Class Of Multivariable Nonlinear Systems Research Articles

Output regulation by postprocessing internal models for a class of multivariable nonlinear systems

SummaryIn this paper we propose a new design paradigm, which employs a postprocessing internal model unit, to approach the problem of output regulation for a class of multivariable minimum‐phase nonlinear systems possessing a partial normal form. Contrary to previous approaches, the proposed regulator handles control inputs of dimension larger than the number of regulated variables, provided that a controllability assumption holds, and can employ additional measurements that need not to vanish at the ideal error‐zeroing steady state, but that can be useful for stabilization purposes or to fulfill the minimum‐phase requirement. Conditions for practical and asymptotic output regulation are given, underlying how in postprocessing schemes the design of internal models is necessarily intertwined with that of the stabilizer.

Variable-structure backstepping controller for multivariable nonlinear systems with actuator nonlinearities based on adaptive fuzzy system

In this paper, a novel robust adaptive fuzzy control is presented for a quite general class of multivariable nonlinear systems with actuators’ nonlinearities (saturation with dead zone) and uncertain dynamics. The backstepping concept in combination with the variable-structure control framework and Lyapunov approach is used to design this adaptive fuzzy control. The fuzzy systems are incorporated in the controller for approximating online the unknown system dynamics. In the controller design and stability analysis, the control gain matrices, which are not necessarily symmetric and definite, are decomposed via the so-called SDU matrix decomposition lemma into a product of three main useful matrices, namely a symmetric definite-positive matrix, a diagonal constant matrix with + 1 or − 1 in its main diagonal and a unity upper triangular matrix. It is shown that the proposed adaptive fuzzy control is able to ensure the uniform ultimate boundedness of all solutions of the closed-loop system, as well as the convergence of the underlying tracking errors. Finally, in a numerical simulation framework, the effectiveness of the presented controller is illustrated on two practical examples.

Adaptive asymptotic stabilization of a class of unknown nonlinear systems with specified convergence rate

SummaryThis paper focuses on the asymptotic stabilization problem for a class of multivariable nonlinear systems with relative degree one, practical examples of which incorporate the liquid level control of water tanks, and the speed control of interconnected carts. The presence of the unknown (other than uncertain) additive and multiplicative nonlinearities renders asymptotic stability difficult to be achieved by the existing robust control methods. To conquer this obstacle, a novel adaptive control strategy is proposed. In the control design, the state constraint technique is newly introduced to the adaptive design to generate a proper control gain to compensate for unknown nonlinearities, instead of the use of extra approximating structures. By this means, both the prescribed transient performance regarding the convergence rate and the expected asymptotic stability are preserved. Finally, simulation results are given to illustrate the established theoretical findings.

Adaptive sensor fault-tolerant control for a class of multi-input multi-output nonlinear systems: Adaptive first-order filter-based dynamic surface control approach

This paper is concerned with the adaptive fault-tolerant control (FTC) problem for a class of multivariable nonlinear systems with external disturbances, modeling errors and time-varying sensor faults. The bias, drift, loss of accuracy and loss of effectiveness faults can be effectively accommodated by this scheme. The dynamic surface control (DSC) technique and adaptive first-order filters are brought together to design an adaptive FTC scheme which can reduce significantly the computational burden and improve further the control performance. The adaptation laws are constructed using novel low-pass filter based modification terms which enable under high learning or modification gains to achieve robust, fast and high-accuracy estimation without incurring undesired high-frequency oscillations. It is proved that all signals in the closed-loop system are uniformly ultimately bounded and the tracking-errors can be made arbitrary close to zero. Simulation results are provided to verify the effectiveness and superiority of the proposed FTC method.

Output Regulation of Multivariable Nonlinear Systems Using Extra Outputs

We consider the output regulation problem for a class of nonlinear multivariable systems in the case, besides the regulated error, also additional measurements not necessarily zero in steady state are available. To offset the steady state value of the extra measurements and make the latter effective for stabilisation purposes, we propose a control structure in which those measurements are filtered by a post-processor specifically designed to block their steady state value. The specific scenario we have in mind is the one of nonlinear systems that are nonminimum-phase between the input and the regulated error and for which extra measurements are necessary, or simply desirable, to succeed in robust output feedback stabilisation.

