Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.     

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

In this article, the problem of robust finite‐time H_∞ synchronization control is investigated for a class of uncertain discrete‐time master‐slave systems with Markovian switching parameters in the observer‐based case. Parameter uncertainties are assumed to be norm‐bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain. By using stochastic Lyapunov function method and finite‐time analysis techniques, novel sufficient conditions that include the master‐slave parameters are obtained for designing an observer‐based finite‐time H_∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.     

H∞ output tracking control for a class of switched LPV systems and its application to an aero‐engine model

This paper aims to investigate the problem of H_∞ output tracking control for a class of switched linear parameter‐varying (LPV) systems. A sufficient condition ensuring the H_∞ output tracking performance for a switched LPV system is firstly presented in the format of linear matrix inequalities. Then, a set of parameter and mode‐dependent switching signals are designed, and a family of switched LPV controllers are developed via multiple parameter‐dependent Lyapunov functions to enhance control design flexibility. Even though the H_∞ output tracking control problem for each subsystem might be unsolvable, the problem for switched LPV systems is still solved by the designed controllers and the designed switching law. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an H_∞ speed adjustment problem of an aero‐engine. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Composite disturbance‐observer‐based control and H∞ control for complex continuous models

A novel type of control scheme combining the disturbance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of complex continuous models with disturbances. The disturbances are supposed to include two parts. One part in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other part is supposed to have the bounded H₂‐norm. Parametric uncertainties exist both in concerned plant and in exogenous subsystem. The disturbance observers based on regional pole placement and D‐stability theory are designed and integrated with conventional H_∞ control laws. The new composite DOBC and H_∞ control scheme is applied to complex continuous models for the case with known and unknown nonlinearity, respectively. Then the first type of disturbances can be estimated and rejected, and the second type can be attenuated; simultaneously, the desired dynamic performances can be guaranteed. Simulations for a flight control system are given to demonstrate the effectiveness of the results and compare the proposed results with the previous schemes. Copyright © 2009 John Wiley & Sons, Ltd.     

Resilient control for wireless networked control systems under DoS attack via a hierarchical game

In this paper, the resilient control problem is investigated for a wireless networked control system (WNCS) under denial‐of‐service (DoS) attack via a hierarchical game approach. In the presence of a wireless network, a DoS attacker leads to extra packet dropout in the cyber layer of WNCS by launching interference power. A zero‐sum Markov game is exploited to model the interaction between the transmitter and the DoS attacker under dynamic network environment. Additionally, with the attack‐induced packet loss, an H_∞ minimax controller is designed in the physical layer by using a delta operator approach. Both value iteration and Q‐learning methods are used to solve the hierarchical game problem for the WNCS. The proposed method is applied to a load frequency control system to illustrate the effectiveness.     

A robust least squares based approach to min‐max model predictive control

This article deals with the model predictive control (MPC) of linear, time‐invariant discrete‐time polytopic (LTIDP) systems. The 2‐fold aim is to simplify the treatment of complex issues like stability and feasibility analysis of MPC in the presence of parametric uncertainty as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom (2DOF) control scheme, where the output r(k) of the feedforward input estimator (IE) is used as input forcing the closed‐loop system ∑_f. ∑_f is the feedback connection of an LTIDP plant ∑_p with an LTI feedback controller ∑_g. Both cases of plants with measurable and unmeasurable state are considered. The task of ∑_g is to guarantee the quadratic stability of ∑_f, as well as the fulfillment of hard constraints on some physical variables for any input r(k) satisfying an “a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on‐line minimization of a worst‐case finite‐horizon quadratic cost functional and is applied to ∑_f according to the usual receding horizon strategy. The on‐line constrained optimization problem is here simplified, reducing the number of the involved constraints and decision variables. This is obtained modeling r(k) as a B‐spline function, which is known to admit a parsimonious parametric representation. This allows us to reformulate the minimization of the worst‐case cost functional as a box‐constrained robust least squares estimation problem, which can be efficiently solved using second‐order cone programming.     

