Control Of Nonlinear Time-varying Systems Research Articles

Adaptive Control for Nonlinear Time-Varying Systems With Unknown Control Coefficients and External Disturbances

Adaptive Control for Nonlinear Time-Varying Systems With Unknown Control Coefficients and External Disturbances

Global adaptive neural network control of nonlinear time-varying systems with unknown control coefficients and model uncertainties

This paper investigates the adaptive control problem for the strict-feedback nonlinear time-varying system (NTVS) with unknown control coefficients and model uncertainties. To address the problem that the neural network (NN) can only achieve local approximation of unknown nonlinear functions, a novel NN control scheme is proposed. The scheme consists of a NN controller that operates inside the approximation domain and a robust controller that operates outside the approximation domain, and a novel switching function is designed to enable the two controllers to switch smoothly in the vicinity of the approximation domain to ensure that all signals of the closed-loop system are globally uniformly ultimately bounded. To address the problem that unknown time-varying control coefficients are difficult to handle, an adaptive fault-tolerant control scheme is proposed in combination with the congelation of variables method. The scheme employs classical adaptive control to adapt to the variation of unknown control coefficients and robust control to eliminate the time-varying disturbance terms, and introduces a positive integrable time-varying function to achieve asymptotic tracking of an arbitrary reference signal. The combination of these two schemes constitutes a global adaptive neural network control (GANNC) method for the NTVS with unknown control coefficients and model uncertainties. Finally, an adaptive attitude fault-tolerant controller for launch vehicles is designed by using the GANNC method, which can realize the accurate tracking of the attitude control system to the reference command under normal status, strong disturbances and actuator failures, and comparative experiments prove the effectiveness and superiority of the controller.

Event-based adaptive asymptotic tracking control of nonlinear time-varying systems with prescribed performance

This paper is concerned with the adaptive tracking control problem of nonlinear time-varying systems. Based on the backstepping technology, an event-based prescribed performance control scheme is developed. And the time-varying uncertainties of the system are handled by utilising bound estimation method. The proposed controller not only ensures the prescribed tracking performance, but also reduces the communication burden. By using Lyapunov stability analysis, it is proven that all of the closed-loop signals are bounded, and the tracking error can converge to zero. Simultaneously, Zeno behaviour is excluded. Finally, the simulation results are utilised to illustrate the effectiveness of the proposed adaptive control scheme.

Signal Transmission by Sampled-time Adaptive Synchronization of Time-varying Chaotic Systems

In the paper, the adaptive synchronization problem is studied for a class of time-varying nonlinear systems. The only assumption imposed is the boundedness of the rate of change of the controlled system parameters, while the initial uncertainty can be quite large. The adaptation algorithms in the discrete-time form are derived based on adaptive control of nonlinear time-varying systems with an explicit reference model. As the result, the estimate of the limiting deviation of the solution of the closed-loop system from that of the reference model was obtained. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limiting error in the system can be made arbitrarily small despite a possibly big range of system parameter values. The systems based on a direct approach are considered. The procedure for the synthesis of a sampled-time adaptive controller and analysis of the synthesized system is illustrated by an example of the signal transmission system. The results obtained allow one to build and analyze a wide class of adaptive systems with reference models under time-varying conditions.

Lyapunov-Bregman functions for speed-gradient adaptive control of nonlinear time-varying systems

The paper is devoted to application of Bregman divergence to nonlinear adaptive control. Using Bregman divergence instead of quadratic function leads to a new class of Lyapunov functions in adaptive control that can be called Lyapunov-Bregman functions. An extended control algorithms design scheme is proposed and the properties of the designed control systems in presence of disturbances and time-varying parameters are studied. A special case of model reference adaptive control for nonlinear time-varying systems is studied based on the speed-gradient methodology.

Finite Horizon H-Infinity Control of Nonlinear Time-Varying Systems Under WTOD Protocol

The finite horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> control problem is investigated for a class of discrete nonlinear time-varying systems subject to Weighted Try-Once-Discard communication protocol. The equations of state and output under investigation involve both deterministic and stochastic nonlinearities. By resorting to the Taylor series expansion formula, Lyapunov stability theory and cross-amplification lemma, sufficient conditions are established for the existence of the desired observer-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> controller. The gain matrices of the controller and observer are obtained by solving a set of recursive linear matrix inequalities.

