Wavelet-based Technique for Feedback Control of Uncertain Systems : a case study

In designing control systems an important aim is minimizing the effects of uncertainties on system performance. The time-frequency characteristics of wavelets are useful for applications that require online response, such as controlling a process. It is proven, that the wavelet based controllers perform extremely well under certain definite conditions. In this paper, the multiscale representation of the error signal is investigated in direct feedback. The control method is applied to a temperature control task. Simulation results show satisfactory performance and highly efficient disturbance rejection. Advantages and drawbacks of the wavelet based control strategy are also discussed

Fuzzy Expert System for Automatic Wavelet Shrinkage Procedure Selection for Noise Suppression

Signal processing is an indispensable issue of several technical areas. Wavelet shrinkage, i.e. thresholding in the wavelet coefficient domain, has been successfully used for signal and image noise removal problems. Although, the selection of the suitable wavelet threshold procedure is still a challenging task, because the applied method has significant impact on the result. Furthermore, the specific choice of wavelet, decomposition level and threshold rule, etc., allows a wide variability of the shrinkage method. This paper presents a new supervisory fuzzy expert system for automatic wavelet shrinkage method selection for noise suppression of unknown signals. Simulation results show efficient performance of the system

Combination of RFPT-based Adaptive Control and Classical Model Identification

The traditional approach in the design of adaptive controllers for nonlinear dynamic systems normally applies Lyapunov's "direct" method that has the main characteristic features as follows: a) it yields satisfactory conditions for the stability, b) instead focusing on the primary design intent (e.g. the precise prescription of the trajectory tracking error relaxation) it concentrates on proving "global stability" that often is "too much" for common practical applications, c) in the identification of the model parameters of the controlled system it provides a tuning algorithm that contains certain components of the Lyapunov functions therefore it works with a large number of arbitrary adaptive control parameters; d) the parameter identification process in certain cases is vulnerable if unknown external perturbations can disturb the system under control. In order to replace this technique by a simpler approach concentrating on the primary design intent the "Robust Fixed Point Transformation (RFPT)"-based technique was suggested that - at the cost of sacrificing the need for global stability - applied iteratively deformed control signal sequences that on the basis of Banach Fixed Point Theorem converged to the appropriate control signal only within a bounded basin of attraction. This method was found to be applicable for a wide class of systems to be controlled, it was robust against the unknown external disturbances, used only three adaptive control parameters and later was completed by fine tuning of only one of these control parameters to keep the system in the region of convergence. In the present paper theoretical and simulations based considerations are presented revealing that the two methods can be combined in the control of certain physical systems

Novel Generation of Fixed Point Transformation for the Adaptive Control of a Nonlinear Neuron Model

The neurons as living cells work as essentially nonlinear oscillators or spike generators. In the case of a particular model the "ideal", the till acceptable i.e. "healthy", and the impaired ("sick") operation of a neuron can be represented by appropriate parameter settings. A practically interesting control task may be forcing the motion of a "sick" neuron to trace the trajectory generated by an "ideal" one on the basis of an available approximate model. In both cases the existence of three different parameter settings is assumed. As is well known essentially nonlinear systems cannot be well controlled on the basis of linearized models and linear techniques. The general nonlinear technique uses Lyapunov's "direct" method that guarantees global stability of the solution that otherwise suffers from several deficiencies. An alternative approach that removes these deficiencies at the cost of giving up global stability uses a special iteration created by a particular fixed point transformation. In the present paper a systematic method is presented for the generation of whole families of fixed point transformations that can be used in nonlinear adaptive control of Single Input - Single Output (SISO) systems. The applicability of the novel method is demonstrated by the adaptive control of the FitzHugh-Nagumo neuron model investigated by simulations

Adaptive Controller using Fuzzy Modeling and Sigmoid Generated Fixed Point Transformation

The great majority of the adaptive nonlinear control design are based on Lyapunov's 2nd or commonly referred to as the Direct method. In the last years the "Sigmoid Generated Fixed Point Transformation (SGFPT)" has been introduced for replacing the Lyapunov technique. This systematic method has been proposed for the generation of whole families of Fixed Point Transformations. In addition it has been extended from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems. Recently, several model building issues are increasingly replaced by soft-computing based methods. In spite of the classical hard-computing methods the intelligent methodologies are able to deal with imprecisions, uncertainties, etc. by an efficient and robust way. Fuzzy logic is widely used for modeling complex and ill-defined systems. In this paper we apply the fuzzy modeling in the SGFPT control design. The applicability of the proposed scheme is confirmed by the adaptive control of the inverted pendulum system. In the investigations an "affine", and a "soft computing-based" model were compared. Simulation results validate that the presented technique fulfills the performance criteria

