A nonlinear regulator scheme using sliding mode for SISO nonlinear systems

Multi-dimensional prediction method based on Bi-LSTMC for ship roll

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. >

A novel auto-tuning PID control mechanism for nonlinear systems

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.

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.

Linear regressive realizations of LTI state space models

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.

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.

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

We evaluate the performance of single- and multi-antenna multi-carrier code division multiple access (MC-CDMA) downlink (base station to mobile terminal) systems in multi-cell environments. We first propose a minimum mean square error (MMSE) filter for a single input single output (SISO) MC-CDMA downlink system. Then, we apply it to a SIMO (single input multiple output) system with a conventional turbo coding. Furthermore, we compare the performance of SISO (1 /spl times/ 1) and SIMO (1 /spl times/ 2) MC-CDMA systems with that of a multiple input multiple output (MIMO) (2 /spl times/ 2) system employing space-time turbo coded modulation (STTuCM) in a multi-cell environment with 7 cells by computer simulation. Based on the computer simulation results, it is found that the considered MIMO system can achieve twofold capacity with the same transmission power in the multi-cell environment.

Cooperative Non-Orthogonal Multiple Access (CNOMA) is a superior solution to increase the reliability of the far user. This technique treated the near user as relay for the far user or cell edge user which required significant power consumption. Hence hybrid simultaneous wireless information and power transfer (HS) protocol is considered with CNOMA downlink transmission to energize the relay operation without draining the battery of near user. Transmit antenna selection scheme is also integrated with the considered system. So this paper investigates the dominant factor among the fraction of block time for energy harvesting or power-splitting ratio in case of outage probabilities and channel capacity for the far user of the considered system with Single Input Single Output (SISO) scheme and Multiple Input Single Output (MISO) scheme as well. The simulation results of the channel capacities of the far user are compared with analytical results respectively.

A EROSPACE engineering applications greatly stimulated the development of optimal control theory during the 1950s and 1960s, where the objective was to drive the system states in such a way that some defined cost was minimized. This turned out to have very useful applications in the design of regulators (where some steady state is to be maintained) and in tracking control strategies (where some predetermined state trajectory is to be followed). Among such applications was the problem of optimal flight trajectories for aircraft and space vehicles. Linear optimal control theory in particular has been very well documented and widely applied, where the plant that is controlled is assumed linear and the feedback controller is constrained to be linear with respect to its input. However, the availability of powerful low-cost microprocessors has spurred great advantages in the theory and applications of nonlinear control. The competitive era of rapid technological change, particularly in aerospace exploration, now demands stringent accuracy and cost requirements in nonlinear control systems. This has motivated the rapid development of nonlinear control theory for application to challenging, complex, dynamical real-world problems, particularly those that bear major practical significance in aerospace, marine, and defense industries. Infinite-time horizon nonlinear optimal control (ITHNOC) presents a viable option for synthesizing stabilizing controllers for nonlinear systems by making a state-input tradeoff, where the objective is to minimize the cost given by a performance index. The original theory of nonlinear optimal control dates from the 1960s. Various theoretical and practical aspects of the problem have been addressed in the literature over the decades since. In particular, the continuous-time nonlinear deterministic optimal control problem associated with autonomous (time-invariant) nonlinear regulator systems that are affine (linear) in the controls has been studied by many authors. The long-established theory of optimal control offers quite mature and well-documented techniques for solving this control-affine nonlinear optimization problem, based on dynamic programming or calculus of variations, but their application is generally a very tedious task. Bellman’s dynamic programming approach reduces to solving a nonlinear first-order partial differential equation (PDE), expressed by the Hamilton–Jacobi–Bellman (HJB) equation. The solution to the HJB equation gives the optimal performance/cost value (or storage) function and determines an optimal control in feedback form under some smoothness assumptions. Alternatively, in the classical calculus of variations, optimal control problems can be characterized locally in terms of the Hamiltonian dynamics arising from Pontryagin’s minimum principle. These are the characteristic equations of the HJB PDE, which result in a nonlinear, constrained two-point boundary value problem (TPBVP) that, in general, can only be solved by successive approximation of the optimal control input using iterative numerical techniques for each set of initial conditions. Numerically, even though the nonlinear TPBVP is somewhat easier to solve than the HJBPDE, control signals can only be determined offline and are thus best suited for feedforward control of plants for which the state trajectories are known a priori. Therefore, contrary to the dynamic programming approach, the resultant control law is not generally in feedback form. Open-loop control, however, is sensitive to random disturbances and requires that the initial state be on the optimal trajectory. In contrast, nonlinear optimal feedback has inherent robustness properties (inherent in the sense that it is obtained by ignoring uncertainty and disturbances). The potential difficulty with the HJB approach is that no efficient algorithm is available to solve the PDE when it is nonlinear and the problem dimension is high, making it impossible to derive exact expressions for optimal controls for most nontrivial problems of interest. The optimal can only be computed in special cases, such as linear dynamics and quadratic cost, or very low-dimensional systems. In particular, if the plant is linear time invariant (LTI) and the (infinite-time) performance index is quadratic, then the corresponding HJB equation for this infamous linear-quadratic regulator (LQR) problem reduces to an algebraic Riccati equation (ARE). Contrary to the well-developed and widely applied theory and computational tools for theRiccati equation (for example, see [1]), theHJB equation is difficult, if not impossible, to solve for most practical applications. The exact solution for the optimal control policies is very complex

In this paper, a new method is presented for identification of single-input single-output (SISO) nonlinear systems with long time delay. The proposed dynamic extreme learning machine (DELM) is different from extreme learning machine in that it adds adaptive delay parameters in the output layer of the network, and the delay parameter is optimized by use of particle swarm algorithm. The dynamic extreme learning machine has two main advantages: First, for any system, it needs only two input nodes. Second, it does not need to know the specific delay time. A pH neutralization process and a nonlinear dynamic system process are used to evaluate the performance of the proposed method. Simulation results demonstrate the effectiveness of the proposed identification algorithm for a class of nonlinear system with long time delay.

The combination of the automatic control theory courses, simulation verification and practical implementation of the designed controller algorithms in real-time conditions is very important for training of the control engineers.This contribution present structure and usage of Self-tuning Controllers Simulink Library (STCSL) for real time control.The STCSL was created for design, simulation verification and especially realtime implementation of single input -single output (SISO) digital self-tuning controllers.The proposed adaptive controllers, which are included in the library, can be divided into three groups (PID controllers, controllers based on the polynomial approach and the controllers derived on the other approaches (minimum variance etc.).This Library is very successfully used in Adaptive Control Course in education practice for design and verification of self-tuning control systems in simulation and real-time conditions.It is suitable also for design and verification of industrial digital controllers.The highly nonlinear laboratory model, the DR300 Speed Control with Variable Load, has been chosen as example for real-time control.

The output tracking control problem via state feedback is addressed for a class of single input-single output nonlinear systems which are affected by extended matching unstructured uncertainties. Under the assumption that the output reference signal is sufficiently smooth and periodic with known period, a robust adaptive learning control is designed, which learns the unstructured unknown periodic disturbance signals due to system uncertainties by identifying the Fourier coefficients of any truncated approximation while guaranteeing L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> transient performances. For any initial condition of the system in an arbitrary given compact set, by properly setting the control parameters: i) the output tracking error exponentially converges to a residual set which may be arbitrarily reduced by increasing the number of terms in the truncated Fourier series expansions; ii) when the unknown periodic disturbances can be represented by finite Fourier series expansions, the output tracking error exponentially converges to zero.