Inverse control of single-input/single-output nonlinear time-varying systems with noise disturbances by multi-dimensional Taylor network

In this paper, an inverse control scheme based on the novel dynamic network (multi-dimensional Taylor network (MTN)) is proposed for the real-time tracking control of nonlinear time-varying systems with noise disturbances. Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling, the adaptive inverse controller for inverse modeling, and the adaptive nonlinear filter for eliminating the noise disturbances, whose weights are modified by the variable forgetting factor recursive least squares (VFF-RLS), back propagation through model (BPTM), normalized least mean square (NLMS) algorithms, respectively. To avoid “compromise”, this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbances are implemented in two relatively independent processes. Furthermore, the weight-elimination algorithm is introduced for choice of effective regression items to avoid the dimension explosion, thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network. After a certain number of training, the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application. To ensure that MTN inverse control is strict in theory, the general conditions for the existence of single-input/single-output (SISO) nonlinear inverse systems are identified. Simulation of the MTN inverse control is conducted to confirm the effectiveness of the proposed method.

Robust Adaptive Dynamic Surface Control of Nonlinear Time-varying Systems in Strict-feedback Form

In this paper, the problem of robust adaptive control for nonlinear systems with unknown time-varying parameters and disturbance is considered. For this purpose, an indirect adaptive controller based on the Dynamic Surface Control (DSC) is proposed where an adaptive scheme is presented to provide estimations of unknown time-varying parameters. First, the parameters are approximated in terms of polynomials with unknown coefficients using the Taylor series expansion. Then, these unknown coefficients are estimated using a novel adaptive law. It is shown that the proposed control scheme guarantees the stability of the overall system and the tracking error can converge to a desired small residual. Finally, simulation results are given to demonstrate the effectiveness of the proposed method.

Finite-time partial stability and stabilization, and optimal feedback control

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control design for finite-time partial stability and finite-time, partial-state stabilization. Finite-time partial stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state, satisfies a differential inequality involving fractional powers, and can clearly be seen to be the solution to the steady-state form of the Hamilton-Jacobi-Bellman equation guaranteeing both partial stability and optimality. The overall framework provides the foundation for extending optimal linear-quadratic controller synthesis to nonlinear-nonquadratic optimal finite-time, partial-state stabilization. In addition, we specialize our results to address the problem of optimal finite-time control for nonlinear time-varying systems. Finally, we develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the finite-time, partial-state stabilization problem and use this result to address finite-time, partial-state stabilizing sublinear controllers that minimize a derived performance criterion involving subquadratic terms.

A suboptimal feedback control for nonlinear time-varying systems with continuous inequality constraints

A feedback control law, which is constructed as a first-order approximation to the optimal control, is proposed for nonlinear time-varying systems subject to continuous inequality constraints on the control and state. This control law is effective under small state perturbations caused by changes on initial conditions and/or modeling uncertainty.

A new approach for instantaneous pole placement with recurrent neural networks and its application in control of nonlinear time-varying systems

In this paper, we first show that online computation of feedback gain used for pole placement of nonlinear systems in recent years is not reliable, and then we present a new approach for instantaneous pole placement and apply it with dynamical recurrent neural networks for online computation of feedback gain. Because of high-speed convergence of neural network to feedback gain, we can apply this method for pole placement of nonlinear time-varying systems. One strategy for realization of this method is instantaneous linearization, as we do here by simulation. The advantage of the proposed method is a global uniform asymptotical exponential stability (GUAES) of closed-loop system around the equilibrium point.

STRONG STABILIZATION FOR A CLASS OF NONLINEAR CONTROL SYSTEMS WITH STATE DELAYS

This paper deals with the strong stabilization problem of a class of nonlinear time-varying control systems with state delays. Under appropriate growth conditions on the nonlinear perturbation, new sufficient conditions for the strong stabilizability are established based on the global null-controllability of the nominal linear system. These conditions are presented in terms of the solution of a standard Riccati differential equation. A constructive procedure for finding feedback stabilizing controls is also given.

