Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan; Chris J. Sangwin; Philip Townsend

Displaying similar documents to “Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance”

Output feedback $H_{\infty}$ control of networked control systems based on two channel event-triggered mechanisms

Yanjun Shen, Zhenguo Li, Gang Yu (2021)

Kybernetika

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In this paper, we study dynamical output feedback $H_{\infty}$ control for networked control systems (NCSs) based on two channel event-triggered mechanisms, which are proposed on both sides of the sensor and the controller. The output feedback $H_{\infty}$ controller is constructed by taking random network-induced delays into consideration without data buffer units. The controlled plant and the output feedback controller are updated immediately by the sampled input and the sampled output, respectively. By...

Improving the performance of semiglobal output controllers for nonlinear systems

Abdallah Benabdallah, Walid Hdidi (2017)

Kybernetika

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For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers ${(𝒰_{R})}_{R > 0}$ with increasing regions of attraction ${(Ω_{R})}_{R > 0}$ is that, when the region of attraction $Ω_{R}$ is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is...

Dual-terminal event triggered control for cyber-physical systems under false data injection attacks

Zhiwen Wang, Xiangnan Xu, Hongtao Sun, Long Li (2020)

Kybernetika

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This paper deals with the problem of security-based dynamic output feedback control of cyber-physical systems (CPSs) with the dual-terminal event triggered mechanisms (DT-ETM) under false data injection (FDI) attacks. Considering the limited attack energy, FDI attacks taking place in transmission channels are modeled as extra bounded disturbances for the resulting closed-loop system, thus enabling $H_{\infty}$ performance analysis with a suitable $ϱ$ attenuation level. Then two buffers at the controller...

Event-triggered $H_{\infty}$ static output feedback control of discrete time piecewise-affine systems

Zhuyun Xue, Mouquan Shen (2021)

Kybernetika

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This paper is concerned with the problem of $H_{\infty}$ event-triggered output feedback control of discrete time piecewise-affine systems. Relying on system outputs, a piecewise-affine triggering condition is constructed to release communication burden. Resorting to piecewise Lyapunov functional and robust control techniques, sufficient conditions are built to ensure the closed-loop systems to be asymptotically stable with the prescribed $H_{\infty}$ performance. By utilizing a separation strategy, the static...

Tracking with prescribed transient behaviour

Achim Ilchmann, E. P. Ryan, C. J. Sangwin (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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Universal tracking control is investigated in the context of a class $𝒮$ of $M$ -input, $M$ -output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary $ℝ^{M}$ -valued reference signal $r$ of class...

A tracking controller design with preview action for a class of nonlinear Lur'e systems with time-varying delays and external disturbances

Xiao Yu, Fucheng Liao (2021)

Kybernetika

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In this paper, the tracking control problem for a class of discrete-time nonlinear Lur’e systems with time-varying delays and external disturbances is studied via a preview control method. First, a novel translation approach is introduced to construct the augmented error system for Lur’e systems. The output tracking problem is thereby transformed into a guaranteed cost $H_{\infty}$ controller design problem. To produce an integral control action that can eliminate the static error, a discrete integrator...

Robust observer-based finite-time $H_{\infty}$ control designs for discrete nonlinear systems with time-varying delay

Yali Dong, Huimin Wang, Mengxiao Deng (2021)

Kybernetika

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This paper investigates the problem of observer-based finite-time $H_{\infty}$ control for the uncertain discrete-time systems with nonlinear perturbations and time-varying delay. The Luenberger observer is designed to measure the system state. The observer-based controller is constructed. By constructing an appropriated Lyapunov-.Krasovskii functional, sufficient conditions are derived to ensure the resulting closed-loop system is $H_{\infty}$ finite-time bounded via observer-based control. The observer-based...

Disturbance observer based integral terminal sliding mode control for permanent magnet synchronous motor system

Junxiao Wang, Fengxiang Wang, Xianbo Wang, Li Yu (2019)

Kybernetika

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This paper presents speed regulation issue of Permanent Magnet Synchronous Motor (PMSM) using a composite integral terminal sliding mode control scheme via a disturbance compensation technique. The PMSM $q$ -axis and $d$ -axis subsystems are firstly transformed into two linear subsystems by using feedback linearization technique, then, integral terminal sliding mode controller and finite-time controller are designed respectively. The proof of finite time stability are given for the PMSM closed-loop...

Model following control system with time delays

Dazhong Wang, Shujing Wu, Wei Zhang, Guoqiang Wang, Fei Wu, Shigenori Okubo (2016)

Kybernetika

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Design of model following control system (MFCS) for nonlinear system with time delays and disturbances is discussed. In this paper, the method of MFCS will be extended to nonlinear system with time delays. We set the nonlinear part $f (v (t))$ of the controlled object as $| | f (v (t)) | | \leq α + {β | | v (t) | |}^{γ}$ , and show the bounded of internal states by separating the nonlinear part into $γ \geq 0$ . Some preliminary numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem

Masoud Taleb Ziabari, Mohammad Reza Jahed-Motlagh, Karim Salahshoor, Amin Ramezani, Ali Moarefianpour (2017)

Kybernetika

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This paper presents a new robust adaptive model predictive control for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound, as well as constraints on input states. An adaptive control is used in the new controller to estimate the system uncertainty. Also, to avoid the system disturbances, a $H_{\infty}$ method is employed to find the appropriate gain in Tube-MPC. Finally, a surge avoidance problem in centrifugal...

Linearization techniques for $𝕃^{\infty}$ See PDF-control problems and dynamic programming principles in classical and $𝕃^{\infty}$ See PDF-control problems

Dan Goreac, Oana-Silvia Serea (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of the paper is to provide a linearization approach to the $𝕃^{\infty}$ See PDF-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the $𝕃^{p}$ See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating $𝕃^{\infty}$ See PDF problems in continuous and...

Synthesis of optimal control for nonlinear third order systems

Wiesław Szwiec

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The paper is devoted to a certain problem in the theory of synthesis of optimal control. The fundamental results of research in the synthesis of optimal control for second order systems are given in [1], [2], [5], [10]. In particular, in [2] and [5] some specific nonlinear systems are investigated, namely the systems related with the differential equations of the forms̈ + F(s,ṡ) = u or s̈ + F(s,ṡ,u) = 0where u is a control parameter in the interval [—1,1]. Some results concerning third...

Distances to convex sets

Antonio S. Granero, Marcos Sánchez (2007)

Studia Mathematica

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If X is a Banach space and C a convex subset of X*, we investigate whether the distance $d ̂ ({\bar{c o}}^{w *} (K), C) : = s u p i n f | | k - c | | : c \in C : k \in {\bar{c o}}^{w *} (K)$ from ${\bar{c o}}^{w *} (K)$ to C is M-controlled by the distance d̂(K,C) (that is, if $d ̂ ({\bar{c o}}^{w *} (K), C) \leq M d ̂ (K, C)$ for some 1 ≤ M < ∞), when K is any weak*-compact subset of X*. We prove, for example, that: (i) C has 3-control if C contains no copy of the basis of ℓ₁(c); (ii) C has 1-control when C ⊂ Y ⊂ X* and Y is a subspace with weak*-angelic closed dual unit ball B(Y*); (iii) if C is a convex subset of X and X is considered canonically...

Stability and sensitivity analysis for optimal control problems with control-state constraints

Kazimierz Malanowski

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A family of parameter dependent optimal control problems ${(O)}_{h}$ with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of ${(O)}_{h ₀}$ exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to ${(O)}_{h}$ and the associated Lagrange...