Continuous-time Adaptive Control Research Articles

Half-quadratic criterion-based continuous-time adaptive control for robust LCL-filtered grid-tied inverter

Half-quadratic criterion-based continuous-time adaptive control for robust LCL-filtered grid-tied inverter

Online continuous-time adaptive predictive control of the technological glass conditioning process

Online continuous-time adaptive predictive control of the technological glass conditioning process

Model-free continuation of periodic orbits in certain nonlinear systems using continuous-time adaptive control

This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger class of periodically excited nonlinear systems with matched uncertainties and known structure. A candidate adaptive feedback design is also proposed in the case of scalar problems with unmodeled nonlinearities. In the former case, rigorous analysis shows guaranteed performance bounds for the associated prediction and estimation errors. Together with an assumption of persistent excitation, there follows asymptotic convergence to periodic responses determined uniquely by an a priori unknown periodic reference input and independent of initial conditions, as required by the control-based continuation paradigm. In particular, when the reference input equals the sought periodic response, the steady-state control input vanishes. Identical conclusions follow for the case of scalar dynamics with unmodeled nonlinearities, albeit with slow rates of convergence. Numerical simulations validate the theoretical predictions for individual parameter values. Integration with the software package coco demonstrates successful continuation along families of stable and unstable periodic orbits with a minimum of parameter tuning. The results expand the envelope of known noninvasive feedback strategies for use in experimental model validation and engineering design.

Analog Control Circuit Designs for a Class of Continuous-Time Adaptive Fault-Tolerant Control Systems.

This article is concerned with the robust adaptive fault-tolerant control (FTC) circuit designs for a class of continuous-time disturbed systems. A circuit realization method is investigated to convert the robust adaptive FTC control schemes into analog control circuits. An adaptive compensation control scheme against state-dependent and partially bounded actuator faults and disturbances is first developed to demonstrate the approach clearly, then its equivalent control circuits are implemented by using the circuit theory. Compared with simulation results achieved by MATLAB and professional circuit simulation software, the effectiveness of the proposed robust adaptive FTC circuits is validated by a rocket fairing system and a Chua's circuit system.

A Projection Operator-Based Discrete-Time Adaptive Architecture for Control of Uncertain Dynamical Systems With Actuator Dynamics

Stability analyses of discrete-time adaptive control algorithms are generally predicated on quadratic Lyapunov-based frameworks that result in unavoidable complexity due to the resulting terms in the Lyapunov difference equations. This prevents generalizations of valuable continuous-time adaptive control results to their discrete-time settings. To this end, one important generalization is the consideration of actuator dynamics, which is present in any uncertain dynamical system. To address this problem, we propose a novel discrete-time adaptive control architecture predicated on the hedging method and a new projection operator. A logarithmic Lyapunov function is used for proving the asymptotic stability of the error between uncertain dynamical system states and hedging-based reference model states. An illustrative numerical example is then presented to demonstrate the efficacy of the proposed architecture.

Optimal control of port-Hamiltonian systems: A continuous-time learning approach

In this paper, we propose a continuous-time adaptive feedback controller for the optimal control of input-state-output port-Hamiltonian systems with respect to general Lagrangian performance indices. The proposed control law implements an online learning procedure which uses the Hamiltonian of the system as an initial value function candidate. The continuous-time learning of the value function is achieved by means of a certain Lagrange multiplier that allows to evaluate the optimality of the current solution. In particular, constructive conditions for stabilizing initial value function candidates are stated and asymptotic stability of the closed-loop equilibrium is proven. Simulations of an exemplary nonlinear optimal control problem demonstrate the performance of the controller resulting from the proposed online learning procedure.

Adaptive Control for a Class of Systems with Output Deadzone Nonlinearity

This paper presents a continuous-time adaptive control scheme for systems with uncertain non-symmetrical deadzone nonlinearity located at the output of a plant. An adaptive inverse function is developed and used in conjunction with a robust adaptive controller to reduce the effect of deadzone nonlinearity. The deadzone inverse function is also implemented in continuous time, and an adaptive update law is designed to estimate the deadzone parameters. The adaptive output deadzone inverse controller is smoothly differentiable and is combined with a robust adaptive nonlinear controller to ensure robustness and boundedness of all the states of the system as well as the output signal. The mismatch between the ideal deadzone inverse function and our proposed implantation is treated as a disturbance that can be upper bounded by a polynomial in the system states. The overall stability of the closed-loop system is proven by using Lyapunov method, and simulations confirm the efficacy of the control methodology.