Adaptive neural/fuzzy control for interpolated nonlinear systems

Adaptive control for nonlinear time-varying systems is of both theoretical and practical importance. We propose an adaptive control methodology for a class of nonlinear systems with a time-varying structure. This class of systems is composed of interpolations of nonlinear subsystems which are input-output feedback linearizable. Both indirect and direct adaptive control methods are developed, where the spatially localized models (in the form of Takagi-Sugeno fuzzy systems or radial basis function neural networks) are used as online approximators to learn the unknown dynamics of the system. Without assumptions on rate of change of system dynamics, the proposed adaptive control methods guarantee that all internal signals of the system are bounded and the tracking error is asymptotically stable. The performance of the adaptive controller is demonstrated using a jet engine control problem.

Robust control for nonlinear time-varying systems with application to a robotic manipulator

Sliding mode control methods have been used widely because they provide robustness against parameter variations and disturbances. This paper focuses on the problem of a robust output-sliding control design for a class of nonlinear time-varying systems. Output signals are used for the switching function definition. The control law formulation is emphasized. Input and output linearization is used. Output tracking can be achieved against a class of time-varying parameter variations and external disturbances. An application to a two-degree-of-freedom manipulator indicates that the proposed switching control law drives the system state trajectories onto the chosen sliding mode in finite time and the output tracking is guaranteed.

D-Type learning control for nonlinear time-varying systems with unknown initial states and inputs

In this paper, D-type iterative learning control schemes, which guarantee that the desired output is tracked precisely through iteration, are presented. Both off-line and on-line schemes are considered for a class of nonlinear systems. In both schemes, the learning gain may be time-varying and thus possesses larger scope for adjustment. Specifically, not only the input but also the initial state is iterated in the algorithms, and the output channel is fully nonlinear. Then, sufficient conditions are presented which guarantee the convergence of the proposed algorithms. The desired input and desired state are not assumed to be known a priori. Finally, the results are applied to a robotic system through simulation, which demonstrates the effectiveness of the method.

An analytic approach to the design of nonlinear time-varying control systems

This paper addresses a controller design approach for a specific class of nonlinear time-varying systems based on an appropriate choice of a nonlinear time-varying dynamic feedback. A general form of the nonlinear time-varying dynamic controller is proposed. Lyapunov function theory was extensively used to prove global stability of closed systems. Conditions of local and global asymptotic stability of the nonlinear time-varying system are given. An analytic algorithm of controller design is presented. It is shown that the proposed design technique can successfully be applied to the specific class of the systems, the state variables of which are not fully observed. Simulation results show that the proposed approach to the nonlinear time-varying controller design is effective, and the closed-loop system is robust to small parametrical variations.

&lt;I&gt;D&lt;/I&gt;-Type learning control for nonlinear time-varying systems with unknown initial states and inputs

&lt;I&gt;D&lt;/I&gt;-Type learning control for nonlinear time-varying systems with unknown initial states and inputs

An analytic approach to the design of nonlinear time-varying control systems

This paper addresses a controller design approach for a specific class of nonlinear time-varying systems based on an appropriate choice of a nonlinear time-varying dynamic feedback. A general form of the nonlinear time-varying dynamic controller is proposed. Lyapunov function theory was extensively used to prove global stability of closed systems. Conditions of local and global asymptotic stability of the nonlinear time-varying system are given. An analytic algorithm of controller design is presented. It is shown that the proposed design technique can successfully be applied to the specific class of the systems, the state variables of which are not fully observed. Simulation results show that the proposed approach to the nonlinear time-varying controller design is effective, and the closed-loop system is robust to small parametrical variations.

Discrete-time robust backstepping adaptive control for nonlinear time-varying systems

This paper studies the problem of adaptive control for a class of nonlinear time-varying discrete-time systems with nonparametric uncertainties. The plant parameters considered here are not necessarily slowly time-varying in a uniform way. They are allowed to have a finite number of big jumps. By using the backstepping procedures with parameter projection update laws, a robust adaptive controller can be designed to achieve adaptive tracking of a reference signal for this class of systems. It is shown that the proposed controller can guarantee the global boundedness of the states of the whole adaptive system in the presence of parametric and nonparametric uncertainties. It can also ensure that the tracking error falls within a compact set whose size is proportional to the size of the uncertainties and disturbances. In the ideal case when there is no nonparametric uncertainties and time-varying parameters, perfect tracking can be achieved.

The stability for the hyperneutral type nonlinear time varying control systems (1)

We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization. Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function. Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms.