Robust H∞ nonlinear control via measurement feedback

This paper deals with the problem of finite-time-horizon robust H_∞ control via measurement feedback, for affine nonlinear systems with nonlinear time-varying parameter uncertainty. The problem addressed is the design of a control law, which processes the measured output and guarantees a prescribed level of closed-loop disturbance attenuation. Conditions for the existence of such a controller are obtained by solving an auxiliary control problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. This approach allows us to apply the recently developed H_∞ nonlinear control techniques to solve the robust control problem. The problem is investigated in both the continuous- and discrete-time cases. The results are demonstrated by a simple example. © 1997 by John Wiley & Sons, Ltd.     

Application of real/mixed μ computational techniques to an H∞ missile autopilot

A multivariable missile autopilot is synthesized using an H_∞ approach. A tradeoff is achieved between performance, actuators solicitation and uncertainties in the actuators and bending modes dynamics. Robust stability and performance of the control law are then studied in the face of large real parametric aerodynamic uncertainties: computational techniques for real and mixed μ analysis (namely De Gaston and Safonov's, Dailey's, Jones’, Young and Doyle's, Fan, Tits and Doyle's and Safonov and Lee's methods) are briefly reviewed before being used to compute either the exact value, or an interval of the structured singular value (SSV). For small amounts of parameters, the upper and lower bounds provided by these methods are compared to the exact value, computed by De Gaston and Safonov's method. For larger amounts of parameters, NP hardness of the problem prohibits the use of algorithms which compute the exact value: these algorithms are indeed necessarily exponential-time. As an alternative in this case, the use of polynomial-time methods for computing upper and lower bounds leads in our examples to accurate approximates of the real and mixed structured singular values.     

Robust nonlinear H ∞ control based on the incremental gain

The incremental gain is proposed as an alternative to the usual gain for designing nonlinear H _∞ controllers. Considering a class of plants with Lipschitz nonlinearities and using linear matrix inequalities, a state feedback controller is designed such that the closed‐loop system is exponentially stable in the absence of disturbance inputs and has incremental gain less than or equal to a minimized number in the presence of disturbances as well as model uncertainties. Moreover, a norm‐wise robustness analysis of the proposed technique against nonlinear uncertainties has been accomplished. Our result is verified through stabilization of both certain and uncertain systems in an incremental sense and also input tracking of a chaotic plant. Copyright © 2014 John Wiley & Sons, Ltd.     

Singular H∞ control for nonlinear systems

This paper presents a solution to the singular H_∞ control problem via state feedback for a class of nonlinear systems. It is shown that the problem of almost disturbance decoupling with stability plays a fundamental role in the solution of the considered problem. We also point out when the singular problem can be reduced to a regular one or solved via standard H_∞ technique. We must stress that the solution of the singular problem is obtained without making any approximation of it by means of regular problems. © 1997 John Wiley & Sons, Ltd.     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Discrete‐time robust H∞control of a class of nonlinear uncertain systems

This paper presents an approach to discrete‐time robust H^∞ control for a class of nonlinear uncertain systems on the basis of the use of Sum Quadratic Constraints. The approach involves controllers, which include copies of the system nonlinearities in the controller. The nonlinearities being considered are those that satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using linear robust H^∞ control theory, and this leads to a nonlinear controller, which gives an upper bound on the attainable disturbance attenuation level. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust passivity‐based H∞ control for uncertain switched nonlinear systems

In this paper, we investigate the H_∞ control problem for uncertain switched nonlinear systems with passive and non‐passive subsystems. For any given average dwell time, any given passivity rate and any given disturbance attenuation level, we design feedback controllers of subsystems, which may depend on the pre‐given constants, to solve the H_∞ control problem for the uncertain switched nonlinear systems for all admissible uncertainties. For linear systems, the exponential small‐time norm‐observability is shown to be preserved under disturbance. Two examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

The current article discusses the H_∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H_∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.     

