MIXED H2/H∞ ADAPTIVE TRACKING CONTROL DESIGN FOR UNCERTAIN CONSTRAINED ROBOTS

In this study, a PID‐type controller incorporating an adaptive learning scheme for the mixed H₂/H_∞ tracking performance is developed for constrained robots under unknown or uncertain plant parameters and external disturbances. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance and the adaptive control scheme is used to compensate the plant uncertainties. By virtue of the skew‐symmetric property of the constrained robotic systems and an adequate choice of state variable transformation, sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled nonlinear differential equations. The proposed methods are simple and the coupled algebraic equations can be solved analytically. Simulation results indicate that the desired performance of the proposed adaptive mixed H₂/H_∞ tracking control schemes for the uncertain constrained robotic systems can be achieved.     

A mixed PI/VI design method for nonlinear H∞ Control

This paper proposes a new mixed policy iteration and value iteration (PI/VI) design method for nonlinear H_∞ control based on the theories of polynomial optimization and Lasserre's hierarchy. The design of a mixed PI/VI controller can be carried out in four steps: firstly, initialize design parameters and expand nonlinear system matrices; secondly, obtain a polynomial matrix inequality for policy improvement; thirdly, obtain the Lasserre's hierarchy of a global polynomial optimization problem for value improvement; fourthly, perform the mixed PI/VI algorithm to approximate the optimal nonlinear H_∞ control law. The novelty of this work lies in that the problem of designing a nonlinear H_∞ controller is translated into a polynomial global optimization problem, which can be solved by Lasserre's hierarchy directly, and then, the mixed PI/VI algorithm is presented to approximate the optimal nonlinear H_∞ control law by updating global optimizers iteratively. The main results of this paper consist of the mixed PI/VI algorithm and the related three theorems, which guarantee robust stability and performance of the closed‐loop nonlinear system. Numerical simulations show that the mixed PI/VI algorithm converges very fast and achieves good robust stability and performance in transient behavior, disturbance rejection, and enlarging the domain of attraction of the close‐loop system.     

ADAPTIVE FUZZY‐BASED MIXED H2/H∞ TRACKING CONTROL DESIGN IN UNCERTAIN ROBOTIC SYSTEMS

In this study, an adaptive fuzzy‐based mixed H₂/H_∞ tracking control design is developed in robotic systems under unknown or uncertain plant parameters and external disturbances. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance and the fuzzy adaptive control scheme is used to compensate for the plant uncertainties. By virtue of the skew‐symmetric property in the robotic systems and adequate choice of state variable transformation, sufficient conditions are developed for the adaptive fuzzy‐based mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled differential equations. The proposed methods are simple and the coupled algebraic equations can be solved analytically. Simulation results indicate that the desired performance of the proposed adaptive fuzzy‐based mixed H₂/H_∞ tracking control schemes for the uncertain robotic systems can be achieved.     

A new iterative algorithm for solving H∞ control problem of continuous‐time Markovian jumping linear systems based on online implementation

A new online iterative algorithm for solving the H_∞ control problem of continuous‐time Markovian jumping linear systems is developed. For comparison, an available offline iterative algorithm for converging to the solution of the H_∞ control problem is firstly proposed. Based on the offline iterative algorithm and a new online decoupling technique named subsystems transformation method, a set of linear subsystems, which implementation in parallel, are obtained. By means of the adaptive dynamic programming technique, the two‐player zero‐sum game with the coupled game algebraic Riccati equation is solved online thereafter. The convergence of the novel policy iteration algorithm is also established. At last, simulation results have illustrated the effectiveness and applicability of these two methods. 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.     

H∞ prediction and unconstrained H∞ predictive control: multi‐input–multi‐output case

Through the combination of the sequential spectral factorization and the coprime factorization, a k‐step ahead MIMO H_∞ (cumulative minimax) predictor is derived which is stable for the unstable noise model. This predictor and the modified internal model of the reference signal are embedded into the H_∞ optimization framework, yielding a single degree of freedom multi‐input–multi‐output H_∞ predictive controller that provides stochastic disturbance rejection and asymptotic tracking of the reference signals described by the internal model. It is shown that for a plant/disturbance model, that represents a large class of systems, the inclusion of the H_∞ predictor into the H_∞ control algorithm introduces a performance/robustness tuning knob: an increase of the prediction horizon enforces a more conservative control effort and, correspondingly, results in deterioration of the transient and the steady‐state (tracking error variance) performance, but guarantees large robustness margin, while the decrease of the prediction horizon results in a more aggressive control signal and better transient and steady‐state performance, but smaller robustness margin. Copyright © 2001 John Wiley & Sons, Ltd.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> suboptimal tracking controller design for a class of nonlinear systems

In this paper, a new technique is proposed to solve the H _∞ tracking problem for a broad class of nonlinear systems. Towards this end, based on a discounted cost function, a nonlinear two-player zero-sum differential (NTPZSD) game is defined. Then, the problem is converted to another NTPZSD game without any discount factor in its corresponding cost function. A state-dependent Riccati equation (SDRE) technique is applied to the latter NTPZSD game in order to find its approximate solution which leads to obtain a feedback-feedforward control law for the original game. It is proved that the tracking error between the system state and its desired trajectory converges asymptotically to zero under mild conditions on the discount factor. The proposed H _∞ tracking controller is applied to two nonlinear systems (the Vander Pol’s oscillator and the insulin-glucose regulatory system of type I diabetic patients). Simulation results demonstrate that the proposed H _∞ tracking controller is so effective to solve the problem of tracking time-varying desired trajectories in nonlinear dynamical systems.     

