Passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems

The potential clinical applications of adaptive neural network control for pharmacology in general, and anesthesia and critical care unit medicine in particular, are clearly apparent. Specifically, monitoring and controlling the depth of anesthesia in surgery is of particular importance. Nonnegative and compartmental models provide a broad framework for biological and physiological systems, including clinical pharmacology, and are well suited for developing models for closed-loop control of drug administration. In this paper, we develop a neural adaptive output feedback control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. The approach is applicable to nonlinear nonnegative systems with unmodeled dynamics of unknown dimension and guarantees that the physical system states remain in the nonnegative orthant of the state-space for nonnegative initial conditions. Finally, a numerical example involving the infusion of the anesthetic drug midazolam for maintaining a desired constant level of depth of anesthesia for noncardiac surgery is provided to demonstrate the efficacy of the proposed approach.     

输出反馈实现一类带不确定输入动态非线性系统的鲁棒几乎干扰解耦

研究一类带不确定输入动态非线性系统的输出反馈干扰抑制问题并基于观测器给出了输出反馈控制器 构造性的设计方法.所设计的控制器具有对可允许不确定动态的鲁棒性.不仅在L₂增益意义上抑制了干扰对输出 的影响,同时在ISS镇定意义上抑制了干扰对状态的影响.     

Passivity-based robust control of systems with redundant sensors and actuators

This paper considers passivity-based control of a class of uncertain linear, time-invariant systems having redundant sensors and actuators. The approach consists of robustly 'passifying'(i.e. rendering passive) the system, which is assumed to have affine parametric uncertainties in the system matrix as well as the input and output matrices. The passification is accomplished by finding constant matrices to be placed at the input and output of the system which will appropriately combine the sensor signals and distribute the control signals to the actuators. Sufficient conditions are first obtained for the system to remain passive for all parameter values that lie in a hyper-rectangular region in the parameter space. The conditions take the form of a set of linear matrix inequalities (LMIs). Next, the problem of finding an optimal sensor blending matrix is considered, which will maximize the region in the parameter space in which the system remains robustly passive. The dual problem of optimal control allocation is also considered, and a method is given for combined sensor blending and control allocation for robust passification. A method for reduction of the number of LMIs is investigated, and a numerical example is given for demonstrating the approach.     

State feedback for non-linear control systems

A theory of static state feedback for non-linear discrete-time systems is developed. The theory applies to non-linear systems possessing a recursive representation of the form x _k+1 =?(x _k , u_k ), where ? is a continuous function, and it deals with the construction of continuous state feedback functions that internally stabilize a given system. The theory yields an explicit method for the computation of stabilizing feedback functions, and several examples of the computation of such functions are provided.     

Internal model control with feedback compensation for uncertain non-linear systems

Control of non-linear systems by model-based strategies is often affected by model uncertainties. For these systems, internal model control with feedback compensation (IMC-FC), which consists of a non-linear model control and an error feedback loop, to achieve disturbance attenuation and offset-free performance, is proposed in this study. The matching conditions for the uncertainties of non-linear systems are not necessary, and adjustable parameters can easily be tuned to satisfy the particular specification. The underlying theoretical approach for the feedback compensation is the Lyapunov stability theory. The effectiveness of the proposed approach is illustrated by a simulation example on the composition control of a continuous stirred tank reactor. The theoretical analysis and simulation results show that the proposed IMCFC can reduce the effect of modelling uncertainties such that the performance of the control system is greatly improved.     

Optimal feedback control of non-linear systems

A method is proposed for computing optimal nonlinear feedback control laws. It is shown that the feedback loop satisfies a system of quasi-linear partial differential equations. This system is of first order when the dimensions of the state and the control vector are the same. Hereby, it degenerates into algebraic equations when the performance index does not depend on the control. These important results offer new ways for determining optimal feedback laws. Connections with the Volterra series and the Hamilton-Jacobi-Bellman equation are treated. Some examples are given to illustrate the advantages of this method.     