Robust H ∞ control via a stable decentralized nonlinear output feedback controller

This paper presents a new method to construct a decentralized nonlinear robust H ^∞ controller for a class of large‐scale nonlinear uncertain systems. The admissible uncertainties and nonlinearities in the system satisfy integral quadratic constraints and global Lipschitz conditions, respectively. The decentralized controller, which is required to be stable, is capable of exploiting known nonlinearities and interconnections between subsystems without treating them as uncertainties. Instead, additional uncertainties are introduced because of the discrepancies between nondecentralized and decentralized nonlinear output feedback controllers. The H ^∞ control objective is to achieve an absolutely stable closed‐loop system with a specified disturbance attenuation level. A solution to this control problem involves stabilizing solutions to algebraic Riccati equations parametrized by scaling constants corresponding to the uncertainties and nonlinearities. This formulation is nonconvex; hence, an evolutionary optimization method is applied to solve the control problem considered. Copyright © 2012 John Wiley & Sons, Ltd.     

H∞ control for a class of cascade switched nonlinear systems

In this paper, we investigate the H_∞ control problem for a class of cascade switched nonlinear systems consisting of two nonlinear parts which are also switched systems using the multiple Lyapunov function method. Firstly, we design the state feedback controller and the switching law, which guarantees that the corresponding closed‐loop system is globally asymptotically stable and has a prescribed H_∞ performance level. This method is suitable for a case where none of the switched subsystems is asymptotically stable. Then, as an application, we study the hybrid H_∞ control problem for a class of nonlinear cascade systems. Finally, an example is given to illustrate the feasibility of our results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ control of phase‐locked loops with polytopic type uncertainties

A robust H_∞ control method is applied in the design of loop filters for phase‐locked loop (PLL) carrier phase tracking. The proposed method successfully copes with large S‐curve slope uncertainty and with a significant decision delay in the closed loop that may stem from the decoder and/or the equalizer there. The design problem is transformed into a state‐feedback control problem where phase and gain margins should be guaranteed in spite of the uncertainty. Of all the loop filters that achieve the required margins the one that minimizes an upper bound on the effect of the phase and the measurement noise signals is derived. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust H∞ Control Problem For General Nonlinear Systems With Uncertainty

In this paper, both state and output feedback robust H^∞ control problems for general nonlinear systems with norm‐bound uncertainty are considered. Sufficient conditions for the existence of robust output feedback H^∞ controller are provided. State space formulas for robust H^∞ output controller are provided.     

Three‐dimensional nonlinear H∞ guidance law

This paper proposes a novel three‐dimensional missile guidance law design based on nonlinear H_∞ control. The complete nonlinear kinematics of pursuit–evasion motion is considered in the three‐dimensional spherical co‐ordinates system; neither linearization nor small angle assumption is made here. The nonlinear H_∞ guidance law is expressed in a simple form by solving the associated Hamilton–Jacobi partial differential inequality analytically. Unlike adaptive guidance laws, the implement of the proposed robust H_∞ guidance law does not require the information of target acceleration, while ensuring acceptable interceptive performance for arbitrary target with finite acceleration. The resulting pursuit–evasion trajectories for both the H_∞‐guided missile and the worst‐case target are determined in closed form, and the performance robustness against variations in target acceleration, in engagement condition, and in control loop gain, is verified by numerical simulations. Copyright © 2001 John Wiley & Sons, Ltd.     

Observer‐based H ∞ control on nonhomogeneous Markov jump systems with nonlinear input

This paper considers the problem of observer‐based H _∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H _∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

H∞ nonlinear filtering

This paper investigates the problem of H_∞ estimation of nonlinear processes. An estimator, which may be nonlinear, is looked for so that a given bound on the ratio between the energy of the estimation error and the energy of the oxogeneous inputs to the estimated process is achieved. Conditions for the existence of such an estimator and formulas for its derivation are obtained using both the game theory approach and the theory of dissipative systems. The results of the paper extend the recent results on H_∞ nonlinear control. They are demonstrated by a simple example of a linear system with a nonlinear measurement rule and compared with corresponding results that are obtained by the extended Kalman filter.     

On H∞-control of discrete-time nonlinear systems

Following recent works on continuous-time nonlinear H_∞-control, where connections with game theory and passivity conditions have been set, the present paper studies the corresponding problem for discrete-time systems. The paper describes sufficient conditions for the existence and the construction of a feedback law which imposes a prescribed level of disturbance attenuation with internal stability. Both cases of state feedback and measurement feedback are considered.     

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.