Adaptive Control Of Nonlinear Systems Research Articles

Event-Based Neural Networks Adaptive Control of Nonlinear Systems: A Fully Actuated System Approach

Event-Based Neural Networks Adaptive Control of Nonlinear Systems: A Fully Actuated System Approach

Adaptive control for nonlinear systems with unknown actuator dynamics based on a novel extended Nussbaum function

AbstractIn this article, we introduced a novel definition for a class of extended Nussbaum functions that have looser requirements than the traditional Nussbaum function. The extended Nussbaum function achieves comparable performance to the traditional Nussbaum function while addressing the challenges of unknown control directions and time‐varying actuator faults. We then provide a specific example function based on the extended Nussbaum function definition. Unlike the traditional Nussbaum function, which oscillates with fixed frequency and constantly increasing amplitude, this example function constrains the amplitude and oscillates with decreasing frequency. Consequently, its amplitude and derivative remain bounded. The oscillation of the system caused by the too large amplitude of the traditional Nussbaum function can be avoided. Furthermore, this example function is constructed using portions of elliptic curve. As a result, it is continuous and differentiable, in contrast to the normal decreasing‐frequency Nussbaum function using trigonometric function, which is only continuous. The overall closed‐loop system's global stability and asymptotic convergence of system states are successfully achieved. Simulation results demonstrate the effectiveness of the proposed function.

Adaptive Control for Nonlinear Systems With Discontinuous Tracking and Output Constraint Within Predefined Time Interval

Adaptive Control for Nonlinear Systems With Discontinuous Tracking and Output Constraint Within Predefined Time Interval

Event-triggered adaptive control for nonlinear systems using time-receding horizons without initial dependence

This paper investigates the full-state constraint event-triggered adaptive control for a class of uncertain strict-feedback systems. The lack of information on the coupling dynamics of virtual variables in backstepping increases the complexity of feedback design. Given this, the requirements of shaping system performance constraints, eliminating initial dependence, and reducing data transfer costs together give rise to an interesting and challenging problem. Constructing the time-receding horizon (TRH) and stitching it with the quadratic Lyapunov function (QLF) is the key to constrained tracking. Specifying TRHs as a set of smooth bounds with fixed-time convergence and forcing the system to stabilize within the constrained region before the prescribed settling time provide a sufficient condition for practical finite-time stability (PFS). For relaxing the initial dependence, a tuning function is designed to match the performance constraints under arbitrary system initial conditions. A dual-channel event-triggered mechanism (ETM) is developed to automatically adjust the controller and estimator data flow updates with less transmission burden. By combining a specific inequality with backstepping, uncertainties are overcome without the “complexity explosion” in recursion steps. Finally, simulations demonstrate the effectiveness of the proposed method.

Filter-based Immersion and Invariance Adaptive Control of Nonlinear Systems

Filter-based Immersion and Invariance Adaptive Control of Nonlinear Systems

Static Gain Function-Based Adaptive Control for Nonlinear Systems with Unknown Time Delays

Static Gain Function-Based Adaptive Control for Nonlinear Systems with Unknown Time Delays

Valid RBFNN Adaptive Control for Nonlinear Systems With Unmatched Uncertainties.

In this article, an adaptive tracking controller based on radial basis function neural networks (RBFNNs) is proposed for nonlinear plants with unmatched uncertainties and smooth reference signals. The concept of valid RBFNN adaptive control is introduced where all closed-loop arguments of the involved RBFNNs should always remain inside their corresponding compact sets. Considering the local approximation capacity of RBFNNs, validity requirements are necessary for ensuring reliable closed-loop approximation accuracy and stability. To obtain valid RBFNN adaptive controllers, a novel iterative design method is proposed and embedded into the traditional backstepping approach. In the initial iteration, an ideal RBFNN and its online estimated version are introduced in each step where the initial compact set guarantees the validity requirement for only a finite time interval. Then, by carefully investigating the dependence among different signals and introducing some auxiliary variables, the compact sets are redesigned for prolonging the time interval satisfying validity requirements to infinity as the iteration goes on. Consequently, a closed-loop system model can be formulated during the entire control process, which underlies a rigorous proof on closed-loop stability and some guidelines on practical implementation. Meanwhile, rigorous analysis from validity requirements reveals, for the first time, a new feature of RBFNN adaptive controllers in the presence of unmatched uncertainties: excessively large scales of RBFNNs in intermediate steps may impair the closed-loop performance. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Adaptive control of a nonaffine nonlinear system using self-organising kernel extreme learning machine

