Disturbance Attenuation State-Feedback Control for Uncertain Interconnected Systems

This paper studies the problem of robust H∞ control design for a class of uncertain interconnected systems via state feedback. This class of systems are described by a state space model, which contains unknown nonlinear interaction and time-varying norm-bounded parametric uncertainties in state equation. Using the Riccati-equation-based approach we design state feedback control laws, which guarantee the decentralized stability with disturbance attenuation for the interconnected uncertain systems. A simple example of an interconnected uncertain linear system is presented to illustrate the results.     

H 2/H ∞ control problems of backward stochastic systems

This paper is concerned with the mixed H2/H∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations（BSDEs）.The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H2/H∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H2/H∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

Mixed H2／H∞ Optimal Guaranteed Cost Control of Uncertain Linear Systems

The mixed H2/H∞ guaranteed cost control problem via state feedback control laws is considered in this paper for linear systems with norm-bounded parameter uncertainty. Based on the linear matrix inequality (LMI) approach, sufficient conditions are derived for the existence of guaranteed cost controllers whihc guarantee not only a prespecified H∞ disturbance attenuation level on one controlled output for all admissible parameter uncertainties, but also the worst-case H2 performance index on the other controlled output to be no more than a specified bound. Furthermore, a convex optimization problem is formulated to design an optimal H2/H∞ guaranteed cost controller.     

H_∞-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system(NCS) with packet dropout and delay is investigated.A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and networkinduced non-uniformly distributed time-varying delay in both from sensor to controller(S/C) and from controller to actuator(C/A).Based on the obtained NCS model,employing an observer-based fault detection filter as the residual generator,the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem.Then,with the help of Lyapunov functional approach,a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities,which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate.Especially,a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found,which is typically resulted from the limited bandwidth of communication networks.The effectiveness of the proposed method is demonstrated by a simulation example.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.     

H_∞ Control for Nonlinear Stochastic Markov Systems with Time-Delay and Multiplicative Noise

This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities(HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly,by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities(LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.     

Solution of the HJI equations for nonlinear H∞ control design by state-dependent Riccati equations approach

The relationship between the technique by statedependent Riccati equations (SDRE) and Hamilton-Jacobi-Isaacs (HJI) equations for nonlinear H ∞ control design is investigated.By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices,a method is proposed for examining whether the SDRE method admits a global optimal control equivalent to that solved by the HJI equation method.Two examples with simulation are given to illustrate the method is effective.     

FTC of hidden Markov process with application to resource allocation in air operation

This paper investigates the feedback control of hidden Markov process(HMP) in the face of loss of some observation processes.The control action facilitates or impedes some particular transitions from an inferred current state in the attempt to maximize the probability that the HMP is driven to a desirable absorbing state.This control problem is motivated by the need for judicious resource allocation to win an air operation involving two opposing forces.The effectiveness of a receding horizon control scheme based on the inferred discrete state is examined.Tolerance to loss of sensors that help determine the state of the air operation is achieved through a decentralized scheme that estimates a continuous state from measurements of linear models with additive noise.The discrete state of the HMP is identified using three well-known detection schemes.The sub-optimal control policy based on the detected state is implemented on-line in a closed-loop,where the air operation is simulated as a stochastic process with SimEvents,and the measurement process is simulated for a range of single sensor loss rates.     

Robust H_∞ Control of Switched Nonlinear Systems Under Sampled Data

This paper investigates the globally asymptotically stable and L₂-gain of robust H∞ control for switched nonlinear systems under sampled data. By considering the relationship between the sampling period and the dwell time, the non-switching and one switching are discussed in the sampling interval, respectively. Firstly, a state feedback sampled-data controller is constructed by the back-stepping method, and the switching converts to asynchronous switching if it happens within the samp...     

Delay-dependent robust H∞ control of convex polyhedral uncertain fuzzy systems

The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.     

L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given.     

Adaptive Stabilization for a Class of Feedforward Systems with Zero-Dynamics

This paper investigates adaptive state feedback stabilization for a class of feedforward nonlinear systems with zero-dynamics,unknown linear growth rate and control coefficient.For design convenience,the state transformation is first introduced and the new system is obtained.Then,the estimation law is constructed for the unknown control coefficient,and the state feedback controller is proposed with a gain updated on-hne.By appropriate choice of the estimation law for the control coefficient and the dynamic gain,the states of the closed-loop system are globally bounded,and the state of the original system converges to zero.Finally,a simulation example is given to illustrate the correctness of the theoretical results.     

Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H ∞ regulator

In this paper,the variable universe adaptive fuzzy controller based on variable gain H_∞ regulator(VGH_∞ R.) is designed to stabilize a quadruple inverted pendulum.The VGH_∞ R is a novel robust gain-scheduling approach.By utilizing VGH_∞ R technique,a more precise real-time feedback gain matrix,which is changing with states,is obtained.Via the variable gain matrix 10 state variables of quadruple inverted pendulum are transformed into a kind of synthesis error(E) and synthesis rate of change of error(EC) at sampling time.Therefore,the dimension of the multivariable system is reduced and the variable Universe adaptive fuzzy controller is built.Experiments illustrate the effectiveness of the proposed control scheme.     

Control of Chaos in Lu System Subject to Mismatch Uncertainties Using Sliding Mode Design

A strategy is proposed to control Lu It is implemented by using sliding mode control system with mismatch uncertainties. The proposed controller ensures the occurrence of the sliding mode motion. It is guaranteed that under the proposed control law, the system state can be regulated to a specific point or in a predictable neighborhood of desired points in the state space even with mismatch uncertainties. Simulation results have illustrated the effectiveness and robustness of the proposed schemes even though the control input is nonlinear.     

Fault-tolerant control of linear uncertain systems using H∞ robust predictive control

The robust fault-tolerant control problem of linear uncertain systems is studied. It is shown that a solution for this problem can be obtained from a H∞ robust predictive controller （RMPC） by the method of linear matrix inequality （LMI）. This approach has the advantages of both H∞ control and MPC： the robustness and ability to handle constraints explicitly. The robust closed-loop stability of the linear uncertain system with input and output constraints is proven under an actuator and sensor faults condition. Finally, satisfactory results of simulation experiments verify the validity of this algorithm.     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Unpower aerocraft augmented state feedback tracking guaranteed cost control

Aimed at designing the unpower aerocraft attitude control system in a simple and practical way, the guaranteed cost control is adopted. To eliminate the steady-error, a novel tracking control approach--augmented state feedback tracking guaranteed cost control is proposed. Firstly, the unpower aerocraft is modeled as a linear system with norm bounded parameter uncertain, then the linear matrix inequality based state feedback guaranteed cost control law is combined with the augmented state feedback tracking control from a new point of view. The sufficient condition of the existence of the augmented state feedback tracking guaranteed cost control is derived and converted to the feasible problem of the linear matrix inequality. Finally, the proposed approach is applied to a specified unpower aerocraft. The six dimensions of freedom simulation results show that the proposed approach is effective and feasible.     

An Application of the Stability Theory in Constrained Nonlinear Optimization

1　 IntroductionIt is known that a given constrained nonlinear optimization problem can be transformedand solved by ordinary differential equations(ODE) [4,5] .Based on the preliminary resultsof [8～ 1 2 ] ,this paper uses a stability theory of ODE systems to analyze the asymptoticalproperties of differential equations which are derived from a given constrained nonlinearoptimization problem.We also state conditions of the overall uniform asymptoticalstability of the singular points aboutpart…     

Stabilization of discrete nonlinear systems based on control Lyapunov functions

The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.