Mixed Event/Time‐Triggered Static Output Feedback L2‐Gain Control for Networked Control Systems

This paper considers the design of mixed event/time‐triggered controllers for networked control systems (NCSs) under transmission delay and possible packet dropout. Assuming that a conventional delayed static output feedback L₂‐gain controller exists, we propose an output‐based mixed event/time‐triggered communication scheme for reducing the network traffic in a NCS. Moreover, we show that a conventional delayed static output feedback L₂‐gain controller can be obtained by solving a linear matrix inequality with a matrix equality constraint. A numerical example is proposed for demonstrating the theoretical results.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

Improved H∞ sampled‐data control for semilinear parabolic PDE systems

In this paper, an H_∞ sampled‐data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time‐dependent Lyapunov functional and vector Poincare's inequality, a sampled‐data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H_∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh‐Nagumo equation are given to illustrate the effectiveness of the proposed design method.     

Finite‐time H∞ bumpless transfer control for switched systems: A state‐dependent switching approach

This paper addresses the finite‐time H_∞ bumpless transfer control problem for switched systems. The main idea lies in designing a state‐feedback controller with amplitude limitation and a state‐dependent switching law to reduce control bumps caused by switching. First, a local bumpless transfer condition is proposed to limit the amplitude of switching controllers at switching points. Second, by introducing a state‐dependent switching law, a prescribed finite‐time H_∞ bumpless transfer control performance is attained even if it does not hold for each subsystem or system state remaining on a switching surface. Third, a sufficient condition verifying the solvability of finite‐time H_∞ bumpless transfer control problem is established by resorting to multiple Lyapunov function method. Finally, the effectiveness of developed method is illustrated by a numerical example.     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

A Receding Horizon Sliding Controller for Automotive Engine Coldstart: Design and Hardware‐in‐the‐Loop Testing With an Echo State Network High‐Fidelity Model

The aim of the current study is to probe the potential of receding horizon sliding control (RHSC) technique for reducing the coldstart hydrocarbon (HC) emissions of automotive spark‐ignited (SI) engines. The RHSC approach incorporates the potentials of sliding control (SC) and nonlinear model predictive control (NMPC) to employ the future information of the considered engine to keep the system's trajectories close to a stable manifold. To calculate the control commands, the authors adopt an efficient optimization technique, known as the multivariate quadratic fit sectioning algorithm (MQFSA), and also, define three different objective functions, based on l₁, l₂, and l_∞ norms. To demonstrate the efficacy of RHSC controller, its performance is compared with two other well‐known controllers extracted from the literature, namely NMPC and Pontryagin's minimum principle (PMP)‐based controllers. Through numerical simulations for three distinctive operating conditions, it is demonstrated that the RHSC controller is very effective for reducing the total tailpipe HC emissions over the coldstart period of the considered engine system. Moreover, by conducting a hardware‐in‐the‐loop (HIL) test using an echo state network high‐fidelity model, it is indicated that the computational speed of calculating control commands is fast enough to enable RHSC to be used for real‐time implementations in practice.     

Boundary control of linear stochastic reaction‐diffusion systems

This paper considers the boundary control problem for linear stochastic reaction‐diffusion systems with Neumann boundary conditions. First, when the full‐domain system states are accessible, a boundary control is designed, and a sufficient condition is established to ensure the mean‐square exponential stability of the resulting closed‐loop system. Next, when the full‐domain system states are not available, an observer‐based control is proposed such that the underlying closed‐loop system is stable. Furthermore, observer‐based controller is designed for the systems with an H_∞ performance. Simulation examples are given to demonstrate the effectiveness and potential of the new design techniques.     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Event‐triggered H∞ control for a class of nonlinear networked control systems using novel integral inequalities

This paper is concerned with event‐triggered H_∞ control for a class of nonlinear networked control systems. An event‐triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event‐triggered transmission scheme, the closed‐loop system is modeled as a system with an interval time‐varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov–Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event‐triggered H_∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to the robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality‐based conditions are formulated to design both event‐triggered and time‐triggered H_∞ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS

In this paper, the robust delay‐dependent H_∞ control for a class of uncertain systems with time‐varying delay is considered. An improved state feedback H_∞ control is proposed to minimize the H_∞‐norm bound via the LMI optimization approach. Based on the proposed result, delay‐dependent criteria are obtained without using the model transformation technique or bounded inequalities on cross product terms. The linear matrix inequality (LMI) optimization approach is used to design the robust H_∞ state feedback control. Some numerical examples are given to illustrate the effectiveness of the approach.