We propose a self-organising kernel extreme learning machine (KELM) adaptive controller for nonaffine nonlinear systems. Literature survey reveals that neural network (NN) is extensively used to design adaptive controllers for nonlinear systems. When conventional NN, like multilayer feedforward NN and radial basis function NN (RBFNN), is used for controller design, the parameters of these networks converge slowly. Researchers have overcome this shortcoming by using extreme learning machine (ELM). The motivation to use KELM for controller design in our research is to utilise the advantages of ELM and radial basis function kernels. The structure of neural networks is seldom altered during training, resulting in unnecessarily small or large networks. The self-organising nature of our proposed controller caters to solving this problem. The structure of the self-organising KELM updates itself based on a threshold value set for the normalised change in the output weight. In our work, the control input meets three objectives: feedback linearisation, stabilisation of the linearised system and providing immunity to process and measurement noises. The update law for the hidden layer parameters of the KELM is obtained using the Lyapunov technique to ensure the overall stability of the system. A comparative analysis of different performance criteria is performed for trajectory tracking control, in the presence of process and measurement noises, for a numerical example and the Duffing–Holmes chaotic nonlinear system. The simulation results of these analyses demonstrate the superiority of the self-organising KELM compared to ELM and RBFNN based adaptive controllers. The experimental results with a rotary servo system validate the efficacy of the proposed controller in real-time systems. Furthermore, the robustness of the self-organising adaptive controller is verified with the results obtained for the servo system on varying the system parameter and operating condition.

Nonsingleton Gaussian type-3 fuzzy system with fractional order NTSMC for path tracking of autonomous cars

Path-tracking and lane-keeping tasks are critical to guarantee safety and navigation performance considerations for deploying autonomous cars. This paper presents a novel control framework for the path-tracking control of high-speed autonomous cars with structured uncertainties. This study introduces a nonlinear adaptive control system based on a fractional-order terminal sliding mode system while incorporating a novel Gaussian Nonsingleton type-3 fuzzy system (FOTSM-NT3FS). Therefore, the proposed controller is independent of the information about the ego vehicle’s dynamic information, and instead, the dynamics are approximated through a developed NT3FLS. The developed control system exhibits robustness to measurement errors and faulty sensors, because the inputs to the NT3FS are uncertain. In order to guarantee the boundedness of the adaptation parameters, the σ−mod approach is employed. The Lyapunov stability theorem and Barbalat’s lemma are used to ensure the uniform ultimate boundedness of the closed loop system and the convergence of tracking errors to the origin in finite time. High-fidelity co-simulations with CarSim and MATLAB are performed to verify the effectiveness of the proposed control scheme and are also compared to other reported methods in the literature. Based on the obtained results, the schemed controller exhibits competitive effectiveness in path-tracking tasks and strong efficiency under various road conditions, parametric uncertainties, and unknown disturbances.

Event-triggered model-free adaptive control for nonlinear systems using intuitionistic fuzzy neural network: simulation and experimental validation

This article presents model-free adaptive control based on an intuitionistic fuzzy neural network for nonlinear systems with event-triggered output. Essentially, model-free adaptive control (MFAC) is constructed by establishing an online approximate model of the controlled system using the pseudo-partial derivative (PPD) form. By the proposed scheme, first, an intuitionistic fuzzy neural network (IFNN) is developed as an estimator for time-varying PPD in both compact-form dynamic linearization (CFDL) and partial-form dynamic linearization (PFDL) for the MFAC technique. Second, two periodic event-triggered output methods are integrated with the proposed IFNN-based MFAC in both forms to save communication resources and reduce the computation burden and energy consumption. Based on the Lyapunov theory and BIBO stability approach, necessary conditions are established to guarantee the convergence of the adaptive law of the IFNN controller and the boundary of the tracking error of the closed loop system. Third, regarding the feasibility and the effectiveness of the developed control method, two simulation examples including the continuous stirred-tank reactor (CSTR) system and the heat exchanger system are given. Finally, the practical validation of the proposed data-driven control method is conducted via the speed control of a DC motor.

