Jing Na

Adaptive Prescribed Performance Motion Control of Servo Mechanisms with Friction Compensation

This paper proposes an adaptive control for a class of nonlinear mechanisms with guaranteed transient and steady-state performance. A performance function characterizing the convergence rate, maximum overshoot, and steady-state error is used for the output error transformation, such that stabilizing the transformed system is sufficient to achieve the tracking control of the original system with a priori prescribed performance. A continuously differentiable friction model is adopted to account for the friction nonlinearities, for which primary model parameters are online updated. A novel high-order neural network with only a scalar weight is developed to approximate unknown nonlinearities and to dramatically diminish the computational costs. Comparative experiments on a turntable servo system are included to verify the reliability and effectiveness.

Adaptive Control for Nonlinear Pure-Feedback Systems With High-Order Sliding Mode Observer

Most of the available control schemes for pure-feedback systems are derived based on the backstepping technique. On the contrary, this paper presents a novel adaptive control design for nonlinear pure-feedback systems without using backstepping. By introducing a set of alternative state variables and the corresponding transform, state-feedback control of the pure-feedback system can be viewed as output-feedback control of a canonical system. Consequently, backstepping is not necessary and the previously encountered explosion of complexity and circular issue are also circumvented. To estimate unknown states of the newly derived canonical system, a high-order sliding mode observer is adopted, for which finite-time observer error convergence is guaranteed. Two adaptive neural controllers are then proposed to achieve tracking control. In the first scheme, a robust term is introduced to account for the neural approximation error. In the second scheme, a novel neural network with only a scalar weight updated online is constructed to further reduce the computational costs. The closed-loop stability and the convergence of the tracking error to a small compact set around zero are all proved. Comparative simulation and practical experiments on a servo motor system are included to verify the reliability and effectiveness.

Robust adaptive finite-time parameter estimation and control of nonlinear systems

This paper exploits an alternative adaptive parameter estimation and control approach for nonlinear systems. An auxiliary filter is developed to derive a representation of the parameter estimation error, which is combined with an adaptive law to guarantee the exponential convergence of the control error as well as the estimation error. The proposed method is further improved via a sliding mode technique to achieve the finite-time (FT) error convergence. The traditional persistent excitation (PE) is simplified as an a priori verifiable sufficiently rich (SR) requirements on the demand signal. The robustness of the control schemes with bounded disturbances is also investigated. The developed methods are finally tested via simulations.

Online adaptive approximate optimal tracking control with simplified dual approximation structure for continuous-time unknown nonlinear systems

This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control problem of continuous-time nonlinear systems with unknown dynamics. The requirement of the complete knowledge of system dynamics is avoided by employing an adaptive identifier in conjunction with a novel adaptive law, such that the estimated identifier weights converge to a small neighborhood of their ideal values. An adaptive steady-state controller is developed to maintain the desired tracking performance at the steady-state, and an adaptive optimal controller is designed to stabilize the tracking error dynamics in an optimal manner. For this purpose, a critic neural network (NN) is utilized to approximate the optimal value function of the Hamilton-Jacobi-Bellman (HJB) equation, which is used in the construction of the optimal controller. The learning of two NNs, i.e., the identifier NN and the critic NN, is continuous and simultaneous by means of a novel adaptive law design methodology based on the parameter estimation error. Stability of the whole system consisting of the identifier NN, the critic NN and the optimal tracking control is guaranteed using Lyapunov theory; convergence to a near-optimal control law is proved. Simulation results exemplify the effectiveness of the proposed method.

Adaptive Observer-Based Parameter Estimation With Application to Road Gradient and Vehicle Mass Estimation

A novel observer-based parameter estimation scheme with sliding mode term has been developed to estimate the road gradient and the vehicle weight using only the vehicles velocity and the driving torque. The estimation algorithm exploits all known terms in the system dynamics and a low-pass filtered representation of the dynamics to derive an explicit expression of the parameter estimation error without measuring the acceleration. The proposed parameter estimation scheme which features a sliding-mode term to ensure the fast and robust convergence of the estimation in the presence of persistent excitation is augmented to an adaptive observer and analyzed using Lyapunov Theory. The analytical results show that the algorithm is stable and ensures finite-time error convergence to a bounded error even in the presence of disturbances. In the absence of disturbances, convergence to the true values in finite time is guaranteed. A simple practical method for validating persistent excitation is provided using the new theoretical approach to estimation. This is validated by the practical implementation of the algorithm on a small-scaled vehicle, emulating a car system. The slope gradient as well as the vehicles mass/weight are estimated online. The algorithm shows a significant improvement over previous results.

