Performance improvement of robust controllers for polynomially uncertain systems

This paper is concerned with the high-performance robust control of discrete-time linear time-invariant (LTI) systems with semi-algebraic uncertainty regions. It is assumed that a robustly stabilizing static controller is given whose gain depends polynomially on the uncertain variables. The problem of tuning this parameter-dependent gain with respect to a prescribed quadratic cost function is formulated as a sum-of-squares (SOS) optimization. This method leads to a near-optimal controller whose performance is better than that of the initial controller. It is shown that the results derived in the present work encompass the ones obtained in a recent paper. The efficacy of the results is elucidated by an example.     

Robust controllability of linear stochastic uncertain systems

The paper extends the concept of robust controllability via linear state feedback to stochastic uncertain systems. We show that the controllability of a stochastic uncertain system can be characterized using solutions to a game-type differential Riccati equation.     

Robust stabilization of uncertain nonholonomic systems with strong nonlinear drifts

This paper investigates the robust stabilization of the nonholonomic control systems with strongly non- linear uncertainties. In order to make the state scaling effective and to prevent the finite time escape phenomenon from happening, the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization. The recursive integrator backstepping technique is applied to the design of the robust controller. The simulation example demonstrates the efficiency and robust features of the proposed method.     

Robust observability for a class of time-varying discrete-time uncertain systems

This paper introduces a concept of robust observability for a class of uncertain discrete-time systems. This notion is an extension of the standard notion of observability for discrete-time, linear time-varying systems. The uncertainty and noise are modelled deterministically via a sum quadratic constraint. A necessary and sufficient condition for robust observability is presented in terms of existence of a suitable solution to a Riccati difference equation. The set of possible initial states given noisy measurements over a finite number of sampling periods is shown to be an ellipsoid.     

Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria

This paper focuses on a class of uncertain nonlinear systems which are subject to norm-bounded parameter uncertainty in the forward path and a vector-valued periodic nonlinearity in the feedback path, and addresses robust analysis and synthesis problems for such systems. Sufficient conditions for global asymptotic stability are derived in terms of linear matrix inequalities (LMIs) and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. The problem of robust synthesis is concerned with designing a feedback controller such that the resulting closed-loop system is globally asymptotically stable for all admissible uncertainties. It is shown that a solution to the robust synthesis problem for the uncertain system can be obtained by solving a synthesis problem for an uncertainty free system. A concrete example is presented to demonstrate the applicability and validity of the proposed approach.     

随机不确定时滞系统的鲁棒H∞控制

本文研究了随机不确定时滞系统的鲁棒稳定性与鲁棒H∞控制问题,系统的不确性具有凸多面体形式.利用线性矩阵不等式方法,通过依赖于参数的Lyapunov函数,得到了此类系统鲁棒随机镇定的充分条件.在此基础上,又给出了H∞状态反馈控制器的设计.     

On controllability and observability for a class of impulsive systems

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. These complex dynamic behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability for a class of time-varying impulsive control systems. Several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time-invariant impulsive control systems are also obtained. Meanwhile, several new results associated with variation of parameters for time-varying impulsive control systems are derived.     

Exact observability and controllability for linear neutral type systems

The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllability problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.     

Local observability and controllability of nonlinear discrete-time fractional order systems based on their linearisation

The concepts of local controllability and observability of nonlinear discrete-time systems with the Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type h-difference fractional order operators are studied. The Implicit Function Theorem is used in order to show that the nonlinear systems are locally observable or controllable in a finite number of steps if their linear approximations are observable or controllable, respectively, in the same number of steps.     

The average-case identifiability and controllability of large scale systems

Needs for increased product quality, reduced pollution, and reduced energy and material consumption are driving enhanced process integration. This increases the number of manipulated and measured variables required by the control system to achieve its objectives. This paper addresses the question of whether processes tend to become increasingly more difficult to identify and control as the process dimension increases. Tools and results of multivariable statistics are used to show that, under a variety of assumed distributions on the elements, square processes of higher dimension tend to be more difficult to identify and control, whereas the expected controllability and identifiability of nonsquare processes depends on the relative numbers of measured and manipulated variables. These results suggest that the procedure of simplifying the control problem so that only a square process is considered is a poor practice for large scale systems.     