A new method of parameter estimation and adaptive control of nonlinear systems with filterless least‐squares

AbstractThis paper is concerned with the parameter estimation and adaptive control problem for a sort of strict‐feedback nonlinear systems with unknown parameters. In order to deal with the nonlinear functions, we develop a kind of least‐squares estimator in the parameter estimation part. With such an estimator, we design the state‐feedback control law and analyze the properties of the closed‐loop system. To be concrete, the parameter estimator can guarantee the boundedness of parameter estimate error. At the same time, the adaptive control law is proposed to make the system states converge to zero and the equilibrium stable globally under some common assumptions. Finally, simulations are given to demonstrate the theoretical results.

A small-gain approach to inverse optimal adaptive control of nonlinear systems with unmodeled dynamics

This work formulates and solves the problem of inverse optimal adaptive control for nonlinear systems with parametric and dynamic uncertainties. A concept and sufficient conditions for solving this problem are first introduced and derived based on adaptive control Lyapunov function method. One difficulty obstructing current works to solve this problem is that inverse optimality and stability of the closed-loop system are not necessarily achieved simultaneously in the presence of both parametric uncertainties and unmodeled dynamics. To this end, a new auxiliary system and a cost functional that puts integral penalty on the state, control, parameter estimate and unmodeled dynamics are proposed to develop a new inverse optimal adaptive feedback approach. Then a small-gain approach is proposed to establish the links between inverse optimality and stability of the closed-loop system. It is proved that if inverse optimality is achieved and the small-gain condition holds, the closed-loop system is uniformly bounded and the system state converges to an arbitrarily small neighborhood of the origin. Finally, an example is given to illustrate the obtained results.

Robust Adaptive Dynamic Event-Triggered Control of Switched Nonlinear Systems

This paper investigates the robust adaptive event-triggered control (ETC) problem for switched nonlinear systems. A novel robust adaptive controller for nonlinear systems under dwell-time switching is first constructed based on a common virtual control Lyapunov function method using backstepping. Then, a dynamic ETC (DETC) strategy is integrated into the switching controller to constitute an overall solution to the problem under investigation while the challenges caused by interaction of switching and triggering instants are well addressed. In particular, global asymptotic stability and exclusion of Zeno behavior are guaranteed for the resulting closed-loop system. Furthermore, the solution is extended to a larger class of switched nonlinear systems whose subsystems are not assumed to be asymptotically stable. In this case, a state-dependent switching strategy with guaranteed dwell-time must be constructed such that the proposed switching DETC can be applied. Finally, three examples are presented to demonstrate the effectiveness of the proposed design strategies.

Event‐triggered model‐free adaptive control for nonlinear systems with output saturation

AbstractIn this article, an original event‐triggered model‐free adaptive control is presented for nonlinear systems with output constraints. Firstly, a compact form dynamic linear model for this nonlinear system is established. Based on the output saturated data, the pseudo partial derivative (PPD) parameter is designed to identify the linear model. Then, a novel event‐triggered mechanism is inserted into the controller. The mechanism will be activated only if the event‐triggered error satisfies the predefined condition; Otherwise, it keeps the last triggering state. The purpose is to alleviate the transmission burden and save the communication resources. Varying from the existing studies, the main innovation of this article is that the controller is reconstructed in virtue of saturated data and event‐triggered condition. The present algorithm convergence is proved. Finally, the simulation study illustrates the feasibility of the plan.

Conceptual Design of a Robotic Ground-Aerial Vehicle with an Aeroelastic Wing Model for Mars Planetary Exploration

This paper presents the technical barriers and an analysis to advance the conceptual development of novel robotic ground-aerial vehicles (RGAVs) for exploration missions to Mars prior to human arrival and the establishment of a base. The concept for RGAVs for Mars planetary exploration is novel, and will require innovations that are at various stages of development or use by the aerospace community. The RGAV concept will utilize inflatable wing technology, which increases the flexibility of the wing, and thus the possibility of structural dynamic instabilities that must be studied in the context of the Martian atmosphere. An aeroelastic model for wing bending is proposed, which considers wind gusts where the change in wind direction is up to ±6° from the mean, and a turbulence intensity of up to 20%. Their effect on the bending displacement of a semi-elastic wing is quantified, resulting in a maximum wing tip displacement of 16.2 cm. Low-fidelity computational aerodynamic analysis is performed using OpenVSP (3.31.1, NASA, Washington, DC, USA) to compute mean aerodynamic loads during cruise conditions at a cruise Mach number of 0.70. Finally, a non-linear adaptive control system is proposed for the longitudinal aerial dynamics and a proportional integral derivative (PID) controller is outlined for the ground roving lateral dynamics.