H∞ output tracking control for uncertain networked control systems via a switched system approach

In this paper, the problem of H_∞ output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output tracking H_∞ performance analysis is presented, and robust switching H_∞ model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive H2/H∞ tracking control for a class of uncertain robotic systems

This paper addresses the problem of designing mixed H₂/H_∞ tracking control for a large class of uncertain robotic systems. Nonlinear H_∞ control theory, H₂ control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H₂/H_∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H_∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H₂/H_∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H₂/H_∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.     

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.     

A new finite sum inequality approach to delay‐dependent H∞ control of discrete‐time systems with time‐varying delay

This paper deals with delay‐dependent H_∞ control for discrete‐time systems with time‐varying delay. A new finite sum inequality is first established to derive a delay‐dependent condition, under which the resulting closed‐loop system via a state feedback is asymptotically stable with a prescribed H_∞ noise attenuation level. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H_∞ controller. Finally, two numerical examples are given to show the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Robust H∞ Tracking Control of Uncertain Robotic Systems with Periodic Disturbances

This paper addresses the problem of designing robust tracking control for a large class of uncertain robotic systems. A more general model of the external disturbance is employed in the sense that the external disturbance can be expressed as the sum of a modeled disturbance and an unmodeled disturbance, for example, any periodic disturbance can be expressed in this general form. An adaptive neural network system is constructed to approximate the behavior of unknown robot dynamics. An adaptive control algorithm is designed to estimate the behavior of the modeled disturbance, and in turn the robust H_∞ control algorithm is required to attenuate the effects of the unmodeled disturbance only. Consequently, an intelligent adaptive/robust tracking control scheme is constructed such that an H_∞ tracking control is achieved in the sense that all the states and signals of the closed‐loop system are bounded and the effect due to the unmodeled disturbance on the tracking error can be attenuated to any preassigned level. Finally, simulations are provided to demonstrate the effectiveness and performance of the proposed control algorithm.     

A further result of the nonlinear mixed H2/H∞ tracking control problem for robotic systems

The design objective of a mixed H₂/H_∞ control is to find the H₂ optimal tracking control law under a prescribed disturbance attenuation level. With the help of the technique of completing the squares, a further result of the mixed H₂/H_∞ optimal tracking control problem is presented, by combining it with standard LQ optimal control technique. In this paper, only a nonlinear time‐varying Riccati equation is required to solve the problem in the design procedure—instead of two coupled nonlinear time‐varying Riccati equations, or two coupled linear algebraic Riccati‐Iike equations—with some assumptions made regarding the weighting matrices in the existing results. A closed‐form controller for the mixed H₂/H_∞ robotic tracking problem is simply constructed with a matrix inequality check. Moreover, it shows that the existing results are the special cases of these results. Finally, detailed comparison is performed by numerical simulation of a two‐link robotic manipulator. © 2002 John Wiley & Sons, Inc.     

Design of fault‐tolerant control for MTTF

Mean time to failure (MTTF) is an important reliability index of fault‐tolerant control systems, which is chosen as a design objective in this paper. However, it is usually evaluated from stochastic reliability models, and no analytical expression is available to relate MTTF to controller parameters. To overcome this difficulty, a two‐stage design scheme is proposed in this paper: A gradient‐based search is firstly carried out on probabilistic H_∞ performance characteristics for MTTF requirement; a sequential randomized algorithm with a weighted violation function is then developed for a controller design to satisfy the required H_∞ performance, and its convergence is guaranteed with probability 1. Two iterative algorithms are carried out alternately to implement this scheme, and a controller can be designed for MTTF requirement. Copyright © 2008 John Wiley & Sons, Ltd.     

RECEDING HORIZON H∞ CONTROL FOR SYSTEMS WITH A STATE‐DELAY

This paper proposes the receding horizon H_∞ control (RHHC) for linear systems with a state‐delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terms, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and H_∞‐norm boundedness of the closed‐loop system controlled by the proposed RHHC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon H_∞‐norm bound.     

H∞ Model Reduction for Positive Fractional Order Systems

This paper focuses on the H_∞ model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced‐order fractional system such that the associated error system is stable with a prescribed H_∞ performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H_∞‐norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced‐order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.     

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.     

Optimal‐switched extended H∞ filter for nonlinear systems with stochastic uncertainties

The extended H_∞ filter (EH_∞F) is a conservative solution with infinite‐horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH_∞F design, we developed an optimal‐switched (OS) filtering mechanism based on the standard EH_∞F to obtain an optimal‐switched extended H_∞ filter (OS‐EH_∞F). The OS mechanism has an error‐tolerant switched (ETS) structure, which switches the filtering mode between optimal and H_∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS‐EH_∞F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS‐EH_∞F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.