Solving the Synthesis Problem Self-Organizing Control System in the Class of Elliptical Accidents Optics for Objects with One Input and One Output

In this paper, the problem of designing a tracking controller for uncertain nonlinear second-order SISO (single input single output) systems which can suppress the effects of both the model uncertainty and noisy measurements is considered. Based on the framework of linear systems with nonlinear uncertainties whose norm-bounds are known we construct not only a sliding mode controller but a sliding observer for uncertain nonlinear second-order SISO systems, and we show the robust stability of the closed-loop control system. >

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

We present the parameter robust risk-sensitive control theory to deal with the parameter uncertainties of a system. In this synthesis, the parameter uncertainties are decomposed into three parts, and are reflected in the cost function and the noise models. This new method improves the tolerance of a controller to parameter uncertainties in a system. We apply the newly developed method to satellite structure attitude control application. The linearized version of the satellite structure attitude model is derived for the attitude hold mode. To determine the performance of the parameter robust risk-sensitive control method, the steady-state mean square histories of the state and input variables are calculated by finding the covariance matrices. Moreover, the performance robustness of parameter robust risk-sensitive control is compared with the classical linear quadratic Gaussian control. Finally, as an application of this parameter robust risk-sensitive control, we consider commercially operating remote sensing satellite. The numerical simulations show that the parameter robust risk-sensitive control method has better performance and stability characteristics than the classical linear quadratic Gaussian control method, especially when the parameter uncertainties are large.

The paper presents a novel robust control of one class of nonlinear single-input single-output (SISO) systems with distributed delay on state used the auxiliary loop method. The problem is solved by introducing an auxiliary loop and using two Khalil observers to compensate for a generalized disturbance signal containing information not only about the parametric uncertainty of the installation model, but also information about distributed delay and disturbances. The designed control law is investigated in MATLAB. To illustrate the obtained results, an example of a nonlinear system with a distributed time delay is given. It is shown that the proposed control law under conditions of parametric uncertainty ensures the achievement of the goal with a given accuracy.

An experimental approach to multi-input multi-output nonlinear active vibration control of a clamped sandwich beam

Autoregulation refers to the automatic adjustment of blood flow to supply the required oxygen and glucose and remove waste, in proportion to the tissue's requirement at any instant of time. For the brain, cerebral autoregulation is an active process by which cerebral blood flow is controlled at an approximately steady level despite changes in the arterial blood pressure. Robust assessment of the cerebral autoregulation by a model that characterizes this system has been the goal of many studies, searching for techniques that can be used in clinical scenarios to detect potentially dangerous impairment of control. Multiple input, single output (MISO) models can be used to assess autoregulation, and system parameters can be estimated from spontaneous beat-to-beat variations in arterial blood pressure (ABP) and breath-by-breath end-tidal carbon dioxide (P(ETCO2)) as inputs, and cerebral blood flow velocity (CBFV) as the output. In this study a non-linear, multivariate approach, based on Volterra-type kernel estimation models is employed. The results are compared with linear models as well as nonlinear single-input single-output (SISO) models. The normalized mean squared error was used as the criteria of performance of each model in assessing cerebral autoregulation. Our simulation results indicate that for relatively short signals (around 300 sec), nonlinear, multiple-input models based on Volterra systems performed best, though the benefit varied considerably between subjects. When using a fixed model for all recordings, a linear SISO model with ABP as input provided the smallest average modeling error.

This paper presents a method of continuous-time simple adaptive control (SAC) using multiple neural networks for a single-input single-output (SISO) nonlinear systems with unknown parameters and dynamics, bounded-input bounded- output, and bounded nonlinearities. The control input is given by the sum of the output of the simple adaptive controller and the sum of the outputs of the parallel small-scale neural networks. The parallel small-scale neural networks are used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the parallel small- scale neural networks is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems. Finally, the stability analysis of the proposed method is carried out, and the effectiveness of this method is confirmed through computer simulations.

