Adaptive Control Of Nonlinear Systems Research Articles

Adaptive H∞ control of polynomial Hamiltonian systems via symbolic computation: controller parameterisation

ABSTRACTThis paper deals with controller parameterisation method of adaptive control for polynomial Hamiltonian systems (PHSs) with disturbances and unknown parameters. We design a simplified controller with a set of tuning parameters which can guarantee that the systems are adaptive stable by using Hamiltonian function method. Then, a method for solving the set of tuning parameters of the controller with symbolic computation is presented. The proposed parameterisation method avoids solving Hamilton–Jacobi–Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Simulation example shows that the controller is effective as it can optimise adaptive control by adjusting tuning parameters. All these results are expected to be of use in the study of adaptive control for nonlinear systems with disturbances and unknown parameters.

A new approach to design asymptotically stabilizing control and adaptive control

SummaryIn this paper, we propose a new approach to design the asymptotically stabilizing control and adaptive control for nonlinear systems. We first propose an infinite‐horizon optimal control (OC) problem according to the nonlinear control system. We prove that its OC can be an asymptotically stabilizing control or adaptive control for the original nonlinear system. Then, we convert the infinite‐horizon OC problem into an equivalent finite‐horizon OC problem. Moreover, we utilize the Legendre pseudospectral method to solve the proposed problem. Finally, several examples are given to illustrate the efficiency of the approach.

Learning‐based iterative modular adaptive control for nonlinear systems

SummaryIn this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.

Comparative Study of Neural Networks for Control of Nonlinear Dynamical Systems with Lyapunov Stability-Based Adaptive Learning Rates

This paper performs the comparative study of two feed-forward neural networks: radial basis function network (RBFN), multilayer feed-forward neural network (MLFFNN) and a recurrent neural network: nonlinear auto-regressive with exogenous inputs (NARX) neural network for their ability to provide an adaptive control of nonlinear systems. Dynamic back-propagation algorithm is used to derive parameter update equations. To ensure stability and faster convergence, an adaptive learning rate is developed in the sense of discrete Lyapunov stability method. Both parameter variation and disturbance signal cases are considered for checking and comparing the robustness of controller. Three simulation examples are considered for carrying out this study. The results so obtained reveal that RBFN-based controller is performing better than that of NARX- and MLFFNN-based controllers.

Tuning function design for nonlinear adaptive control systems with multiple unknown control directions

To overcome the drawback of overparametrization in existing nonlinear adaptive control design with multiple unknown control directions, we propose a new algorithm which combines nonlinear integrator backstepping, tuning function design and a logic-based switching mechanism that tunes the control directions online in a switching manner. Global asymptotic tracking control is achieved for parametric-strict-feedback systems without overparametrization. The logic-based switching criterion is based on monitoring incremental errors caused during two consecutive switching moments, and thus can identify the true control direction quickly.

A Generalized functional model of State regulation of foreign trade as a multiparameter nonlinear adaptive control system

A Generalized functional model of State regulation of foreign trade as a multiparameter nonlinear adaptive control system

Optimal adaptive reset control with guaranteed transient and steady state tracking error bounds

In this paper, a solution for improvement of transient performance in adaptive control of nonlinear systems is proposed. An optimal adaptive controller based on a reset mechanism and a prescribed performance bound is devised. The suggested controller has the structure of adaptive backstepping controller in which the estimated parameters are reset to an optimal value. The designed controller ensures both the transient bound and the asymptotical convergence of the states. It is shown that the tracking error satisfies the prescribed performance bound all the time, besides the speed of the convergence rate is increased by resetting the estimated parameters. The results have been proved through both the analytical and simulation studies. The proposed method is applied to an Augmented Quarter Car Model as a case study. Simulation results verify the established theoretical consequences that the prescribed performance bound based optimal adaptive reset controller can enhance the transient performance of the adaptive controller.

On the robust PID adaptive controller for exoskeletons: A particle swarm optimization based approach

This article proposes a robust PID adaptive controller for nonlinear systems with one or more degrees of freedom (DoF). The adaptive controller aims at minimizing the errors in trajectory tracking without requiring a prior modeling of the targeted nonlinear system. Furthermore, the proposed controller requires only the inputs and outputs of the system. And it is based on modified particle swarm optimization algorithm whose goal is to find the best PID parameters that optimize the execution of desired task by minimizing an objective function. The adaptation by the controller addresses two critical problems: The first problem is the instability of the control signal provided by the convergence phase of the classical PSO algorithm. This behavior adversely affects the lifetime of any actuator and, therefore, is undesirable. The second problem is the stagnation of the classical PSO algorithm after convergence at the immediately found optimal solution. The proposed adaptive PID controller is initially tested in simulation on a dynamical model of a robot manipulator evolving in the vertical plan. Which is followed by experimental tests performed on an actuated joint orthosis worn by human subjects having different morphologies. A comparative study with two other algorithms has been also conducted. Based on the obtained results, we conclude the efficiency of the proposed approach.

