Nonlinear feedback control of multivariable non-minimum-phase processes

A new method of controlling nonlinear processes with a non-minimum-phase delay-free part is presented. Two control laws are derived for stable, multiple-input multiple-output processes. They are obtained by requesting an approximately linear, input–output response and exploiting the connections between model-predictive control and input–output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The application and performance of the control laws are illustrated using numerical simulation of two chemical reactor examples that exhibit non-minimum-phase behavior.     

Robust nonlinear feedback–feedforward control of a coupled kinetic Monte Carlo–finite difference simulation

Robust nonlinear feedforward–feedback controllers are designed for a multiscale system that dynamically couples kinetic Monte Carlo (KMC) and finite difference (FD) simulation codes. The coupled codes simulate the copper electrodeposition process for manufacturing on-chip copper interconnects in electronic devices. The control objective is to regulate the current density subject to the condition that the steady-state fluctuation of the overpotential remains bounded within ±0.01 V. The controller designs incorporate a low-order stochastic model that captures the input–output behavior of the coupled KMC–FD code. The controllers achieve the objectives and the closed-loop responses implemented on the low-order model and the coupled KMC–FD code match well within stochastic variations. The nonlinear feedforward control reduces the rise time of the controller response while the feedback control ensures robustness in the presence of model uncertainty.     

Hankel singular value functions from Schmidt pairs for nonlinear input–output systems

This paper presents three results in singular value analysis of Hankel operators for nonlinear input–output systems. First, the notion of a Schmidt pair is defined for a nonlinear Hankel operator. This makes it possible to define a Hankel singular value function from a purely input–output point of view and without introducing a state space setting. However, if a state space realization is known to exist then a set of sufficient conditions is given for the existence of a Schmidt pair, and the state space provides a convenient representation of the corresponding singular value function. Finally, it is shown that in a specific coordinate frame it is possible to relate this new singular value function definition to the original state space notion used to describe nonlinear balanced realizations.     

Fuzzy control of an ANFIS model representing a nonlinear liquid-level system

This paper aims to serve two main objectives; one is to demonstrate the modelling capabilities of a neuro-fuzzy approach, namely ANFIS (adaptive-network based fuzzy inference system) to a nonlinear system; and the other is to design a fuzzy controller to control such a system. The nonlinear system, which is a liquid-level system, is represented first by its mathematical model and then by ANFIS architecture. The ANFIS model is formed by means of input–output data set taken from the mathematical model. Then a PID-type fuzzy controller, which linguistically approximates the classical three-term compensation, was designed to control the system represented by both its mathematical and ANFIS models in order to perform an agreement comparison between them. It is shown that the ANFIS architecture can model a nonlinear system very accurately by means of input–output pairs obtained either from the actual system or its mathematical model. It is also shown that such a system can be controlled effectively by a fuzzy controller.     

Relationship between poles and zeros of input–output and chain-scattering systems

A system is frequently represented by transfer functions in an input–output characterization. However, such a system (under mild assumptions) can also be represented by transfer functions in a port characterization, frequently referred to as a chain-scattering representation. Due to its cascade properties, the chain-scattering representation is used throughout many fields of engineering. This paper studies the relationship between poles and zeros of input–output and chain-scattering representations of the same system.     

Input–output decoupling of nonlinear systems by static measurement feedback

This paper gives necessary and sufficient conditions for solvability of the strong input–output decoupling problem by static measurement feedback for nonlinear control systems.     

Asymptotic characterizations of input–output-to-state stability for discrete-time systems

We establish the equivalence between global detectability and output-to-state stability for difference inclusions with outputs, and we present equivalent asymptotic characterizations of input–output-to-state stability for discrete-time nonlinear systems. These new stability characterizations for discrete-time systems parallel what have been developed for continuous-time systems in Angeli et al. [Uniform global asymptotic stability of differential inclusions, J. Dynamical Control Systems 10 (2004) 391–412] and Angeli et al. [Seperation principles for input–output and integral-input-to-state stability, SIAM J. Control Optim. 43 (2004) 256–276].     