Treating non-linear systems as equivalent time-invariant systems with associated uncertainty is often excessively conservative and significantly reduces the achievable robust performance. This paper presents a method for reducing the associated uncertainty of non-linear uncertain single-input single-output systems based on Horowitz's method for non-linear quantitative feedback theory. The new method implements a non-linear compensator based on an approximate causal inversion of an identified nominal model. The inverse system compensator reduces the uncertainty associated with the linear time-invariant equivalent system. The method is applied and experimentally validated on the idle speed dynamics of an automotive SI engine system using an electric dynamometer.

Given a SISO (single-input single-output) system with arbitrary poles and zeros in the closed right half plane and having time delay uncertainty, the question arises as to the maximum time delay margin available before the closed-loop system becomes unstable when an arbitrary controller is connected to the SISO system in the closed loop. The authors provide a solution to this problem and show how to derive the controller corresponding to the optimum condition. The method of solution is based on general framework of P.P. Khargonekar and R. Tannenbaum (1985) for the robust stabilization of SISO systems with parameter uncertainty using Nevanlinna-Pick interpolation theory and the theory of conformal mapping. >

This paper addresses stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. First, the Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties is used as the model for the uncertain nonlinear system. Based on the fuzzy Lyapunov function approach and a parallel distributed compensation (PDC) scheme, we give stabilization conditions for closed-loop fuzzy systems with parametric uncertainties. Second, all the conditions are formulated in the format of linear matrix inequalities (LMIs) and contain upper bounds of the time derivative of premise membership functions as LMI variables. Finally, the T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. A numerical example of the chaotic Lorenz system is given to illustrate the utility of the fuzzy Lyapunov function approach.

The controlled atmospheric re-entry associated with the precision soft-landing of Reusable Launch Vehicles (RLVs) on Earth is very challenging as it depends on multiple parameters [1]. Over the last decade, the cost-effectiveness of such a technology has been finally demonstrated with the successful recoveries of SpaceX’s Falcon 9 first-stage rocket first [2], then followed by other companies such as the Rocket Lab’s Electron micro-launcher [3]. This breakthrough has been made possible by the development of advanced and robust computational methods able to generate in real time the flight conditions and to command the optimal vehicle's deflections accordingly to achieve a safe pinpoint landing. Indeed, during an Earth atmospheric re-entry, the vehicle is subjected to fast system dynamics changes partly induced by external loads associated with the terrestrial environment (e.g., lift, drag, wind and gusts), but also by the actuation commands to answer the landing constraints satisfaction and the vehicle integrity preservation. All those involve uncertainties and nonlinearities, which lead to vehicle’s instability and therefore give reason why for a highly performant Guidance, Navigation and Control system implementation [4]. More particularly, one of the critical aspects is the design of a robust control strategy capable of counteracting the previously defined disturbances and uncertainties while satisfying the strict accuracy requirements associated with the pinpoint landing [5]. As demonstrated by the current state-of-the-art on control design for launchers [6-7], the classical linear control theory represents a rich heritage with a lot of applications. This choice was motivated by its relative easiness of implementation and the possibility to use gain-scheduling techniques to adapt to nonlinear systems. Nevertheless, these techniques are well-adapted to the control system design of single-input single-output systems, such as for example a reusable rocket using a Thrust Vector Control (TVC) system as the unique actuator. The implementation of multiple-input multiple-output control systems becomes then complex since every channel is addressed in a single-loop fashion. This capability is however required for the future generation of reusable rocket, using also aerodynamic steering based on fins in addition to the TVC system for enhancing control authorities. Moreover, model uncertainties are not accurately considered in the design process, developed only with nominal conditions and stability margin requirements. For all these reasons, it results in an extensive (both in terms of time and cost) Verification and Validation campaign with many iterations and Monte-Carlo analyses to assess the performance and robustness of the control system. To overcome these drawbacks, the H-infinity family of methods, introduced a few years ago [8], provides with a powerful solution for robust control design. It relies on defining the control requirements in the frequency domain in terms of weighting functions and minimising the maximum gain of the resulting weighted system from the exogenous inputs to the outputs to be controlled. Moreover, the control-plant interaction is modelled through a Linear Fractional Transformation (LFT) representing the feedback action. Finally, the structured H-infinity method [9] allows to directly impose a specific control structure – like a Proportional-Integral-Derivative (PID), enabling the re-use of gain-scheduling techniques – and to consider parametric uncertainties for enhanced robustness. This paper studies the synthesis of a robust control system via structured H-infinity for the RLV atmospheric re-entry problem. First, the nonlinear 6-Degree-of-Freedom (6-DoF) RLV re-entry dynamics are simplified into a linear model and then linearised along a reference trajectory to get the nominal LFT of the system, then augmented with parametric uncertainties. The model covers the atmospheric re-entry and vertical landing of a first-stage rocket equipped with a TVC system and steerable planar fins. The controllers are built at different points of the re-entry trajectory, using the structured H-infinity framework through PID-like structures. Weighting functions considering the control objectives and requirements of a realistic RLV re-entry scenario are implemented. A robust stability analysis of the obtained system is performed via classical stability margins and structured singular value. Finally, the controllers are gain-scheduled and validated via Monte-Carlo analyses, using a nonlinear 6-DoF RLV re-entry dynamics simulator equipped with successive convex optimisation guidance. The performance of the resulting guidance and control architecture is compared with the baseline developed in previous works [10], using a TVC system only and classical linear feedback control through gain-scheduled PID controllers. This study lies within the ASCenSIon (Advancing Space Access Capabilities - Reusability and Multiple Satellite Injection) project, an innovative training network funded within H2020.