Adaptive Fuzzy Control for a Class of Multivariable Nonlinear Systems with Unknown Control Direction

In this paper, a direct adaptive fuzzy control scheme is presented for a class of uncertain MIMO nonlinear systems with unknown sign of the control gain matrix. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller which can achieve the control objectives. The free parameters of the used fuzzy systems are adjusted online using the error between the unknown ideal controller and the fuzzy controller. Unlike previous works, the Nussbaum function technique is not used to deal with the unknown sign of the control gain matrix. In fact, in this paper, the unknown control direction is considered as an unknown constant parameter and it is estimated online by an appropriate adaptation law. The stability of the closed-loop system is analyzed using a Lyapunov approach. Simulation results are given to demonstrate the effectiveness of the proposed control design.

Global adaptive output feedback tracking for a class of multivariable nonlinear systems

In this paper, global adaptive output feedback tracking problem is considered for a class of multivariable nonlinear systems with unknown parameters and nonlinear terms linear in unmeasured states. Based on a modified high-gain observer and symmetric positive diagonal unity upper triangular factorisation of high-frequency gain matrix, an adaptive backstepping design is proposed, which is able to guarantee global stability of the closed-loop system and circumvent the over-parameterisation problem raised by using conventional backstepping method. Moreover, with the introduction of an error modification and an initialisation technique, it is proved that the tracking performance can be achieved.

Design of an adaptive terminal sliding‐function controller for nonlinear multivariable systems

SummaryThis paper presents an adaptive terminal sliding‐function controller approach for controlling a class of nonlinear multivariable systems with uncertainty. An appropriate terminal sliding function (TSF) is designed and then applied to the control law. Based on the Lyapunov stability theory, the adaptive terminal sliding‐function controller for nonlinear multivariable systems guarantees that the TSF is asymptotically convergent. Different from classical terminal sliding mode control, which uses a discontinuous switching control law, the TSF control uses a continuous TSF and thus avoids the chattering problem. The simulation results demonstrate that the proposed method achieves satisfactory stability. Copyright © 2013 John Wiley & Sons, Ltd.

Adaptive Output Feedback Control of Multivariable Nonlinear Systems Based on Hurwitz Assumption

In this paper, global adaptive output feedback tracking problem is considered for a class of multivariable nonlinear systems with unknown parameters and nonlinear terms linear in unmeasured states. Based on a modified high-gain observer and Hurwitz assumption of high frequency gain matrix, an adaptive backstepping design is proposed, which is able to guarantee global stability of the closed-loop system and circumvent the over-parameterization problem raised by using conventional back stepping method.

Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics

This paper addresses the problems of observer design and output feedback stabilization for a class of nonlinear multivariable systems, where the nonlinear system dynamics are described by ordinary differential equations (ODEs), and the sensor dynamics are governed by diffusion partial differential equations (PDEs). Based on the Luenberger observer theory, a Luenberger-type PDE-ODE cascaded observer is derived to estimate the state variables of the system. Then, an observer-based output feedback stabilizing controller is developed. The exponential stability of both the observer error system and closed-loop control system is proven via the Lyapunov direct method. Finally, numerical examples are provided to illustrate the effectiveness of the proposed design methods.

Output‐feedback robust adaptive backstepping control for a class of multivariable nonlinear systems with guaranteed tracking performance

SUMMARYThis paper is devoted to output‐feedback adaptive control for a class of multivariable nonlinear systems with both unknown parameters and unknown nonlinear functions. Under the Hurwitz condition for the high‐frequency gain matrix, a robust adaptive backstepping control scheme is proposed, which is able to guarantee the tracking performance and needs only one parameter to be updated online regardless of the system order and input–output dimension. To cope with the unknown nonlinear functions and improve the tracking performance, a kind of high‐gain K‐filters is introduced. It is proved that all signals of the closed‐loop system are globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.

Global robust output regulation for a class of multivariable systems

SUMMARYIn this paper, we study the global robust output regulation problem for a class of multivariable nonlinear systems. The problem is first converted into a stabilization problem of an augmented system composed of the original plant and an internal model. The augmented system is a multi‐input system containing both dynamic uncertainty and time‐varying static uncertainty. By decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by solving several single‐input control problems via a recursive approach utilizing the changing supply function technique. The theoretical result is applied to the speed tracking control and load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2011 John Wiley & Sons, Ltd.