Piecewise regression for fuzzy input–output data with automatic change-point detection by quadratic programming

To handle the large variation issues in fuzzy input–output data, the proposed quadratic programming (QP) method uses a piecewise approach to simultaneously generate the possibility and necessity models, as well as the change-points. According to Tanaka and Lee [H. Tanaka, H. Lee, Interval regression analysis by quadratic programming approach, IEEE Transactions on Fuzzy Systems 6 (1998) 473–481], the QP approach gives more diversely spread coefficients than linear programming (LP) does. However, their approach only deals with crisp input and fuzzy output data. Moreover, their method is weak in handling fluctuating data. So far, no method has been developed to cope with the large variation problems in fuzzy input–output data. Hence, we propose a piecewise regression for fuzzy input–output data with a QP approach. There are three advantages in our method. First, the QP technique gives a more diversely spread coefficient than does a linear programming technique. Second, the piecewise approach is used to detect the change-points in the estimated model automatically, and handle the large variation data such as outliers well. Third, the possibility and necessity models with better fitness in data processing are obtained at the same time. Two examples are presented to demonstrate the merits of the proposed method.     

On the nonuniqueness of singular value functions and balanced nonlinear realizations

The notion of balanced realizations for nonlinear state space model reduction problems was first introduced by Scherpen in 1993. Analogous to the linear case, the so-called singular value functions of a system describe the relative importance of each state component from an input–output point of view. In this paper it is shown that the procedure for nonlinear balancing has some interesting ambiguities that do not occur in the linear case. Specifically, distinct sets of singular value functions and balanced realizations are possible.     

Irreducibility, reduction and transfer equivalence of nonlinear input–output equations on homogeneous time scales

The purpose of this paper is to present a necessary and sufficient condition for irreducibility of nonlinear input–output delta differential equations. The condition is presented in terms of the common left divisor of two differential polynomials describing the behaviour of the system defined on a homogenous time scale. The concept of reduction is explained. Subsequently, the definition of transfer equivalence based upon the notion of an irreducible differential form of the system is introduced, inspired by the analogous definition for continuous-time systems.     

Input–output approach to stability and -gain analysis of systems with time-varying delays

Stability and L₂ (l₂)-gain of linear (continuous-time and discrete-time) systems with uncertain bounded time-varying delays are analyzed under the assumption that the nominal delay values are not equal to zero. The delay derivatives (in the continuous-time) are not assumed to be less than q<1. An input–output approach is applied by introducing a new input–output model, which leads to effective frequency domain and time domain criteria. The new method significantly improves the existing results for delays with derivatives not greater than 1, which were treated in the past as fast-varying delays (without any constraints on the delay derivatives). New bounded real lemmas (BRLs) are derived for systems with state and objective vector delays and norm-bounded uncertainties. Numerical examples illustrate the efficiency of the new method.     

A new nonlinear robust disturbance observer

This paper presents a new nonlinear robust disturbance observer by using only the input–output information for minimum phase dynamical systems with arbitrarily relative degrees. The model uncertainties, the nonlinear parts of the system are merged into the disturbance term, and are regarded as a part of the disturbance. The disturbance is assumed bounded. However, the upper and lower bounds are assumed unknown. The new disturbance observer is inspired by the VSS control theory, whereas the upper and lower bounds of the disturbance are adaptively updated. The estimation error of the disturbance can be made as small as necessary by choosing the design parameters. The attraction of the proposed method lies in its robustness to disturbance and easiness to be implemented. Example and simulation results show the effectiveness of the proposed algorithm.     

Admissible factorizations of Hankel operators induce well-posed linear systems

One of the basic axioms of a well-posed linear system says that the Hankel operator of the input–output map of the system factors into the product of the input map and the output map. Here we prove the converse: every factorization of the Hankel operator of a bounded causal time-invariant map from L² to L² which satisfies a certain admissibility condition induces a stable well-posed linear system. In particular, there is a one-to-one correspondence between the set of all minimal stable well-posed realizations of a given stable causal time-invariant input–output map (or equivalently, of a given H^∞ transfer function) and all minimal stable admissible factorizations of the Hankel operator of this input–output map.     

