Sliding mode control of nonlinear uncertain systems using a sliding observer

In this paper, an adaptive fuzzy controller for single-input single-output (SISO) nonlinear systems with higher-order and unmatched uncertainties is provided. The design is based on the principle of sliding mode control, input-output linearizing controller, and the approximation capability of adaptive fuzzy systems. Finally, the suggested controller is applied to a flexible joint robot. Simulation results indicate its efficiency.

In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients.

Nonlinear single-input single-output (SISO) systems operating under parametric uncertainty often exhibit bifurcations, multistability, and deterministic chaos, which significantly limit the effectiveness of classical linear, adaptive, and switching control methods. This paper proposes a novel synthesis framework for self-organizing control systems based on catastrophe theory, specifically within the class of elliptic catastrophes. Unlike conventional approaches that stabilize a predefined system structure, the proposed method embeds the control law directly into a structurally stable catastrophe model, enabling autonomous bifurcation-driven transitions between stable equilibria. The synthesis procedure is formulated using a Lyapunov vector-function gradient–velocity method, which guarantees aperiodic robust stability under parametric uncertainty. The definiteness of the Lyapunov functions is established using Morse’s lemma, providing a rigorous stability foundation. To support practical implementation, a data-driven parameter tuning mechanism based on self-organizing maps (SOM) is integrated, allowing adaptive adjustment of controller coefficients while preserving Lyapunov stability conditions. Simulation results demonstrate suppression of chaotic regimes, smooth bifurcation-induced transitions between stable operating modes, and improved transient performance compared to benchmark adaptive control schemes. The proposed framework provides a structurally robust alternative for controlling nonlinear systems in uncertain and dynamically changing environments.

The demand for ubiquitous telecommunications services forces operators to have a special concern about signal quality and the coverage area they offer to their customers. This was usually checked by using suitable propagation models for Single Input Single Output (SISO) systems, which are no longer the case for new and future mobile generations, such as 5G and beyond. To guarantee good signal quality coverage, operators started to replace these models with Multiple Input Multiple Output (MIMO) ones. To achieve the best results, these models are usually calibrated with Drive Test (DT) measures; however, the DTs available for MIMO propagation models are sparse, in contrast to SISO ones. The main contribution presented in this paper is a methodology to extend the propagation models of SISO systems so they can be applied in MIMO sytems with Single-Carrier and Frequency-Domain Equalization (SC-FDE), while still using DTs acquired for SISO systems. This paper presents the impact on Bit Error Rate (BER) performance and its coverage area resulting from the application of our proposed method. We consider a MIMO SC-FDE system with an Iterative Block Decision Feedback Equalization (IB-DFE) receiver and we present the improvement expressions for the BER that we illustrate with some simulations.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

The design of a multi-level fuzzy-logic control system for the control of turbine engines using type-1 fuzzy-logic is presented in this paper. A Matlab-Simulink model of an advanced turbine engine was used to test and validate the performance of the developed fuzzy control system. The model provided comprehensive and complex model of a turbine engine. As with most modeling of turbine engines, it was assumed that the fundamental dynamic characteristics of a turbine engine can be achieved by control of the engine fuel flow. In this model a single input single output (SISO) system is used to control the engine fuel flow, where the input to the SISO system is the low spool speed error signal and the output is the fuel flow actuator control signal. A fuzzy controller was developed for the SISO system and its performance is compared with that of the existing proportional integral (PI) controller. Both controllers were tested under normal operating conditions and with introduction of engine faults embedded in the model.

A novel auto-tuning PID control mechanism for nonlinear systems

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. >

Chattering mitigated sliding mode control of uncertain nonlinear systems

In this paper, a novel constrained composite sliding mode controller is studied for uncertain nonlinear systems with input saturation. Based on integral sliding mode and approximate dynamic programming theory, the proposed sliding mode control consists of discontinuous control used for completely compensating matched uncertainties and continuous control that results in an optimal sliding mode dynamics. Without using linearization techniques, the constrained optimal control law for nominal nonlinear systems is approximated by using an online approximate learning algorithm with actor-critic NN framework. Lyapunov techniques are used to demonstrate the uniform ultimate bounded convergence condition for closed-loop nominal system and the weight errors.

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.

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

Sliding mode control (SMC) has a strong capability of controlling nonlinear systems with uncertainties. However, it requires thorough knowledge of parameters and dynamics of the controlled plant, which are difficult to be obtained or may be unknown. This will cause difficulties in calculating equivalent control law of SMC. To overcome this problem, this paper proposes an adaptive SMC using simple adaptive control (SAC) developed for single-input single-output (SISO) nonlinear systems with unknown parameters and dynamics. The role of SAC is to construct an equivalent control input of adaptive SMC. To construct a corrective control input, this paper applies the method using the sign function with a modified sliding surface. Finally, the effectiveness of the proposed method is confirmed through computer simulation.

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.