Robust adaptive parameter estimation of sinusoidal signals

A novel two step adaptive identification framework is proposed for sinusoidal signals to estimate the unknown offset, amplitude, frequency and phase, where only the output measurements are used. After representing the sinusoidal signal as a linearly parameterized form, several adaptive laws are developed. The proposed adaptive laws are driven by parameter estimation error information that is derived by applying filter operations on the output measurements, so that globally exponential convergence of the parameter estimation is proved. By using the sliding mode technique, we further improve the design of adaptations to achieve finite-time (FT) parameter estimation. The proposed approaches are independent of any observer/predictor design and robust to bounded measurement noises. The developed estimation methods are finally extended to the full parameter estimation of multi-sinusoids with only output measurements. Comparative simulation results are provided to illustrate the efficacy of the proposed methods.

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

Extended-State-Observer-Based Funnel Control for Nonlinear Servomechanisms With Prescribed Tracking Performance

In this paper, an approximation-free funnel feedback controller is proposed for a class of nonlinear servomechanisms to achieve prescribed tracking error performance. An improved funnel function is proposed to guarantee the transient and asymptotic behavior of the tracking error within a given funnel boundary. The proposed funnel function removes the imposed assumption used in conventional funnel controls (e.g., systems with relative degree one or two) and avoids the potential singularity problem in prescribed performance controls. Moreover, an extended state observer (ESO) is used to address the effect of unknown dynamics in the control system (e.g., friction and disturbances), where the ESO parameters can be easily designed based on the control system bandwidth. The stability of the proposed control system with ESO and funnel function is analyzed via the Lyapunov theory. Comparative simulations and experimental results are conducted based on a practical turntable servomechanisms to validate the efficacy of the proposed method.

An adaptive observer-based parameter estimation algorithm with application to road gradient and vehicle's mass estimation

A novel observer-based parameter estimation algorithm with sliding mode term has been developed to estimate the road gradient and vehicle weight using only the vehicles velocity and the driving torque from the engine. The estimation algorithm exploits all known terms in the system dynamics and a low pass filtered representation to derive an explicit expression of the parameter estimation error without measuring the acceleration. The proposed algorithm which features a sliding-mode term to ensure the fast and robust convergence of the estimation in the presence of persistent excitation is augmented to an adaptive observer and analyzed using Lyapunov Theory. The analytical results show that the algorithm is stable and ensures finite-time error convergence to a bounded error even in the presence of disturbances. A simple practical method for validating persistent excitation is provided using the new theoretical approach to estimation. This is validated by the practical implementation of the algorithm on a small-scaled vehicle, emulating a car system. The slope gradient as well as the vehicles mass/weight are estimated online. The algorithm shows a significant improvement over a previous result.

Vehicle Engine Torque Estimation via Unknown Input Observer and Adaptive Parameter Estimation

This paper presents two torque estimation methods for vehicle engines: unknown input observer (UIO) and adaptive parameter estimation. We first propose a novel yet simple unknown input observer based on the crankshaft rotation dynamics only. For this purpose, an invariant manifold is derived by defining auxiliary variables in terms of first-order low-pass filters, where only one constant (filter coefficient) needs to be tuned. These filtered variables are used to calculate the estimated torque. Robustness of this UIO against sensor noise is studied and compared to two other estimators. On the other hand, since the engine torque dynamics can be formulated as a parameterized form with unknown time-varying parameters, we further present several adaptive laws for time-varying parameter estimation. The parameter estimation errors are derived to drive these adaptive laws and time-varying adaptive gains are introduced. The two proposed estimators only use the measured air mass flow rate and engine speed, and thus allow for improved computational efficiency. Both estimators are verified via a dynamic engine simulator built in a commercial software GT-Power, and also practically tested via experimental data collected in a dynamometer test-rig. Both simulations and practical tests show very encouraging results with small estimation errors even in the presence of sensor noise.