Nonlinear system modeling and predictive control using the RBF nets-based quasi-linear ARX model

On the basis of the single-input single-output (SISO) RBF-ARX model proposed in previous works [Peng, H., et al. (2003b). Stability analysis of the RBF-ARX model based nonlinear predictive control. In Proceedings of the ECC2003; Peng, H., et al. (2003c). Modeling and control of nonlinear nitrogen oxide decomposition process. In Proceedings of the CDC’03; Peng, H., et al. (2004). RBF-ARX model based nonlinear system modeling and predictive control with application to a NO x decomposition process. Control Engineering Practice, 12, 191–203; Peng, H., et al. (2007). Nonlinear predictive control using neural nets-based local linearization ARX model—Stability and industrial application. IEEE Transactions on Control Systems Technology, 15, 130–143] the multi-input multi-output (MIMO) RBF-ARX model and its state-space representation are derived to describe the dynamics of a class of multivariable nonlinear systems whose working-point varies with time and which may be linearized around the working-point. The proposed MIMO RBF-ARX model has a basic regression-model structure that is analogous to the linear ARX model structure, and the elements of its regression matrices are composed of Gaussian radial basis function (RBF) neural networks that are dependent on the working-point state of the current system. An off-line estimation approach to parameters and orders of the MIMO RBF-ARX model is presented, and, on the basis of the estimated MIMO RBF-ARX model, a predictive control strategy is designed to control the underlying nonlinear system. A case study on a simulator of a thermal power plant is also given to illustrate the effectiveness of the nonlinear modeling and control method proposed in this paper.

Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping

A robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances. The controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique. For each auxiliary system, an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics, and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well. It is shown that the resulting closed-loop systems guarantee a satisfactory transient and asymptotic performance. A simulation example is also presented to illustrate the design procedure and controller performance.

Robust Output Feedback Control for Nonlinear Systems Including Actuators

A robust output feedback control is developed for the stabilization of a class of multivariable nonlinear systems including nonlinear actuators. The class of systems under consideration can be transformed into global normal form with no zero dynamics. The plant model is allowed to depend on constant unknown parameters which do not change the vector relative degree of the system. It is proven that if the actuator dynamics are sufficiently fast, the proposed controller will stabilize the origin of the actual system and will be robust with respect to the unknown parameters. It is also proven that the actuator dynamic need not be faster than the observer dynamics.

Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile.

Stable adaptive control for nonlinear multivariable systems with a triangular control structure

A stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators. By utilizing the system triangular property, integral-type Lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the "decoupling matrix" of the multivariable nonlinear system. It is shown that stability of the adaptive closed-loop system is guaranteed, and transient performance is analytically quantized by mean square and L/sub /spl infin// tracking error bound criteria.

Adaptive Robust Control of a Class of Multivariable Nonlinear Systems

This paper considers the adaptive robust control of a class of multi-input multi-output (MIMO) non linear systems with arbitrary known relative degrees transformable to a semi-strict feedback form. The form allows parametric uncertainties, unknown nonlinear functIons such as modeling errors and external disturbances. Parametric uncertainties can appear in the input channels. The last layer's state equations do not have to be completely linearly parametrized. The method achieves a guaranteed transient performance and a prescribed final tracking accuracy in the presence of both parametric uncertainties and unknown nonlinear functions. In addition, the method achieves asymptotic stability in the presence of parametric uncertainties without using high-gain feedback control. The applications of the method include the motion and force tracking control of robot manipulators in contact with unknown stiffness environments.

Output feedback stabilization using variable structure control

We consider the stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using variable structure output feedback control. In particular, the system can be transformed into a normal form with no zero dynamics. A robust high-grain observer is used to estimate the state variables while rejecting the effect of disturbance. A globally bounded discontinuous variable structure controller is designed to compensate for modelling error. We show that the controller can stabilize the closed-loop system and does not suffer from the peaking phenomenon that exists in previous designs.

Semiglobal stabilization of a class of nonlinear systems using output feedback

The stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback, is considered. In particular, a class of systems which can be transformed into a global normal form with no zero dynamics is treated. Semiglobal stabilization means that for every compact set of initial conditions, an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction can be designed. The system equations are allowed to depend on constant unknown parameters which do not change the vector relative degree of the system, and the controller is robust with respect to these parameters. Global Lipschitz conditions are not required. >