A robust control scheme for the output tracking of SISO (single input, single output) nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. The basic idea consists of designing a nonlinear regulator-based controller and then modifying it by defining a subset of the state space, called a sliding surface, on which the tracking error goes asymptotically to zero. It is found that, under certain conditions, the sliding controller forces the system to reach the sliding surface when perturbations on the plant occur, hence obtaining a tracking error that, in the mean, asymptotically tends to a sufficiently small region around zero. An illustrative example is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper studies the characteristic modeling problem for a class of single input single output (SISO) nonlinear systems with a relative degree of two. Firstly, to deal with the complexities of high-order nonlinear systems, we provide a class of low order and slowly time-varying linear systems to represent the original systems. Secondly, based on the characteristic model, we propose a linear controller by using coefficients obtained from system online identification. Through the above two steps, we solve the stabilization problem of closed-loop system composed of the characteristic model and the linear controller. Furthermore, the stability analysis of the closed-loop system composed of an exact discrete-time model and a linear controller is given. Finally, two simulation examples are given to show the effectiveness of the proposed design.

A two-stage Active Disturbance Rejection Control (ADRC) design procedure is presented for the output trajectory tracking control problem in Single Input Single Output (SISO) nonlinear systems. Aside from the given scalar system output, the plant is assumed to exhibit a second, physically measurable, internal scalar output variable. The system output is controlled in an ADRC manner from an implicit static, or dynamic, nonlinear feedback controller using, in general, a nonlinear differential expression of the internal output variable. A desired internal output trajectory is thus generated. The internal output variable, in turn, is controlled from the original input and forced to track the desired trajectory synthesized in the previous step by the auxiliary controller. Each ADRC controller design is based on a simplified model of the corresponding subsystem, usually relegating interaction variables and additive nonlinearities to be part of a local (total) disturbance input term. The control scheme is reduced to a set of linear ADRC controllers with, possibly, cancellation of nonlinear input gains which are assumed to be known. Two illustrative aerospace examples are presented where the proposed procedure is illustrated via digital computer simulations.

In this paper, the design of a neural network (NN) based adaptive model-based event-triggered control of an uncertain single input single output (SISO) nonlinear discrete time system in affine form is presented. The controller uses an adaptive estimator consisting of a single-layer NN not only to approximate the internal dynamics of an affine nonlinear discrete-time system but also to provide an estimate of the state vector during inter event interval. The NN weights of the adaptive NN estimator are tuned in a aperiodic manner at the event trigger instants unlike periodic updates in standard adaptive neural network (NN) control. A dead zone operator is used to reset the event trigger error to zero as long as the system states continue to remain in a bounded region due to NN reconstruction errors. Lyapunov method is used to derive the event trigger condition, prove uniform ultimate boundedness (UUB) of the NN weight estimation error and system states.