFT for four representative aircraft configurations. Flying qualities are embedded in the longitudinal design by using a control variable which varies with the aircraft's energy state throughout the flight envelope. Linear simulations with realistically large control inputs are used to validate the design. © 1997 by John Wiley & Sons, Ltd. This paper was prepared under the auspices of the US Government and it is therefore not subject to copyright in the US.     

Asymptotic stabilization with group-wise sparse input based on control Lyapunov function approach

This study proposes a novel stabilizing controller for nonlinear systems using group-wise sparse inputs. The input variables are divided into several groups. In the situations when the input constraints can be ignored, one input becomes active for each group at each moment. Our method improves energy efficiency, as sparse input vectors often reduce the standby power of inactive actuators. Large-scale systems, such as those consisting of multiple subsystems, often require the manipulation of multiple inputs simultaneously to be controlled. Our method can be applied to such systems due to the group-wise sparsity of the inputs. The proposed controller is based on the control Lyapunov function approach and includes Sontag's universal formula as a special case. The controllers designed in our method have best-effort property, which means even when a restriction for the decreasing rate of the Lyapunov function cannot be fulfilled, the controller minimizes the time derivative of the Lyapunov function within the input constraint. The effectiveness of the proposed method can be confirmed through simulations.     

A novel redesign framework to extend the application scope of a class of disturbance‐rejection algorithms

In this paper, a novel redesign method is developed for a class of disturbance‐rejection algorithms so that they can be applied to pure‐feedback nonaffine‐in‐control nonlinear systems with matched and mismatched disturbances. First, a series of augmented dynamical equations, which evolve faster than the original system, are constructed to establish a boundary‐layer subsystem to derive the virtual and actual inputs for the nominal system. Then, the composite interconnected system is studied in the standard singular perturbed form. In the slow timescale, the reduced slow subsystem (RSS) is transformed into the chain of integrators form in the error coordinate, for which the existing antidisturbance methods can be employed. The tracking performance of the closed‐loop system is approximated by RSS under singular perturbation theory. The proposed redesign method is adopted to three existing disturbance‐rejection algorithms for a pure‐feedback nonaffine‐in‐control numerical example in the presence of matched and mismatched disturbances. The effectiveness is demonstrated by simulation experimental results.     

网络控制系统的对象建模

网络控制系统(NCS)中的被控对象是包含工业控制对象和通讯网络的广义被控对象,其模型是时变不确定的,十分复杂。在考虑了单包传输、多包传输、数据包丢失、延时、随机干扰等情况下,用一种统一的形式,建立网络控制系统的模型。对广义被控对象进行分析和建模有利于网络控制系统控制器的分析和设计。在实际工程应用中在分析了NCS网络特性基础上。皆可按该方法对广义被控对象建模,然后再进行控制器设计。