Dynamic Recurrent Neural Network Based Indirect Adaptive Control for Nonlinear Systems

In this study, an indirect adaptive controller based on dynamic recurrent neural network (DRNN) is developed in the form of the internal model control structure. This control method includes two learning phases, i.e., off-line and on-line learning. In the offline learning, the DRNN is learned by the epoch wise back propagation through time (BPTT) method to represent the forward dynamics of the system to be controlled. In the online phase, the DRNN is used as the internal model of the controlled system and its parameters can be trained by the Truncated BPTT to cope with the possible change in the system dynamics. Hence, the mathematical inversion of the DRNN internal model is computed online to act as the forward controller. Finally, the controller is then obtained by cascading this inverse model with a robust filter and a linear compensator to improve the closed loop performance. The proposed method is applied to a continuous stirred tank reactor (CSTR) with time varying behavior to evaluate the performance of controller.

Adaptive control of a class of nonlinear time-varying systems with multiple models

The adaptive control of nonlinear systems that are linear in the unknown but time-varying parameters are treated in this paper. Since satisfactory transient performance is an important factor, multiple models are required as these parameters change abruptly in the parameter space. In this paper we consider both the multiple models with switching and tuning methodology as well as multiple models with second level adaptation for this class of systems. We demonstrate that the latter approach is better than the former.

Adaptive control of nonlinear system using online error minimum neural networks

In this paper, a new learning algorithm named OEM-ELM (Online Error Minimized-ELM) is proposed based on ELM (Extreme Learning Machine) neural network algorithm and the spreading of its main structure. The core idea of this OEM-ELM algorithm is: online learning, evaluation of network performance, and increasing of the number of hidden nodes. It combines the advantages of OS-ELM and EM-ELM, which can improve the capability of identification and avoid the redundancy of networks. The adaptive control based on the proposed algorithm OEM-ELM is set up which has stronger adaptive capability to the change of environment. The adaptive control of chemical process Continuous Stirred Tank Reactor (CSTR) is also given for application. The simulation results show that the proposed algorithm with respect to the traditional ELM algorithm can avoid network redundancy and improve the control performance greatly.

Analysis the Parameters of the Adaptive Controller for Quality Control of Dissolved Oxygen Concentration

The wastewater treatment plant can be treated as large scale complex system. The dissolved oxygen concentration in aerobic zones is considered as the most important control parameters. Air is supplied by aeration system. It is a complex dynamic system. In this paper, the sequencing batch reactor and aeration system are modelled and applied for control systems purposes. The cascade nonlinear adaptive control system, extended by anti-windup filter, is applied. Furthermore, analysis the parameters of the adaptive controller for control quality is examined. Simulation results based on real data records for case study plant are presented. DOI: http://dx.doi.org/10.5755/j01.itc.45.1.9246

Output‐Feedback Nonlinear Adaptive Control of Single‐Phase Half‐Bridge Ups Systems

AbstractWe consider the problem of controlling single‐phase half‐bridge power converters in UPS systems operating in the presence of changing load. The control objective is twofold: (i) ensuring a satisfactory power factor correction (PFC) at the grid–UPS connection; (ii) guaranteeing a tight regulation of the DC bus voltage and the half‐bridge inverter output voltage despite changes in load. The considered control problem entails several difficulties including: (i) the high dimension and strong nonlinearity of the system; (ii) the numerous state variables that are inaccessible to measurements; (iii) the uncertainty that prevails on some system parameters. The problem is dealt with using a multi‐loop nonlinear adaptive control system that makes use of the backstepping design technique. The inner loop ensures the PFC objective and involves an adaptive observer estimating the grid voltage and impedance parameters. The intermediary loop regulates the inverter output voltage to its reference, which is a sinusoidal wave, and it also contains an observer estimating the current in the inverter coil. The outer loop regulates the DC bus voltage up to small size ripples. The controller performances are formally analyzed using system averaging theory.

Adaptive control of nonlinear systems with full state constraints using Integral Barrier Lyapunov Functionals

In this study, a controller design for nonlinear strict feedback systems with full state constrains is presented. A backstepping stable controller is designed by using the Integral Barrier Lyapunov Functionals (iBLF). Compared with the previous designs, the systems are required to contain the unknown parameters. Under the backstepping control-based iBLF, the output tracking is well achieved without violation of any constraint and the closed loop signals are bounded. The stability of the closed-loop system is analyzed by using the Lyapunov theorem. Finally, a simulation example is used to verify the effectiveness of the proposed design.

Improving Transient Response in Adaptive Control of Nonlinear Systems

Abstract An important requirement in control systems is an acceptable transient response. When the underlying dynamical systems are unknown, a factor that contributes is how fast an algorithm can identify them. It is well-known that the back propagation algorithm has rather poor convergence properties. Consequently, it sometimes takes several thousand iterations before the transient response is satisfactory. In this paper, we show that a sequential variant of the extreme learning machine considerably improves the transient response.