A novel Lyapunov-stability-based recurrent-fuzzy system for the Identification and adaptive control of nonlinear systems

The requirement to manage complicated nonlinear systems with high uncertainty is one of the main drivers of progress in the identification and control discipline. Since most of the systems are nonlinear, exact identification and control of them using traditional techniques is a challenging task. This paper proposes a novel Takagi–Sugeno (T-S) type Recurrent Fuzzy System (RFS) for nonlinear system identification and adaptive control. To ensure the system’s overall stability, a novel Lyapunov-stability-based learning algorithm is developed to obtain the parameter update equations for the proposed model. The performance of the proposed model is also evaluated with the well-known gradient-descent-based Back Propagation (BP) learning method and compared with the Lyapunov-stability method. To judge the efficacy of the proposed model and the learning algorithm we have performed an extensive comparative study by considering other popular soft-computing models such as Jordan Recurrent Neural Network (JRNN), Feed-Forward Neural Network (FFNN), Radial Basis Function Network (RBFN) and a conventional recurrent fuzzy system. The results obtained from the proposed method (RFS ＋ Lyapunov-stability-based learning algorithm) are compared with those obtained from other models and are found to be superior.

An improved model-free adaptive control for nonlinear systems: An LMI approach

This paper proposes two model-free adaptive control (MFAC) schemes by using the linear matrix inequality (LMI) approach for the single-input single-output (SISO) and multi-input multi-output nonlinear (MIMO) systems, respectively. For each control scheme, with the aid of the dynamic linearization technique, the nonlinear system is transformed into an equivalent linear data model. In such a transformation, the nonlinear characteristic of systems is compressed into a time-varying parameter. Then, with the help of the introduction of the observer method, the tracking control problem can be converted into an optimization problem and the controller parameters can be obtained by using the LMI technique. This conversion cannot only reduce the complexity of the stability analysis but also find the appropriate controller parameters, especially for the MIMO case. Finally, three examples with comparisons are provided to illustrate the validity of the devised MFAC schemes.

Nonlinear adaptive flight control system: Performance enhancement and validation

The problem of decreasing stability margins in L1 adaptive control systems is discussed and an out-of-loop L1 adaptive control scheme based on Lyapunov’s stability theorem is proposed. This scheme enhances the effectiveness of the adaptation, which ensures that the system has sufficient stability margins to achieve the desired performance under parametric uncertainty, additional delays, and actuator faults. The stability of the developed control system is demonstrated through a series of simulations. Compared with an existing control scheme, the constant adjustment of the stability margins by the proposed adaptive scheme allows their range to be extended by a factor of 4–5, bringing the stability margin close to that of variable gain PD control with adaptively scheduled gains. The engineered practicability of adaptive technology is verified. A series of flight tests verify the practicability of the designed adaptive technology. The results of these tests demonstrate the enhanced performance of the proposed control scheme with nonlinear parameter estimations under insufficient stability margins and validate its robustness in the event of actuator failures.

Adaptive Control of Nonlinear Systems with Sinusoidal Uncertainties via Internal Model Principle

In this paper, an adaptive control scheme is established for nonlinear systems with sinusoidal uncertainties from the perspective of internal model principle. We propose to embed the controller with a dynamic compensator which plays the role of an internal model for reproducing the unknown sinusoidal parameter. For linearly parameterized systems, under some full-information stabilizability assumptions, internal-model-based controllers are developed, rendering the closed-loop system trajectories to be bounded and the plant states to be asymptotically convergent to zero. Further, we extend the proposed internal-model-based control scheme to nonlinearly parameterized systems with a (strictly) monotonic assumption. Two simulation examples are given to verify the effectiveness of the proposed schemes.

Multiple Model Adaptive Control of Nonlinear Systems Based on Dynamic Optimization

Multiple Model Adaptive Control of Nonlinear Systems Based on Dynamic Optimization