Robust control for nonlinear systems with structured [formula omitted]2-gain bounded uncertainty

This article investigates the robust observer-based controller design problem for nonlinear parameter-varying systems subject to uncertainty and external disturbances. First, a novel augment vector is constructed, and an corresponding model of the resulting closed-loop system is obtained. Second, by applying the Lyapunov stability theory, a class of state-and-parameter-dependent robust asymptotic stability criteria is established, and the state-and-parameter-dependent sufficient conditions for the design of the robust observer-based controller are then acquired to guarantee the stability of the resulting closed-loop system, which can be effectively solved by sum-of-squares techniques. Different from the previous researches, the proposed control algorithm enables the state-and-parameter-dependent observer and the state-and-parameter-dependent controller design of the nonlinear parameter-varying systems to enjoy the advantage of separate design. The advantage can effectively reduce the computational complexity. Finally, simulation results demonstrate that the proposed robust observer-based controller shows improved performance in presence of uncertainty and external disturbances.

International audience

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

This article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm.

This paper is concerned with the problem of robust controller design for electro-hydraulic servo systems driven by double-rod hydraulic actuators. Firstly, by introducing a linear varying parameter, an electro hydraulic servo system is described as a linear parameter varying(LPV) model. Secondly, based on this LPV model and a parameter-dependent Lyapunov approach, two parameter-dependent controllers are established for the stabilization and tracking problems, respectively. The obtained controllers are simple and their gains can vary with the parameter measured online. Finally, the numerical simulations demonstrate the satisfactory performance of the proposed controllers.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

This article deals with the problem of robust low-order controller design for systems with multimodel representations. Such models are frequently used for the description of nonlinear and complex industrial power systems over an operating profile. We first develop a generalized complex extension of convex direction based on the interpolation and edge theorems. Subsequently, for plant models with parametric-type uncertainty, new vertex results related to robustness margins and system performance are derived. Based on this, new tools to design robust low-order controllers for such systems are presented.

This paper deals with a digital controller and observer design problem for the ball and beam system which is extended version of the previous investigated result. The controller is an extension of robust integral tracking controller. In the discrete-time system, it cannot perform integration and differentiation operation, so we introduce a difference system to design controller for the distance subsystem between reference and output. The observer is designed using dual system LQ design method. The observer gain is able to obtain as the result of robust control design problem of dual system. Each design problem is solved by the guaranteed cost control method. Through the numerical result, we validity and effectiveness of our proposed method.

A formulation of the coupled modeling and robust control design problem is presented. The distinguishing feature is the treatment of the control design model as a degree of design freedom. A simple example highlights the potential improvement in closed-loop performance under the coupled approach. Quantification of the strength of the coupling in terms of performance boundaries is also described. >

The μ analysis method is applied to a class of multivariable separable autonomous nonlinear feedback systems. The nonlinear element is replaced by its sinusoidal input describing function (SIDF) to develop a quasilinear nominal model for control analysis and design. Some properties of the ∞ -norm and structured singular values (SSVs) are shown to hold for the type of systems where the output is a function of control input-signal amplitude and frequency. The model uncertainty induced by the SDIF approximation is calculated and incorporated in the control design as an input multiplicative perturbation to the quasilinear nominal model. The μ analysis technique is then employed to study the stability and performance robustness of the nonlinear control system. Using small gain theorem, the condition for the absence of limit cycle is derived. The information obtained from this analysis is then used to design a bank of controllers using the H ∞ optimization-based μ synthesis technique. These controllers are designed such that the closed loop system is robust over a range of control-input amplitude. A simple scheme is then proposed to select the appropriate controller for the operating range. The simulation results illustrate that the proposed technique may be used to design a high performance robust controller for nonlinear systems and the absence of the limit cycle oscillation may be ensured.

Allowing for simultaneous occurrence of multiple actuator faults in signal channels, the problem of robust reliable tracking controller design for a class of uncertain systems with polytopic type uncertainty is investigated. Based an unstructured quadratic separator, a less conservative condition for the existence of a reliable tracking control is derived. In order to reduce the design conservatism, a parameter dependent formation is introduced in construction of the quadratic separator, which can give rise to the improvement in degree of freedom for controller synthesis. In addition, the condition mentioned above can be reduced to linear matrix inequalities (LMI). Finally an example is given to demonstrate the effectiveness and superiority of presented robust reliable tracking controller.

Based on the RBF neural network, a novel estimator is presented for unmodeled dynamics and a robust adaptive control scheme is proposed for a class of uncertain nonlinear systems with a general set of uncertainties in this paper. A class of more extended semi-strict feedback form system is studied in this paper. With the recent results, it is impossible to design the robust controller for the system. A novel estimator is constructed to estimate the unmeasured states of the unmodeled dynamic. With the novel estimator and the RBF based adaptive backstepping, the overall scheme achieves robust regulation of the output while maintaining boundedness of all the signals and states.

In this paper, a robust genetic control design problem for a class of uncertain neutral delay systems in state and control input is considered. The methodology is based on the constructive use of the Lyapunov functional, and a new delay-dependent stabilization criterion is proposed to guarantee robust stability for the systems via linear control. Linear matrix inequality (LMI) and genetic algorithm (GA) are used to seek the state-feedback gain without complex mathematics.

This paper addresses the problem of robust output feedback controller design with guaranteed cost and multiple quadratic Lyapunov function for linear switched systems in the continuous-time domain. The approach followed in this paper looks at the existence of switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality based conditions allow checking the existence of a family of quadratic Lyapunov functions. Then, a switched robust output feedback design method is established. The proposed method is illustrated on numerical example.

This study considers robust proportional integral derivative (PID) control for attitude stabilization of quad-rotors. The proposed method is designed for maintaining robustness against uncertainty of the system parameters and minimizing the control input for the quad-rotors. The closed-loop poles of the controlled system are placed within a region with specified decay rate and damping ratio for achieving specified transient response. The PID gains are tuned offline using theory. The robust control design problem is converted to optimization problem and solved using genetic algorithm. Finally, the proposed controller is simulated in the nominal and perturbations scenarios.