Robust stability and instability of biochemical networks with parametric uncertainty

Parameter perturbations in dynamical models of biochemical networks affect the qualitative dynamical behaviour observed in the model. Since this qualitative behaviour is in many cases the key model output used to explain biological function, the robustness analysis of the model’s behaviour with respect to parametric uncertainty is a crucial step in systems biology research. In this paper, we develop a new method for robustness analysis of the dynamical behaviour. As a first step, we provide a characterization of non-robust perturbations as a system of polynomial equalities and inequalities. In the second step, we apply the Positivstellensatz and Handelman representation of polynomials to check for the non-existence of solutions to this system, which can be relaxed to solving a linear program. Thereby, a solution to the linear program yields a robustness certificate for the considered dynamical behaviour. With these robustness certificates, we propose an algorithm to compute a lower robustness bound corresponding to a level of parametric uncertainty up to which no local bifurcations can occur. The applicability of the proposed method to biochemical network models is illustrated by analysing the robustness of oscillations in a model of the NF-κB signalling pathway. The results may be used to define a level of confidence in the observed model behaviour under parametric uncertainty, making them valuable for evaluating dynamical models of biological networks.     

On the controllability and observability of discrete-time linear time-delay systems

This article studies the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observability, which imply the stabilisability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. The proofs are based on the equivalent expanded system, but the criteria only involve the delays and matrices of the same dimension as the original system. Finally, the duality between the suggested controllability and observability is presented.     

Robust stability analysis and stabilisation of uncertain impulsive positive systems with time delay

This paper considers the robust stability and stabilisation of uncertain impulsive positive systems with delay in state. The robust global exponential stability criterion under ranged dwell-time is first established by employing an impulse-time-dependent copositive Lyapunov function. Extensions to the exponential stability of the considered system under constant, arbitrary, maximal and minimal dwell-time are then derived. To positively stabilise the considered system under ranged dwell-time, a method of state-feedback controller design is presented based on the derived stability condition. Several numerical examples illustrate the reduced conservatism and effectiveness of the obtained theoretical results.     

Robust stability of MIMO nonlinear uncertain systems using operator-based right coprime factorisation

In this paper, a class of multi-input–multi-output (MIMO) nonlinear systems with uncertainties is considered by using operator-based right coprime factorisation. First, based on proposed quotient operators, coupling effect of the MIMO nonlinear systems is discussed. Second, based on the operator-based right coprime factorisation approach, sufficient conditions for guaranteeing robust stability of the MIMO nonlinear systems with uncertainties are proposed by using a new unimodular operator. Finally, a simulation example is shown to illustrate the proposed design scheme for the MIMO nonlinear systems with uncertainties.     

不确定性区域系统的鲁棒控制

区域模型已经成功应用于模拟生物医学和药物代谢动力学系统中。针对一类具有参数不确定性的正定区域系统,对其质量控制的反馈稳定性提出了一种新的正定鲁棒控制律,该控制律基于李亚普诺夫稳定性理论并且闭环系统满足全局渐进稳定性。通过术后病人神经肌肉阻滞控制的具体实例对其质量控制的性能进行了分析,并通过仿真与其他控制律的性能进行了比较。     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H-infinity滤波设计问题. 假设参数不确定性具有线性分式形式, 而非线性动态满足Lipschitz条件, 给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平. 对参数已知情形, 先建立广义有界实引理, 然后给出H-infinity滤波器的存在条件, 证明了H-infinity滤波器的存在性可归结为线性矩阵不等式的可解性, 基于线性矩阵不等式给出了H-infinity滤波器的综合方法和步骤. 对参数不确定性情形, 通过引进标度参数, 将不确定非线性离散时滞系统的鲁棒H-infinity滤波问题转化为确定系统的H-infinity滤波设计. 最后给出仿真例子验证所得结果的有效性.     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H∞滤波设计问题．假设参数不确定性具有线性分式形式,而非线性动态满足Lipschitz条件,给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平．对参数已知情形,先建立广义有界实引理,然后给出H∞滤波器的存在条件,证明了H∞滤波器的存在性可归结为线性矩阵不等式的可解性,基于线性矩阵不等式给出了H∞滤波器的综合方法和步骤．对参数不确定性情形,通过引进标度参数,将不确定非线性离散时滞系统的鲁棒H∞滤波问题转化为确定系统的H∞滤波设计．最后给出仿真例子验证所得结果的有效性．     

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

In this paper, observers and observability for uncertain nonlinear systems are systematically discussed. It is shown that for the convergence of a large class of observers, featured with the augment state to estimate the uncertainty, it requires not only the observability condition for the augment matrix pair but, more importantly, requires a structural condition first proposed in this paper. Furthermore, it is demonstrated that the combination of this structural condition and the observability of the augment matrix pair is a necessary and sufficient condition for the convergence of the observers and the observability of the original uncertain nonlinear systems. This implies that both the structural condition and the observability condition of the augment matrix pair reveal essential feature of the observing problems for uncertain nonlinear systems. In addition, for unobservable uncertain nonlinear systems, which do not satisfy this necessary and sufficient condition, the biased estimation error is explicitly presented, which can be used to evaluate the estimation performance of this class of observers. The numerical simulations for three typical examples are carried out to validate our theoretical analysis.