Application of policy iteration technique based adaptive optimal control design for automatic voltage regulator of power system

This paper presents an adaptive optimal control design approach for automatic voltage regulator (AVR) system using policy iteration technique based adaptive critic scheme. The infinite horizon optimal control design using linear quadratic regulator (LQR) by solution of algebraic Riccati equation (ARE) and Hamilton–Jacobi–Bellman (HJB) equation require the complete knowledge of the system dynamics, and giving solution offline. Policy iteration technique which is based on actor–critic structure consists of two-step iteration: policy evaluation and policy improvement. The online policy iteration technique based control scheme gives online the continuous-time adaptive optimal control solution without using the complete knowledge of the system’s internal dynamics. The knowledge of systems internal dynamics (i.e. matrix A) is not needed for evaluation of cost or the update of control policy; only the knowledge of input matrix B is required for updating the control policy. Thus this control scheme becomes partially model-free. The proposed control scheme has been implemented for AVR system for its both models neglecting and including sensor dynamics. The simulation results and performance analysis are presented to justify the robustness & effectiveness of control scheme. The comparative performance analysis of adaptive critic control scheme and LQR is also presented.

Adaptive Optimal Control of Nonlinear Inverted Pendulum System Using Policy Iteration Technique

This paper presents the adaptive optimal control of nonlinear inverted pendulum-cart dynamic system using policy iteration technique based adaptive critic scheme. Inverted pendulum is a highly nonlinear unstable system which is used as a benchmark for implementing the control methods. The optimal control design using Hamilton-Jacobi-Bellman (HJB) equation requires the complete knowledge of the system dynamics with an offline solution. Policy iteration technique which is based on actor-critic structure consists of two-step iteration: policy evaluation and policy improvement. The online policy iteration technique gives online continuous-time adaptive optimal control solution without using the complete knowledge of the system's internal dynamics. In this paper the state regulation control problem of cart position control and stabilization of inverted pendulum in vertically upright position is considered. The simulation results justify the effectiveness of the control scheme.

Discrete-time weight updates in neural-adaptive control

Typical neural-adaptive control approaches update neural-network weights as though they were adaptive parameters in a continuous-time adaptive control. However, requiring fast digital rates usually restricts the size of the neural network. In this paper we analyze a delta-rule update for the weights, applied at a relatively slow digital rate. We show that digital weight update causes the neural network to estimate a discrete-time model of the system, assuming that state feedback is still applied in continuous time. A Lyapunov analysis shows uniformly ultimately bounded signals. Furthermore, slowing the update frequency and using the extra computational time to increase the size/accuracy of the neural network results in better performance. Experimental results achieving link tracking of a two-link flexible-joint robot verify the improved performance.

Adaptive nonlinear control of a continuous stirred tank reactor

AbstractThe paper deals with continuous-time nonlinear adaptive control of a continuous stirred tank reactor (CSTR). Control strategy is based on the application of a controller consisting of a linear and a nonlinear part. The static nonlinear part is derived as an inversion and exponential approximation of measured or simulated input-output data. Design of the dynamic linear part is based on an approximation of nonlinear elements in the control loop by a continuous-time external linear model with directly estimated parameters. In the control design procedure, polynomial approach with the pole assignment method was used. The nonlinear adaptive control was tested by simulations on a nonlinear model of a CSTR with a consecutive exothermic reaction.

Sampled-Data Adaptive NN Tracking Control of Uncertain Nonlinear Systems

In this paper, for a class of single-input-single-output (SISO) uncertain nonlinear systems, adaptive neural tracking controllers designed for digital computer implementation are proposed. The overall scheme can be considered as a sampled-data adaptive neural control system. As an intermediate result, it is proven that, for a sufficiently small sampling period, the emulated adaptive neural controller i.e., the discrete implementation of the continuous-time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed-loop system. Then, based on the exact discrete-time model, a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails. The redesigned controller consists of two terms: the emulated control law and an extra robustness term designed to increase the order of the perturbation (with respect to the sampling period) in the Lyapunov difference. In all cases, high-order neural networks are employed to approximate the unknown nonlinearities. Using Lyapunov techniques, it is proven that, for a sufficiently small sampling period, the proposed redesigned controller ensures the (semiglobal) boundedness of all the signals in the closed-loop while the output of the system converges to a small neighborhood of the desired trajectory. Simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis.

