Fuzzy robust sliding mode control of a class of uncertain systems

Aiming at a class of systems under parameter perturbations and unknown external disturbances, a method of fuzzy robust sliding mode control was proposed. Firstly, an integral sliding mode surface containing state feedback item was designed based on robust H∞ control theory. The robust state feedback control was utilized to substitute for the equivalent control of the traditional sliding mode control. Thus the robustness of systems sliding mode motion was improved even the initial states were unknown. Furthermore, when the upper bound of disturbance was unknown, the switching control logic was difficult to design, and the drawbacks of chattering in sliding mode control should also be considered simultaneously. To solve the above-mentioned problems, the fuzzy nonlinear method was applied to approximate the switching control term. Based on the Lyapunov stability theory, the parameter adaptive law which could guarantee the system stability was devised. The proposed control strategy could reduce the system chattering effectively. And the control input would not switch sharply, which improved the practicality of the sliding mode controller. Finally, simulation was conducted on system with parameter perturbations and unknown external disturbances. The result shows that the proposed method could enhance the approaching motion performance effectively. The chattering phenomenon is weakened, and the system possesses stronger robustness against parameter perturbations and external disturbances.

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.

A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay

The robust stabilization problem for uncertain systems with time-varying delay has been discussed. A new sufficient criterion is obtained to guarantee the closed-loop system robust stabilizable. The controller gain matrix is included in a Hamiltonian matrix. The Hamiltonian matrix can be constructed by the boundedness of the uncertainties. Some examples are given to illustrate the feasibility of the criterion.

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.

OPTIMAL CONTROL OF A CLASS OF INFINTIE DIMENSIONAL UNCERTAIN SYSTEMS

In this paper, we use relaxation theory to study a class of relaxed infinite dimensional uncertain systems.We obtained the exisence and some important properties of solutions of relaxed systems first. Then the existence of optimal control of relaxed systems witha correspondingly relaxed cost functional was proved. Lastly, we showed that under someassumptions the set of original trajectories is dense in the set of relaxed trajectories and therelaxed control problem is equivalent to the original one.

New synthesis algorithm of static output feedback sliding mode control for a class of uncertain systems

Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined sliding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

A Data-Based Feedback Relearning Algorithm for Uncertain Nonlinear Systems

In this paper,a data-based feedback relearning algorithm is proposed for the robust control problem of uncertain nonlinear systems.Motivated by the classical on-policy and off-policy algorithms of reinforcement learning,the online feedback relearning(FR)algorithm is developed where the collected data includes the influence of disturbance signals.The FR algorithm has better adaptability to environmental changes(such as the control channel disturbances)compared with the off-policy algorithm,and has higher computational efficiency and better convergence performance compared with the on-policy algorithm.Data processing based on experience replay technology is used for great data efficiency and convergence stability.Simulation experiments are presented to illustrate convergence stability,optimality and algorithmic performance of FR algorithm by comparison.

Tuning of Sampled-Data ADRC for Nonlinear Uncertain Systems

This paper concerns with the parameters tuning of active disturbance rejection control(ADRC) for a class of nonlinear systems with sampling rate not fast enough. The theoretical results show the quantitative relationship between the sampling rate, the parameters of ADRC, the size of uncertainties in system and the properties of the closed-loop system. Furthermore, the capability of the sampled-data ADRC under given sampling rate is quantitatively discussed.

Global robust optimal sliding mode control for uncertain affine nonlinear systems

The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.

Adaptive integral higher order sliding mode controller for uncertain systems

This paper proposes an adaptive integral higher order sliding mode （HOSM） controller for uncertain sys- tems. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discon- tinuous sign function in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used in the proposed controller eliminates the need of prior knowledge about the upper bound of the system uncertainties. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. Simulation results demonstrate the advantages of the proposed control scheme.

ROBUST MODEL PREDICTIVE CONTROL OF CONTINUOUS UNCERTAIN SYSTEMS

The authors concern robust model predictive control for linear continuous systems with polytopic uncertainties and input constraints. At each sampling time, a piecewise constant control sequence is obtained by solving a set of linear matrix inequalities. The sufficient conditions on the existence of the model predictive control are given, and the robust stability of the closed-loop systems is guaranteed. A simulation example illustrates the efficiency of the proposed method.

STABILITY CRITERIA FOR A CLASS OF UNCERTAIN SYSTEMS WITH TIME-DELAY

Some stability criteria are obtained for a class of uncertain systems with time-delay usingLyapunov functional and analytic techniques. It is easy to check the criteria by making use of theboundedness of the uncertainties.

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.

Integral-inequality approach to delay-dependent robust H-infinity control for uncertain neutral systems

This paper focuses on the design problem of a memoryless state feedback robust H-infinity controller for a class of uncertain neutral systems. By using a newly established integral inequality, a new delay-dependent bounded real lemma for such systems is derived without involving a fixed model transformation. Furthermore, new delay-dependent sufficient conditions for the existence of robust H-infinity controllers are presented in terms of nonlinear matrix inequalities. A design procedure involving an iterative algorithm is also proposed to design such controllers. Numerical examples are given to demonstrate the less conservatism of the proposed method.

Adaptive Robust Control for A Class of Nonlinear Systems with Unknown Uncertainties

The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.

Dynamic observer-based controllers for linear uncertain systems

This paper addresses robust controller design for uncertain linear systems via a dynamic observer-based controller. A dynamic observer is an alternative structure for a classical observer which can be regarded as a general form of a usual observer and has additional degrees of freedom in the observer structure. Using this new observer structure, a new observer-based controller for linear systems is proposed. Some strict linear matrix inequalities （LMIs） have been given to find the dynamic observer parameters and controller gain. It is shown that dynamic observer can be used effectively for tackling the drawbacks of the classical observer-based robust controller design methods. As an advantage, LMIs are derived even in the presence of uncertainties in system, input and output matrices simultaneously, whereas by using the traditional observer, bilinear matrix inequalities （BMIs） are given in the presence of such uncertainties. Moreover, the proposed LMIs do not imply the equality constraint. Simulation results are used to illustrate the effectiveness of the proposed design technique.

Robust H_2 control for uncertain sampled-data systems

A new approach is proposed for robust H2 problem of uncertain sampled-data systems. Through introducing a free variable, a new Lyapunov asymptotical stability criterion with less conservativeness is established. Based on this criterion, some sufficient conditions on two classes of robust H2 problems for uncertain sampled-data control systems axe presented through a set of coupled linear matrix inequalities. Finally, the less conservatism and potential of the developed results are illustrated via a numerical example.

Robust H_∞ controller design for sampled-data systems with parametric uncertainties

This article investigates the problem of robust H∞ controller design for sampled-data systems with time-varying norm-bounded parameter uncertainties in the state matrices. Attention is focused on the design of a causal sampled-data controller, which guarantees the asymptotical stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed H∞ performance bound for all admissible uncertainties. Sufficient condition for the solvability of the problem is established in terms of linear matrix inequalities （LMIs）. It is shown that the desired H∞ controller can be constructed by solving certain LMIs. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Robust Variance-Constrained Design for Uncertain Continuous Stochastic Systems via Output Feedback

This paper studies the problem of robust controller design for linear perturbed continuous stochasticsystems with variance constraints via output feedback. The goal is to design static output feedback controllers suchthat the uncertain system has the desil'ed stability margin and the steady-state variance constraints. The existenceconditions for the desired controllers are discussed, and the analytical expression of these controllers is alsocharacterized. A numerical example is provided to demonstrate the directness and effectiveness of the proposedmethod.