A covariance matching approach for identifying errors-in-variables systems

The errors-in-variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables models. In this paper a covariance matching approach is proposed to solve the identification problem. It applies for general types of input signals. The method utilizes a small set of covariances of the measured input–output data. This property applies also for some other methods, such as the Frisch scheme and the bias-eliminating least squares method. Algorithmic details for the proposed method are provided. User choices, for example specification of which input–output covariances to utilize, are discussed in some detail. The method is evaluated by using numerical examples, and is shown to have competitive properties as compared to alternative methods.     

Model matching for discrete-time periodic systems with time-varying relative degree and order

This paper extends the well-known solution for the linear time invariant model matching problem to discrete-time periodic systems with time-varying relative degree and order. It is shown that a key step to the design of a periodic output feedback controller is to compute the stable inverse of the periodic system. Using input–output equations, this problem is solved and model matching is achieved with system internal stability.     

Fuzzy neural network quadratic stabilization output feedback control for biped robots via H/sub /spl infin// approach

A novel fuzzy neural network (FNN) quadratic stabilization output feedback control scheme is proposed for the trajectory tracking problems of biped robots with an FNN nonlinear observer. First, a robust quadratic stabilization FNN nonlinear observer is presented to estimate the joint velocities of a biped robot, in which an H/sub /spl infin// approach and variable structure control (VSC) are embedded to attenuate the effect of external disturbances and parametric uncertainties. After the construction of the FNN nonlinear observer, a quadratic stabilization FNN controller is developed with a robust hybrid control scheme. As the employment of a quadratic stability approach, not only does it afford the possibility of trading off the design between FNN, H/sub /spl infin// optimal control, and VSC, but conservative estimation of the FNN reconstruction error bound is also avoided by considering the system matrix uncertainty separately. It is shown that all signals in the closed-loop control system are bounded.     

On converse Lyapunov theorems for ISS and iISS switched nonlinear systems

In this paper we present converse Lyapunov theorems for ISS and integral input to state stable (iISS) switched nonlinear systems. Their proofs are based on existing converse Lyapunov theorems for input–output to state stable and iISS nonlinear systems, and on the association of the switched system with a nonlinear system with inputs and disturbances that take values in a compact set.     

Speech enhancement based on undecimated wavelet packet-perceptual filterbanks and MMSE–STSA estimation in various noise environments

In this paper, we proposed a new speech enhancement system, which integrates a perceptual filterbank and minimum mean square error–short time spectral amplitude (MMSE–STSA) estimation, modified according to speech presence uncertainty. The perceptual filterbank was designed by adjusting undecimated wavelet packet decomposition (UWPD) tree, according to critical bands of psycho-acoustic model of human auditory system. The MMSE–STSA estimation (modified according to speech presence uncertainty) was used for estimation of speech in undecimated wavelet packet domain. The perceptual filterbank provides a good auditory representation (sufficient frequency resolution), good perceptual quality of speech and low computational load. The MMSE–STSA estimator is based on a priori SNR estimation. A priori SNR estimation, which is a key parameter in MMSE–STSA estimator, was performed by using “decision directed method.” The “decision directed method” provides a trade off between noise reduction and signal distortion when correctly tuned. The experiments were conducted for various noise types. The results of proposed method were compared with those of other popular methods, Wiener estimation and MMSE–log spectral amplitude (MMSE–LSA) estimation in frequency domain. To test the performance of the proposed speech enhancement system, three objective quality measurement tests (SNR, segSNR and Itakura–Saito distance (ISd)) were conducted for various noise types and SNRs. Experimental results and objective quality measurement test results proved the performance of proposed speech enhancement system. The proposed speech enhancement system provided sufficient noise reduction and good intelligibility and perceptual quality, without causing considerable signal distortion and musical background noise.     

Direct adaptive fuzzy-neural control with state observer andsupervisory controller for unknown nonlinear dynamical systems

In this paper, an observer-based direct adaptive fuzzy-neural network (FNN) controller with supervisory mode for a certain class of high order unknown nonlinear dynamical system is presented. The direct adaptive control (DAC) has the advantage of less design effort by not using FNN to model the plant. By using an observer-based output feedback control law and adaptive law, the free parameters of the adaptive FNN controller can be tuned on-line based on the Lyapunov synthesis approach. A supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be de-activated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Simulation results also show that our initial control effort is much less than those in previous works, while preserving the tracking performance