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.

Discrete time adaptive control for a MEMS gyroscope

AbstractThis paper presents a discrete time version of the observer‐based adaptive control system for micro‐electro‐mechanical systems gyroscopes, which can be implemented using digital processors. A stochastic analysis of this control algorithm is developed and it shows that the estimates of the angular rate and the fabrication imperfections are biased due to the signal discretization errors in the feedforward control path introduced by the sampler and holder. Thus, a two‐rate discrete time control is proposed as a compromise between the measurement biases and the computational burden imposed on the controller. The convergence analysis of this algorithm is also conducted and an analysis method is developed for determining the trade‐off between the controller sampling frequency and the magnitude of the angular rate estimate biased errors. All convergence and stochastic properties of a continuous time adaptive control are preserved, and this analysis is verified with computer simulations. Copyright © 2005 John Wiley & Sons, Ltd.

Stabilization of Continuous-Time Adaptive Control Systems with Possible Input Saturation through a Controllable Modified Estimation Model

This paper presents an indirect adaptive control scheme for linear continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. An alternative modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also proposed. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the estimation model without modification fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the controllability of the modified estimated model. Both schemes ensure that chattering due to switches associated with the modification is not present. The results are extended to the first-order case when the input is subject to saturation being modeled as a sigmoid function. In this case, a hysteresis-type switching law is used to implement the estimates modification.

Robust backstepping control of a class of nonlinear systems using fuzzy logic

Fuzzy Logic (FL) controllers for the robust back stepping control of a class of nonlinear systems in both continuous and discrete-time are presented. Control action is employed to achieve tracking performance for unknown nonlinear system. Novel parameter tuning algorithms are obtained that are similar to ϵ-modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the fuzzy parameter estimates are presented without using the persistency of excitation (PE) condition. Initialization of the fuzzy parameters is straightforward. Simulation results justify the theoretical conclusions.

Adaptive Control of Active Balancing Systems for Speed-Varying Rotors Using Feedforward Gain Adaptation Technique

This paper presents a new adaptive control method for active balancing of speed-varying rotors. It is developed based on the feedforward gain adaptation problem, which is a classical technique in the continuous-time adaptive control area. The condition for using this technique is the need for strictly positive realness of the transfer function. In this research, the technique is re-examined and modified to be appropriate for the balancing problem. It is also shown that the rotor dynamics of single-plane balancing problem can easily be converted to a strictly positive real transfer function and that, consequently, the feedfoward gain adaptation technique can be applied. This paper demonstrates that the developed method can be applied to a simple Jeffcott rotor and can also be extended to the single-plane balancing problem of general flexible rotor. Simulation studies show that the new method works well as expected.

Continuous-Time Adaptive Controller Design with Adjustments Working in Sliding Mode

This paper deals with a design of a adaptive controller with adjustments working in sliding mode. The mathematical description of the plant is linear continuous single input model. The structure of the adaptive law is chosen linear. Stability problem of the closed loop equation is solved using second method of Lyapunov with the LaSalle‘s extension. It is shown that the stability problem leads to the ‘Normal equations’ in closed loop, but here in differential form. They are solved as optimisation problem by sliding mode technique. The stochastic case in the presence of Gauss white noise is investigated using again the second method, but with stochastic Lyapunov function. Numerical simulations are also carried out.

Robust Backstepping Control of Robotic Systems Using Neural Networks

Neural network (NN) controllers for the robust back stepping control of robotic systems in both continuous and discrete-time are presented. Control action is employed to achieve tracking performance for unknown nonlinear system. Tuning methods are derived for the NN based on delta rule. Novel weight tuning algorithms for the NN are obtained that are similar to e-modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the weight estimates are presented without using the persistency of excitation (PE) condition. Certainty equivalence is not used and regression matrix is not computed. No learning phase is needed for the NN and initialization of the network weights is straightforward. Simulation results justify the theoretical conclusions.

On Stability Conditions for Continuous-Time Systems with Slowly Time-Varying Parameters

This paper presents some new conditions for the exponential stability of continuous-time linear homogeneous systems with slowly time-varying parameters, and investigates conditions for the boundedness of the solutions of a class of continuous time dynamic systems, which result from almost all the available continuous-time adaptive control systems. The conditions are motivated by those used in the stability analysis of continuous-time adaptive control systems with un-modeled dynamics, deterministic or stochastic disturbances as well as slowly time-varying parameters.