Involvement of students and postgraduates into megagrant laboratory under supervision of leading scientist Romeo Ortega at ITMO University

In 2010 the Government of the Russian Federation established particularly large grants aimed to attract world-renowned scientists, including compatriots living abroad, to Russian scientific and educational centres. These grants, known as Megagrants, ensure the creation of research teams that can compete with the leading world laboratories and achieve world-class scientific results. Involvement of young Russian scientists in the projects became one of the main Megagrant features: half of the participants are people under the age of 35 years. Founded as a part of this project in ITMO University the laboratory “Nonlinear Adaptive Control Systems” under Romeo Ortega’s leadership is described in the paper. This laboratory was created at the Department of Control Systems and Informatics. The priority of the laboratory is the preparation and formation of a stable team able to conduct advanced research in the field of nonlinear, adaptive and robust control of various technical objects.

Adaptive Control of Nonlinear Systems with Hysteresis and Unknown Control Direction

An adaptive backstepping controller is proposed for a class of nonlinear systems with hysteresis and unknown control direction. As the unknown gain sign is combined with multi-valued non-smooth hysteresis together, it is more challengeable to mitigate hysteresis effects and meanwhile guarantee stability of the dynamic systems. In this paper, Bouc-Wen model is adopted to describe the hysteresis. Then RBF neural networks are applied to approximate the unknown functions. The unknown control direction is solved by Nussbaum function. The adaptive backstepping controller is developed using prescribed performance function to confine the error to a predefined residual set. It is proved that all the closed-loop signals are bounded and the tracking error converges to an arbitrarily small field. Finally, the simulation result shows the feasibility of the control scheme.

Nonlinear adaptive trajectory control of multi-input multi-output submarines with input constraints

The paper presents a new nonlinear adaptive control system for the dive-plane control of multi-input multi-output submarine models with input constraints, in the presence of external disturbances. It is assumed that all the system parameters, except the signs of the principal minors of the input matrix, are unknown. The objective is to design an adaptive control law for the tracking of reference depth and pitch angle trajectories, despite constraints on the rotation angles of the bow and stern hydroplanes. For the derivation of a singularity-free adaptation law, the decomposition of the input matrix as a product of a positive-definite symmetric matrix, a diagonal matrix, and an upper triangular matrix (termed SDU decomposition) is obtained. Then an adaptive control system is designed which accomplishes uniform ultimate boundedness of the closed-loop system trajectories. The control system includes an auxiliary dynamic system to counter the effect of control input saturation. Simulation results show that the designed adaptive law accomplishes precise depth and pitch angle trajectory control, despite symmetric and non-symmetric input constraints, parametric uncertainties and external disturbance inputs. These results also show that the designed saturating adaptive controller can accomplish certain dive-plane maneuvers using either of the hydroplanes; but the bow hydroplane can execute larger maneuvers than the stern hydroplane. The robust performance of the controller, despite non-symmetric input constraints, is useful in situations in which partial failure of actuators causes rotation of the hydroplanes in unequal ranges.

Nonlinear Dynamic Modeling of a Fixed-Wing Unmanned Aerial Vehicle: a Case Study of Wulung

Developing a nonlinear adaptive control system for a fixed-wing unmanned aerial vehicle (UAV) requires a mathematical representation of the system dynamics analytically as a set of differential equations in the form of a strict-feedback systems. This paper presents a method for modeling a nonlinear flight dynamics of the fixed-wing UAV of BPPT Wulung in any conditions of the flight altitude and airspeed for the first step into designing a nonlinear adaptive controller. The model was formed into 10-DOF differential equations in the form of strict-feedback systems which separates the terms of elevator, aileron, rudder and throttle from the model. The model simulation results show the behavior of the flight dynamics of the Wulung UAV and also prove the compliance with the actual flight test results.

Exact tracking control of uncertain non‐linear systems with additive disturbance

This study deals with adaptive control of non-linear systems in the strict-feedback form with parametric uncertainties and additive disturbance. The disturbance in the systems is assumed to be bounded. No knowledge of the uncertain parameters, an upper bound of the uncertain parameter vector, a bound of unknown disturbance and the differentiability of the external disturbance is required. Under the weakened assumptions, two continuous robust adaptive control schemes are proposed. In the first control scheme, a modified adaptive backstepping design procedure is proposed to remove overparameterisation. A novel damping term with the estimate of unknown disturbance bound and a positive time-varying integral function are introduced in the control law to counteract the destabilising effects of the external disturbance. In the second scheme, an alternative continuous adaptive controller is designed. Instead of the estimate of the disturbance bound, an adaptive parameter is incorporated into the control design. In both of the two control schemes, the design parameters are freely chosen to improve the control performance. It is proved that the proposed two adaptive control schemes can guarantee that the closed-loop signals are bounded and the output tracking error converges to zero asymptotically in spite of the disturbance. Finally, a numerical example is included to show the effectiveness of the presented control methods.