Optimal feedback control of non-linear systems

A fundamental method to solve functional optimization control problems is achieved through Hamilton-Jacobi theory. This method leads to feedback laws satisfying the HJB equation in a sense. On the basis of this approach, a design technique, applicable to a large class of optimization problems, is described. The technique is developed for systems of vth order. An example demonstrates the effectiveness of the determined controller to stabilize the inverted pendulum.     

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.     

遥操作机器人系统带记忆的鲁棒反馈控制

针对遥操作机器人系统的通信通道中存在通信时延，以及机器人模型存在不确定性，可能造成系统不稳定和操作性能降低的问题，提出在环境模型未知的条件下，利用鲁棒控制理论，采用力、位置和速度反馈的控制方法，使得系统稳定，并且具有良好的透明性，控制参数可通过Matlab的LMI工具箱方便地求取，仿真结果表明了该方法的有效性。     

Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.     

A procedure for simultaneously stabilizing a collection of single input linear systems using non-linear state feedback control

This paper considers the problem of simultaneously stabilizing a finite collection of single input linear systems. This stabilization is achieved using a single non-linear state feedback controller. The stability of the resulting closed loop system is established using a collection of quadratic Lyapunov functions. The main result of this paper is a sufficient condition for simultaneous stabilizability. Furthermore, when this sufficient condition is satisfied, the paper gives a formula for constructing the stabilizing feedback control law. The paper includes an example in which the stabilization procedure is applied to the stabilization of an F4E fighter aircraft.     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

Stable robust feedback control system design for unstable plants with input constraints using robust right coprime factorization

A stable robust control system design problem for unstable plants with input constraints is considered using robust right coprime factorization of nonlinear operator. For obtaining strong stability of the closed‐loop system of unstable plants with input constraints, a design scheme of robust nonhyphen‐linear control system is given based on robust right coprime factorization. Some conditions for the robustness and system output tracking of the unstable plant with input constraints are derived. Numerical examples are given to demonstrate the validity of the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Explicit input and output feedback control for discrete-time systems

A new form of output feedback control, referred herein as explicit input and output feedback control (EIOC), is proposed for linear discrete-time systems. Unlike the conventional dynamic output feedback control described by a state-space model, the proposed EIOC has a batch form, where current control is explicitly expressed using current and past system outputs and past control inputs over a recent time horizon. The paper formulates the EIOC law and discusses its features and desirable characteristics. The EIOC is shown to be equivalent to static output feedback control for an augmented system. The coefficients of the EIOC are obtained to achieve the H _∞ performance criterion. Finally, numerical examples are presented to illustrate the effectiveness of the EIOC.     

Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty

The robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with uncertain parameters is studied. Based on the independence of uncertain parameters and stochastic excitations, the non-linear stochastic optimal control for the nominal quasi-Hamiltonian system with average-value parameters is first obtained by using the stochastic averaging method and stochastic dynamical programming principle. Then, the means and standard deviations of root-mean-square responses, control effectiveness and control efficiency for the uncertain quasi-Hamiltonian system are calculated by using the stochastic averaging method and the probabilistic analysis. By introducing the sensitivity of the variation coefficients of controlled root-mean-square responses, control effectiveness and control efficiency to those of uncertain parameters, the robustness of the non-linear stochastic optimal control is evaluated. Two examples are given to illustrate the proposed control procedure and its robustness.     

Vector dissipativity theory and stability of feedback interconnections for large-scale non-linear dynamical systems

Recent technological demands have required the analysis and control design of increasingly complex, large-scale non-linear dynamical systems. In analysing these large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper we develop an analysis framework for large-scale dynamical systems based on vector dissipativity notions. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the composite large-scale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. Furthermore, extended Kalman–Yakubovich–Popov conditions, in terms of the subsystem dynamics and interconnection constraints, characterizing vector dissipativeness via vector system storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for large-scale non-linear dynamical systems using vector Lyapunov functions.     

具有反馈增益不确定的Delta算子系统H∞控制

基于线性矩阵不等式（LMI）方法，研究Delta算子系统状态反馈增益具有加性不确定时的H∞非脆弱控制器的设计问题．给出既能保证闭环Delta算子系统稳定，又有一定H∞性能的充分必要条件．利用相关引理把该充分必要条件转化为LMI形式．数值算例表明。所提出的设计方法是有效的．