Generalization of a Sigmoid Generated Fixed Point Transformation from SISO to MIMO Systems

Recently a systematic method was presented for the generation of whole families of "Fixed Point Transformations" that can be used in nonlinear adaptive control of "Single Input - Single Output (SISO)" systems as alternatives of Lyapunov's "direct method". In the present paper further development of this alternative method is considered. It consists in the generalization of the method for " Multiple Input - Multiple Output (MIMO)" systems. The applicability of the novel method is demonstrated by the adaptive control of a 2 "Degree of Freedom (DoF)" system, a cart indirectly driven in the horizontal direction by a rotated pendulum. Results of numerical simulations illustrate and substantiate the usability of the suggested approach

Application of Fixed Point Transformation to Classical Model Identification using New Tuning Rule

Up to now the fundamental tool of adaptive nonlinear control design is Lyapunov's 2nd or "Direct" Method. Recently the Sigmoid Generated Fixed Point Transformation (SGFPT) has been introduced for evading the application of the Lyapunov technique. This systematic method has been presented for the generation of whole families of Fixed Point Transformations and has been extended from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems. Few studies have been revealed that the original Robust Fixed Point Transformation (RFPT) can be successfully combined with some modification of the classical methods, such as the Modified Adaptive Inverse Dynamic Robot Controller (MAIDRC) and the Modified Adaptive Slotine-Li Robot Controller (MADSLRC). This paper presents that the SGFPT can also well coexist with the MAIDRC control design. Additionally, a novel, even more simplified tuning technique is proposed that also applies fixed point transformation-based tuning rule for parameter identification. The theoretical considerations are validated by numerical simulations made for a 2 Degree of Freedom (DoF) paradigm, in the adaptive control of two coupled mass-points with simultaneous parameter identification

Replacement of parameter tuning with simple calculation in adaptive control using "Sigmoid generated fixed point transformation"

Lately a systematic method was presented for the generation of whole families of Fixed Point Transformations that can be used in nonlinear adaptive control of Single Input - Single Output (SISO) as well as Multiple Input - Multiple Output (MIMO) systems as alternatives of Lyapunov's direct method. This transformation was called Sigmoid Generated Fixed Point Transformation (SGFPT). This paper introduces new improvements on this alternative approach. It is shown that in contrast to the original Robust Fixed Point Transformation (RFPT), for guaranteeing the global stability of the control, instead of tuning, a simple estimation can be done for one of the adaptive control parameters. The novel method is demonstrated by the adaptive control of a 2 Degree of Freedom (DoF) TORA system. Simulation results validate that the suggested approach is beneficial and ensures satisfactory performance

Stabilization of a Modified Slotine-Li Adaptive Robot Controller by Robust Fixed Point Transformations

The \u201cAdaptive Slotine-Li Robot Controller (ASLRC)\u201d of the nineties of the past century was designed by a sophisticated process based on the use of Lyapunov\u2019s 2 nd method. In the possession of the exact analytical form of the system model it generally can achieve global asymptotic stability by learning the system\u2019s exact dynamic parameters. However, it is not robust to friction effects and unknown external disturbances. In contrast to that the adaptive controllers designed by the use of \u201cRobust Fixed Point Transformations (RFPT)\u201d are only locally stable, work on the mathematical basis of Banach\u2019s Fixed Point Theorem, cannot learn the system\u2019s analytical model parameters but they are very robust to modeling deficiencies (e.g. abandoned friction effects) and unknown external forces. In this paper it is shown that by evading the use of Lyapunov function in the adaptive control design an appropriate modification of the ASLRC can be elaborated that is able to properly learn the exact model parameters if external disturbances are missing. It can be combined with the RFPT-based controller that makes it robust to formal modeling inconsistencies and external forces, though in this case it cannot learn the appropriate system parameters. It is also shown that the symbiosis with the RFPT-based method does not disturb the parameter identification process if modeling inconsistencies and disturbances are absent

Adaptive Controller Using Fixed Point Transformation for Regulating Propofol Administration Through Wavelet-based Anesthetic Value

In recent years automated anesthesia has gained much interest. In this paper the applicability of the Fixed Point Transformation-based Adaptive Control design for automatic control of the depth of hypnosis during surgical operation has been investigated. The applied control design assumes the availability of the rough model of the dynamic system under control. The here presented technique regulates the WAV(CNS) index as the only measurable variable by controling the intravenous propofol administration. Simulation results validate that the proposed control design ensures promising performance and is able to cope with unexpected surgical stimulations and anesthetic interactions during surgical procedures